diff options
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 1336 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 7080 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1966 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9242 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 31401 |
5 files changed, 24448 insertions, 26577 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 735ea9ca..14412a20 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2294555 . 3515605025) +(2293007 . 3518066231) (-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."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\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(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4507 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4503 . T) (-4508 . T) (-4502 . T)) +((-4508 . T) (-4506 . T) (-4505 . T) ((-4513 "*") . T) (-4504 . T) (-4509 . T) (-4503 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -4187) +(-32 R -3581) ((|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 -1070) (QUOTE (-560))))) (-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 \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4510))) +((|HasAttribute| |#1| (QUOTE -4511))) (-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 \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL @@ -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}."))) -((-4510 . T) (-4511 . T)) +((-4511 . T) (-4512 . 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"))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) NIL (-39 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) NIL NIL -(-40 -4187 UP UPUP -3861) +(-40 -3581 UP UPUP -3099) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-4128 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-4128 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4128 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4128 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-4128 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-4128 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) -(-41 R -4187) +((-4504 |has| (-421 |#2|) (-376)) (-4509 |has| (-421 |#2|) (-376)) (-4503 |has| (-421 |#2|) (-376)) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-4043 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-4043 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4043 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4043 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-363))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-4043 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-4043 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))))) +(-41 R -3581) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -435) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-319)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4507 |has| |#1| (-571)) (-4505 . T) (-4504 . T)) +((-4508 |has| |#1| (-571)) (-4506 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-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."))) -((-4510 . T) (-4511 . T)) -((-4128 (-12 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2654) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1356) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2654) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1356) (|devaluate| |#2|))))))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-872))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2654) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1356) (|devaluate| |#2|))))))) +((-4511 . T) (-4512 . T)) +((-4043 (-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2300) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-872)))) (-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2300) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133))))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-4043 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-872))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133))) (-4043 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2300) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133))))) (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) ((|HasCategory| $ (QUOTE (-1081))) (|HasCategory| $ (|%list| (QUOTE -1070) (QUOTE (-560))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function `f'.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) -((-4507 . T)) +((-4508 . T)) NIL (-51) ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -4187) +(-54 |Base| R -3581) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -158,77 +158,77 @@ 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}'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"))) -((-4510 . T) (-4511 . T)) +((-4511 . T) (-4512 . T)) NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4511 . T) (-4510 . T)) -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4512 . T) (-4511 . T)) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4043 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-59 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL NIL (-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's."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -4392) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -4056) ((|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 -(-62 -4392) +(-62 -4056) ((|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 -(-63 -4392) +(-63 -4056) ((|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 -(-64 -4392) +(-64 -4056) ((|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 -(-65 -4392) +(-65 -4056) ((|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 -4392) +(-66 -4056) ((|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 -4392) +(-67 -4056) ((|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 -4392) +(-68 -4056) ((|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 -4392) +(-69 -4056) ((|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 -4392) +(-70 -4056) ((|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 -4392) +(-71 -4056) ((|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 -4392) +(-72 -4056) ((|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 -4392) +(-73 -4056) ((|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 -4392) +(-74 -4056) ((|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 -(-75 -4392) +(-75 -4056) ((|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 @@ -240,51 +240,51 @@ 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 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 -(-78 -4392) +(-78 -4056) ((|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 -(-79 -4392) +(-79 -4056) ((|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 -4392) +(-80 -4056) ((|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 -4392) +(-81 -4056) ((|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 -4392) +(-82 -4056) ((|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 -(-83 -4392) +(-83 -4056) ((|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 -(-84 -4392) +(-84 -4056) ((|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 -(-85 -4392) +(-85 -4056) ((|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 -(-86 -4392) +(-86 -4056) ((|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 -(-87 -4392) +(-87 -4056) ((|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 -(-88 -4392) +(-88 -4056) ((|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 -(-89 -4392) +(-89 -4056) ((|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 (-376)))) (-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}."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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\"."))) -((-4510 . T)) +((-4511 . 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."))) -((-4510 . T) ((-4512 "*") . T) (-4511 . T) (-4507 . T) (-4505 . T) (-4504 . T) (-4503 . T) (-4508 . T) (-4502 . T) (-4501 . T) (-4500 . T) (-4499 . T) (-4498 . T) (-4506 . T) (-4509 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4497 . T)) +((-4511 . T) ((-4513 "*") . T) (-4512 . T) (-4508 . T) (-4506 . T) (-4505 . T) (-4504 . T) (-4509 . T) (-4503 . T) (-4502 . T) (-4501 . T) (-4500 . T) (-4499 . T) (-4507 . T) (-4510 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4498 . 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}."))) -((-4507 . T)) +((-4508 . 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{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 pl and pr. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} := \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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 (-4512 "*")))) +((|HasAttribute| |#1| (QUOTE (-4513 "*")))) (-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"))) -((-4510 . T)) +((-4511 . 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."))) -((-4511 . T)) +((-4512 . 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."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4128 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4043 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4043 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) ((-12 (|HasCategory| (-114) (QUOTE (-1133))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-114) (QUOTE (-872))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-114) (QUOTE (-1133))) (|HasCategory| (-114) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-114) (QUOTE (-102)))) (-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}"))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) NIL (-112 S) ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) @@ -396,22 +396,22 @@ NIL ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) NIL NIL -(-117 -4187 UP) +(-117 -3581 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 (-118 |p|) ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-119 |p|) ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-118 |#1|) (QUOTE (-940))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1052))) (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872))) (-4128 (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1184))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| (-118 |#1|) (QUOTE (-940))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1052))) (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872))) (-4043 (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1184))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (-4043 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) (-120 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4511))) +((|HasAttribute| |#1| (QUOTE -4512))) (-121 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -422,15 +422,15 @@ NIL NIL (-123 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"))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-124 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-125) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) NIL (-126 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -438,24 +438,24 @@ NIL NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4510 . T) (-4511 . T)) +((-4511 . T) (-4512 . T)) NIL (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129 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."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) NIL NIL (-131) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|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 `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."))) -((-4511 . T) (-4510 . T)) -((-4128 (-12 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-4128 (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-130) (QUOTE (-872))) (-4128 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) +((-4512 . T) (-4511 . T)) +((-4043 (-12 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-4043 (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4043 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-130) (QUOTE (-872))) (-4043 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-132) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -474,13 +474,13 @@ NIL NIL (-136) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4512 "*") . T)) +(((-4513 "*") . T)) NIL -(-137 |minix| -3258 R) +(-137 |minix| -3106 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|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 -(-138 |minix| -3258 S T$) +(-138 |minix| -3106 S T$) ((|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 @@ -502,8 +502,8 @@ NIL NIL (-143) ((|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}."))) -((-4510 . T) (-4500 . T) (-4511 . T)) -((-4128 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-4511 . T) (-4501 . T) (-4512 . T)) +((-4043 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-144 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL @@ -518,7 +518,7 @@ NIL NIL (-147) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4507 . T)) +((-4508 . T)) NIL (-148 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial 'x,{} then it returns the characteristic polynomial expressed as a polynomial in 'x."))) @@ -526,9 +526,9 @@ NIL NIL (-149) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4507 . T)) +((-4508 . T)) NIL -(-150 -4187 UP UPUP) +(-150 -3581 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 @@ -539,14 +539,14 @@ NIL (-152 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|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 -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasAttribute| |#1| (QUOTE -4510))) +((|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasAttribute| |#1| (QUOTE -4511))) (-153 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|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 (-154 |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."))) -((-4505 . T) (-4504 . T) (-4507 . T)) +((-4506 . T) (-4505 . T) (-4508 . T)) NIL (-155) ((|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."))) @@ -568,7 +568,7 @@ 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 -(-160 R -4187) +(-160 R -3581) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})/P(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} n!.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} n!/(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} n!/(r! * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -599,10 +599,10 @@ NIL (-167 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 (-940))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasAttribute| |#2| (QUOTE -4509)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571)))) +((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4507)) (|HasAttribute| |#2| (QUOTE -4510)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571)))) (-168 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})"))) -((-4503 -4128 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-2869 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 -4043 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4509 |has| |#1| (-376)) (-4503 |has| |#1| (-376)) (-4507 |has| |#1| (-6 -4507)) (-4510 |has| |#1| (-6 -4510)) (-1502 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-169 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."))) @@ -614,8 +614,8 @@ NIL NIL (-171 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}."))) -((-4503 -4128 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-2869 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-4128 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-4128 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-363)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-940))))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-940)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-940))))) (-4128 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1235)))) (|HasCategory| |#1| (QUOTE (-1235))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-571)))) (-4128 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-1235)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4509)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-363))))) +((-4504 -4043 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4509 |has| |#1| (-376)) (-4503 |has| |#1| (-376)) (-4507 |has| |#1| (-6 -4507)) (-4510 |has| |#1| (-6 -4510)) (-1502 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . 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(|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL @@ -630,7 +630,7 @@ NIL NIL (-175) ((|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."))) -(((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-176) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -638,7 +638,7 @@ NIL NIL (-177 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4512 "*") . T) (-4503 . T) (-4508 . T) (-4502 . T) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") . T) (-4504 . T) (-4509 . T) (-4503 . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-178) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -692,7 +692,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL -(-191 R -4187) +(-191 R -3581) ((|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 @@ -804,28 +804,28 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-219 -4187 UP UPUP R) +(-219 -3581 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 -(-220 -4187 FP) +(-220 -3581 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and q= size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-221) ((|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."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4128 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4043 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4043 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-222) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `d'.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-223 R -4187) -((|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}."))) +(-223 R -3581) +((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL (-224 R) -((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) +((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL (-225 R1 R2) @@ -834,19 +834,19 @@ NIL NIL (-226 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}."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-227 |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}."))) -((-4507 . T)) +((-4508 . T)) NIL -(-228 R -4187) +(-228 R -3581) ((|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 (-229) -((|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}."))) -((-2859 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|nan?| (((|Boolean|) $) "\\spad{nan? x} holds if \\spad{x} is a Not a Number floating point data in the IEEE 754 sense.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) +((-4286 . T) (-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-230) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -854,19 +854,19 @@ NIL NIL (-231 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}"))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4513 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-232 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 (-233 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."))) -((-4511 . T)) +((-4512 . T)) NIL (-234 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) -((-4507 . T)) +((-4508 . T)) NIL (-235 S T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -878,7 +878,7 @@ NIL NIL (-237 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) NIL (-238 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) @@ -890,33 +890,33 @@ NIL NIL (-240) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) -((-4507 . T)) +((-4508 . T)) NIL (-241 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 -4510))) +((|HasAttribute| |#1| (QUOTE -4511))) (-242 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}."))) -((-4511 . T)) +((-4512 . T)) NIL (-243) ((|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 -(-244 S -3258 R) +(-244 S -3106 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (QUOTE (-872))) (|HasAttribute| |#3| (QUOTE -4507)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (QUOTE (-1133)))) -(-245 -3258 R) +((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (QUOTE (-872))) (|HasAttribute| |#3| (QUOTE -4508)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (QUOTE (-1133)))) +(-245 -3106 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . T)) +((-4505 |has| |#2| (-1081)) (-4506 |has| |#2| (-1081)) (-4508 |has| |#2| (-6 -4508)) (-4511 . T)) NIL -(-246 -3258 R) +(-246 -3106 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) -((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . 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(QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) +(-247 -3106 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL @@ -930,7 +930,7 @@ NIL NIL (-250) ((|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}."))) -((-4503 . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-251 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.")) 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(QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (QUOTE (-872))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))))) (-4043 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-872))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-1081)))) (-4043 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-872))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (|HasCategory| (-560) (QUOTE (-872))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -660) (QUOTE (-560))))) (-4043 (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -930) (QUOTE (-1209)))))) (-4043 (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1081)))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1081))))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-4043 (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-1081)))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4043 (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -928) (QUOTE (-1209))))) (|HasAttribute| |#3| (QUOTE -4508)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1081))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1081)))) (-12 (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (|%list| (QUOTE -930) (QUOTE (-1209))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (-261 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-240)))) (-262 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-6 -4509)) (-4506 . T) (-4505 . T) (-4508 . T)) NIL (-263 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}."))) -((-4510 . T) (-4511 . T)) +((-4511 . T) (-4512 . T)) NIL (-264 |Ex|) ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -1030,8 +1030,8 @@ NIL NIL (-275 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"))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4128 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4128 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#3| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#3| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-6 -4509)) (-4506 . T) (-4505 . T) (-4508 . T)) +((|HasCategory| |#1| (QUOTE (-940))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4043 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4043 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#3| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#3| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4043 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4509)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) (-276 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}.")) (|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 @@ -1076,11 +1076,11 @@ 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|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-287 R -4187) +(-287 R -3581) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-288 R -4187) +(-288 R -3581) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1106,7 +1106,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133)))) (-294 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}."))) -((-4511 . T)) +((-4512 . T)) NIL (-295 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}."))) @@ -1127,18 +1127,18 @@ NIL (-299 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 -4511))) +((|HasAttribute| |#1| (QUOTE -4512))) (-300 |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 -(-301 S R |Mod| -2235 -4337 |exactQuo|) +(-301 S R |Mod| -2261 -4024 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-302) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4503 . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-303) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1150,16 +1150,16 @@ NIL NIL (-305 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|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."))) -((-4507 -4128 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4504 |has| |#1| (-1081)) (-4505 |has| |#1| (-1081))) -((|HasCategory| |#1| (QUOTE (-376))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4128 (|HasCategory| |#1| (|%list| 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operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL NIL (-307 |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."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2654) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1356) (|devaluate| |#2|)))))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2300) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102)))) (-308) ((|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 @@ -1172,11 +1172,11 @@ NIL ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-311 -4187 S) +(-311 -3581 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 -(-312 E -4187) +(-312 E -3581) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1206,7 +1206,7 @@ NIL NIL (-319) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-320 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -1216,7 +1216,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-322 -4187) +(-322 -3581) ((|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 @@ -1230,12 +1230,12 @@ NIL NIL (-325 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))}."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1052))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872))) (-4128 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1184))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-240))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4128 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1052))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872))) (-4043 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1184))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-240))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940)))) (-4043 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))))) (-326 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."))) -((-4507 -4128 (-12 (|has| |#1| (-571)) (-4128 (|has| |#1| (-1081)) (|has| |#1| (-487)))) (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) -((-4128 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-571))) (-4128 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-21))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-1081))) (-4128 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-147)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-175)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE 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(|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4128 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4128 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571)))) (-4128 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4128 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-21)))) (-4128 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144)))) (-4128 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25)))) (-4128 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4128 (-12 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| $ (QUOTE (-1081))) (|HasCategory| $ (|%list| (QUOTE -1070) (QUOTE (-560))))) +((-4508 -4043 (-12 (|has| |#1| (-571)) (-4043 (|has| |#1| (-1081)) (|has| |#1| (-487)))) (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4506 |has| |#1| (-175)) (-4505 |has| |#1| (-175)) ((-4513 "*") |has| |#1| (-571)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-571)) (-4503 |has| |#1| (-571))) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-571))) (-4043 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-21))) (-4043 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-1081))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE 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(-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-4043 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4043 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4043 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571)))) (-4043 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-21)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-25)))) (-4043 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| $ (QUOTE (-1081))) (|HasCategory| $ (|%list| (QUOTE -1070) (QUOTE (-560))))) (-327 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 @@ -1244,7 +1244,7 @@ NIL ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-329 R -4187) +(-329 R -3581) ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1254,8 +1254,8 @@ NIL NIL (-331 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."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4128 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -4457) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4128 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2243) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -1647) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-376)) (-4503 |has| |#1| (-376)) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4043 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -4462) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4328) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3570) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-332 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1266,7 +1266,7 @@ NIL NIL (-334 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The operation is commutative."))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| (-560) (QUOTE (-816)))) (-335 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}'s.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} \\spad{a1}\\^\\spad{e1} ... an\\^en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1282,19 +1282,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175)))) (-338 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-339 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."))) -((-4511 . T) (-4510 . T)) -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -4187) +((-4512 . T) (-4511 . T)) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4043 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-340 S -3581) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-381)))) -(-341 -4187) +(-341 -3581) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-342) ((|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."))) @@ -1312,7 +1312,7 @@ NIL ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL -(-346 -4187 UP UPUP R) +(-346 -3581 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1320,11 +1320,11 @@ 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 -(-348 S -4187 UP UPUP R) +(-348 S -3581 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-349 -4187 UP UPUP R) +(-349 -3581 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL @@ -1338,19 +1338,19 @@ NIL NIL (-352 |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{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function \\spad{LOG10}")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\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.}"))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) ((|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#3| (|%list| (QUOTE -1070) (QUOTE (-391)))) (|HasCategory| $ (QUOTE (-1081))) (|HasCategory| $ (|%list| (QUOTE -1070) (QUOTE (-560))))) (-353 |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}."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4128 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) -(-354 S -4187 UP UPUP) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((-4043 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +(-354 S -3581 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-376)))) -(-355 -4187 UP UPUP) +(-355 -3581 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 |has| (-421 |#2|) (-376)) (-4509 |has| (-421 |#2|) (-376)) (-4503 |has| (-421 |#2|) (-376)) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-356 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}."))) @@ -1358,16 +1358,16 @@ NIL NIL (-357 |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."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4128 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((-4043 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) (-358 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(GF,{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4128 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((-4043 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-359 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(GF,{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4128 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((-4043 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-360 GF) ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1382,51 +1382,51 @@ NIL NIL (-363) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL -(-364 R UP -4187) +(-364 R UP -3581) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-365 |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."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4128 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((-4043 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) (-366 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4128 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((-4043 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-367 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4128 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((-4043 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-368 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4128 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((-4043 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-369 GF) ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-370 -4187 GF) +(-370 -3581 GF) ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}GF) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-371 -4187 FP FPP) +(-371 -3581 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL (-372 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4128 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((-4043 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-373 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{ls}."))) NIL NIL (-374 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4507 . T)) +((-4508 . T)) NIL (-375 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1434,7 +1434,7 @@ NIL NIL (-376) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-377 S) ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) @@ -1450,7 +1450,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-571)))) (-380 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4507 |has| |#1| (-571)) (-4505 . T) (-4504 . T)) +((-4508 |has| |#1| (-571)) (-4506 . T) (-4505 . T)) NIL (-381) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1462,15 +1462,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-376)))) (-383 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) NIL (-384 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4511)) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133)))) +((|HasAttribute| |#1| (QUOTE -4512)) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133)))) (-385 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4510 . T)) +((-4511 . T)) NIL (-386 S A R B) ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) @@ -1478,7 +1478,7 @@ NIL NIL (-387 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr)")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}xn],{} [\\spad{v1},{}...,{}vn])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4505 . T) (-4504 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4506 . T) (-4505 . T)) NIL (-388 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."))) @@ -1494,7 +1494,7 @@ NIL NIL (-391) ((|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{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}."))) -((-4493 . T) (-4501 . T) (-2859 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4494 . T) (-4502 . T) (-4286 . T) (-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-392 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1506,11 +1506,11 @@ NIL NIL (-394 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."))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133))))) (-395 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.fr)")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175)))) (-396) ((|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}."))) @@ -1518,7 +1518,7 @@ NIL NIL (-397 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.fr)")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|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}."))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) NIL (-398) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) @@ -1534,7 +1534,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-872)))) (-401) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-402) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1546,13 +1546,13 @@ NIL NIL (-404 |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"))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) NIL (-405) ((|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 -(-406 -4187 UP UPUP R) +(-406 -3581 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 @@ -1576,11 +1576,11 @@ NIL ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) NIL NIL -(-412 -4392 |returnType| -3965 |symbols|) +(-412 -4056 |returnType| -1549 |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 -(-413 -4187 UP) +(-413 -3581 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1594,28 +1594,28 @@ NIL NIL (-416) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-417 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4493)) (|HasAttribute| |#1| (QUOTE -4501))) +((|HasAttribute| |#1| (QUOTE -4494)) (|HasAttribute| |#1| (QUOTE -4502))) (-418) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-2859 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4286 . T) (-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-419 R) -((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and gcd are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|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."))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1254))) (-4128 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1254)))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) +((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and gcd are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|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| #1="nil" #2="sqfr" #3="irred" #4="prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| #1# #2# #3# #4#) $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1254))) (-4043 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1254)))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) (-420 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) NIL NIL (-421 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4497 -12 (|has| |#1| (-6 -4508)) (|has| |#1| (-466)) (|has| |#1| (-6 -4497))) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872))) (-4128 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((-4498 -12 (|has| |#1| (-6 -4509)) (|has| |#1| (-466)) (|has| |#1| (-6 -4498))) (-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872))) (-4043 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4498)) (|HasAttribute| |#1| (QUOTE -4509)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) (-422 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL @@ -1626,7 +1626,7 @@ NIL NIL (-424 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) NIL (-425 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1636,15 +1636,15 @@ NIL ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-427 R -4187 UP A) +(-427 R -3581 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4507 . T)) +((-4508 . T)) NIL (-428 R1 F1 U1 A1 R2 F2 U2 A2) ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-429 R -4187 UP A |ibasis|) +(-429 R -3581 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (|%list| (QUOTE -1070) (|devaluate| |#2|)))) @@ -1658,7 +1658,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-376)))) (-432 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4507 |has| |#1| (-571)) (-4505 . T) (-4504 . T)) +((-4508 |has| |#1| (-571)) (-4506 . T) (-4505 . T)) NIL (-433 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)}."))) @@ -1670,7 +1670,7 @@ NIL ((|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (-435 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4507 -4128 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) +((-4508 -4043 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4506 |has| |#1| (-175)) (-4505 |has| |#1| (-175)) ((-4513 "*") |has| |#1| (-571)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-571)) (-4503 |has| |#1| (-571))) NIL (-436 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1690,33 +1690,33 @@ NIL ((|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-381)))) (-440 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4510 . T) (-4500 . T) (-4511 . T)) +((-4511 . T) (-4501 . T) (-4512 . T)) NIL (-441 S A R B) ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-442 R -4187) +(-442 R -3581) ((|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 (-443 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"))) -((-4497 -12 (|has| |#1| (-6 -4497)) (|has| |#2| (-6 -4497))) (-4504 . T) (-4505 . T) (-4507 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4497)) (|HasAttribute| |#2| (QUOTE -4497)))) -(-444 R -4187) +((-4498 -12 (|has| |#1| (-6 -4498)) (|has| |#2| (-6 -4498))) (-4505 . T) (-4506 . T) (-4508 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4498)) (|HasAttribute| |#2| (QUOTE -4498)))) +(-444 R -3581) ((|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 -(-445 R -4187) +(-445 R -3581) ((|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 -(-446 R -4187) +(-446 R -3581) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-447 R -4187) +(-447 R -3581) ((|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 @@ -1724,12 +1724,12 @@ 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 -(-449 R -4187 UP) +(-449 R -3581 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 -1070) (QUOTE (-48))))) (-450) -((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) +((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) NIL NIL (-451) @@ -1756,7 +1756,7 @@ 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's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein's criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-457 R UP -4187) +(-457 R UP -3581) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the lp norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri's norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1794,16 +1794,16 @@ NIL NIL (-466) ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-467 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"))) -((-4507 |has| (-421 (-976 |#1|)) (-571)) (-4505 . T) (-4504 . T)) +((-4508 |has| (-421 (-976 |#1|)) (-571)) (-4506 . T) (-4505 . T)) ((|HasCategory| (-421 (-976 |#1|)) (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| (-421 (-976 |#1|)) (QUOTE (-571)))) (-468 |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"))) -(((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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T)) +((|HasCategory| |#2| (QUOTE (-940))) (-4043 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4043 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4043 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4043 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4043 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4509)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4043 (-12 (|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) (-469 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it's conditional."))) NIL @@ -1830,7 +1830,7 @@ NIL NIL (-475 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) NIL (-476 E V R P Q) ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1838,7 +1838,7 @@ NIL NIL (-477 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#4| (QUOTE (-102)))) (-478 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) @@ -1868,7 +1868,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-485 |lv| -4187 R) +(-485 |lv| -3581 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1878,23 +1878,23 @@ NIL NIL (-487) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4507 . T)) +((-4508 . T)) NIL (-488 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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.")) (|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."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . 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T) (-4506 . T) (-4508 . 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T)) +((-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2300) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-872))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102)))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-490 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)}"))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#4| (QUOTE (-102)))) (-491) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-492) ((|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'."))) @@ -1902,29 +1902,29 @@ NIL NIL (-493 |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."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2654) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1356) (|devaluate| |#2|)))))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2300) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102)))) (-494) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre's book Lie Groups -- Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight <= \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-495 |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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T)) -((|HasCategory| |#2| (QUOTE (-940))) (-4128 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4128 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4128 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4128 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4128 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) -(-496 -3258 S) +(((-4513 "*") |has| |#2| (-175)) (-4504 |has| |#2| (-571)) (-4509 |has| |#2| (-6 -4509)) (-4506 . T) (-4505 . T) (-4508 . 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(|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL NIL (-498 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}."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-499 -4187 UP UPUP R) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-499 -3581 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) 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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 -4510)) (|HasAttribute| |#1| (QUOTE -4511)) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) +((|HasAttribute| |#1| (QUOTE -4511)) (|HasAttribute| |#1| (QUOTE -4512)) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-503 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1960,33 +1960,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-508 -4187 UP |AlExt| |AlPol|) +(-508 -3581 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-509) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) ((|HasCategory| $ (QUOTE (-1081))) (|HasCategory| $ (|%list| (QUOTE -1070) (QUOTE (-560))))) (-510 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) -((-4511 . T) (-4510 . T)) -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4512 . T) (-4511 . T)) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4043 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-511 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'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."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-512 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 -(-513 R UP -4187) +(-513 R UP -3581) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the gcd of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-514 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) ((-12 (|HasCategory| (-114) (QUOTE (-1133))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-114) (QUOTE (-872))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-114) (QUOTE (-1133))) (|HasCategory| (-114) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-114) (QUOTE (-102)))) (-515 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)}."))) @@ -2000,7 +2000,7 @@ 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{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-518 -4187 |Expon| |VarSet| |DPoly|) +(-518 -3581 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-1209))))) @@ -2050,36 +2050,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-816)))) (-530 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) -((-4511 . T) (-4510 . T)) -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4512 . T) (-4511 . T)) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4043 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-531) ((|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 (-532 |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}."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4128 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((-4043 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) (-533 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-534 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."))) -((-4511 . T) (-4510 . T)) -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4512 . T) (-4511 . T)) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4043 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-535 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} m*h and h*m are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -4511))) +((|HasAttribute| |#3| (QUOTE -4512))) (-536 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 -4511))) +((|HasAttribute| |#7| (QUOTE -4512))) (-537 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."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4513 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-538) ((|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 @@ -2111,8 +2111,8 @@ NIL (-545 |Varset|) ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL -((-12 (|HasCategory| (-793) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133))))) -(-546 K -4187 |Par|) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| (-793) (QUOTE (-1133))))) +(-546 K -3581 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to br used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2136,7 +2136,7 @@ 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 -(-552 K -4187 |Par|) +(-552 K -3581 |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 @@ -2157,7 +2157,7 @@ NIL NIL NIL (-557 R UP) -((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) "failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) +((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) NIL NIL (-558 S) @@ -2166,11 +2166,11 @@ NIL NIL (-559) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4508 . T) (-4509 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4509 . T) (-4510 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-560) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \\spad{nothing}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4492 . T) (-4498 . T) (-4502 . T) (-4497 . T) (-4508 . T) (-4509 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4493 . T) (-4499 . T) (-4503 . T) (-4498 . T) (-4509 . T) (-4510 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-561) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2190,13 +2190,13 @@ NIL NIL (-565 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2654) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1356) (|devaluate| |#2|)))))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102)))) -(-566 R -4187) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2300) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102)))) +(-566 R -3581) ((|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 -(-567 R0 -4187 UP UPUP R) +(-567 R0 -3581 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 @@ -2206,7 +2206,7 @@ NIL NIL (-569 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} <= \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-2859 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4286 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-570 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."))) @@ -2214,10 +2214,10 @@ NIL NIL (-571) ((|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."))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL -(-572 R -4187) -((|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},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "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."))) +(-572 R -3581) +((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1="failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1#) |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL (-573 I) @@ -2225,22 +2225,22 @@ NIL NIL NIL (-574) -((|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."))) +((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="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| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) "\\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| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) "\\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 -(-575 R -4187 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,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "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)}."))) +(-575 R -3581 L) +((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| #1#)) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) (-576) ((|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 -(-577 -4187 UP UPUP R) +(-577 -3581 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 -(-578 -4187 UP) +(-578 -3581 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 @@ -2248,15 +2248,15 @@ NIL ((|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,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\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 {\\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,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\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 {\\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,{} {\\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,{} {\\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,{} {\\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,{} {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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 -(-580 R -4187 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,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) +(-580 R -3581 L) +((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) -(-581 R -4187) +(-581 R -3581) ((|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 -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1171)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-649))))) -(-582 -4187 UP) +(-582 -3581 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2264,27 +2264,27 @@ 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 -(-584 -4187) +(-584 -3581) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-585 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."))) -((-2859 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4286 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-586) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL -(-587 R -4187) +(-587 R -3581) ((|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 -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) -(-588 -4187 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' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "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(+,[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}."))) +((-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) +(-588 -3581 UP) +((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1="failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-589 R -4187) +(-589 R -3581) ((|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 @@ -2306,25 +2306,25 @@ NIL NIL (-594 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-595 |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."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) ((|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-381)))) (-596) ((|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 -(-597 -4187) +(-597 -3581) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over F?")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) ((|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209))))) -(-598 E -4187) +(-598 E -3581) ((|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 -(-599 R -4187) +(-599 R -3581) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) NIL NIL @@ -2358,19 +2358,19 @@ NIL NIL (-607 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4511 . T) (-4510 . T)) -((-4128 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4128 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-4128 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-4512 . T) (-4511 . T)) +((-4043 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4043 (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4043 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-4043 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-608 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 (-609 |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}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4457) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4462) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) (-610 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-571)) (-4504 |has| |#1| (-571)) (-4505 . T) (-4506 . T) (-4508 . T)) ((|HasCategory| |#1| (QUOTE (-571)))) (-611) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) @@ -2384,7 +2384,7 @@ 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 -(-614 R -4187 FG) +(-614 R -3581 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2394,12 +2394,12 @@ NIL NIL (-616 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4511 . T) (-4510 . T)) -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4512 . T) (-4511 . T)) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4043 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-617 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 -4511)) (|HasCategory| |#2| (QUOTE (-872))) (|HasAttribute| |#1| (QUOTE -4510)) (|HasCategory| |#3| (QUOTE (-1133)))) +((|HasAttribute| |#1| (QUOTE -4512)) (|HasCategory| |#2| (QUOTE (-872))) (|HasAttribute| |#1| (QUOTE -4511)) (|HasCategory| |#3| (QUOTE (-1133)))) (-618 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2410,8 +2410,8 @@ NIL NIL (-620 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4507 -4128 (-1413 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) -((-4128 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +((-4508 -4043 (-3047 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4506 . T) (-4505 . T)) +((-4043 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-621) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) NIL @@ -2438,15 +2438,15 @@ NIL NIL (-627 |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."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2654 (-1191)) (|:| -1356 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 (-1191)) (|:| -1356 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2654) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -1356) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2654 (-1191)) (|:| -1356 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2654 (-1191)) (|:| -1356 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 (-1191)) (|:| -1356 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 (-1191)) (|:| -1356 |#1|)) (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 (-1191)) (|:| -2300 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4376) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -2300) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4376 (-1191)) (|:| -2300 |#1|)) (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -4376 (-1191)) (|:| -2300 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| (-2 (|:| -4376 (-1191)) (|:| -2300 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 (-1191)) (|:| -2300 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 (-1191)) (|:| -2300 |#1|)) (QUOTE (-102)))) (-628 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 (-629 |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}."))) -((-4511 . T)) +((-4512 . T)) NIL (-630 S) ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,...,an), s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,...,an), f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op, [a1,...,an], m)} returns the kernel \\spad{op(a1,...,an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,...,an))} returns \\spad{[a1,...,an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,...,an))} returns the operator op."))) @@ -2464,7 +2464,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-634 -4187 UP) +(-634 -3581 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2482,7 +2482,7 @@ NIL NIL (-638 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}."))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) ((|HasCategory| |#1| (QUOTE (-871)))) (-639 S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) @@ -2490,15 +2490,15 @@ NIL NIL (-640 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."))) -((-4507 . T)) +((-4508 . T)) NIL -(-641 R -4187) +(-641 R -3581) ((|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 (-642 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"))) -((-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4503 . T) (-4507 . T)) +((-4506 . T) (-4505 . T) ((-4513 "*") . T) (-4504 . T) (-4508 . T)) ((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-643 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(lp,{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(ts)} returns \\axiom{ts} in an normalized shape if \\axiom{ts} is zero-dimensional."))) @@ -2514,13 +2514,13 @@ NIL NIL (-646 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(lv)} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4507 . T)) +((-4508 . T)) NIL (-647 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) NIL NIL -(-648 R -4187) +(-648 R -3581) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL @@ -2528,32 +2528,32 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-650 |lv| -4187) +(-650 |lv| -3581) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) 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Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$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)."))) -((-4507 -4128 (-1413 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . 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T)) +((-4043 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-653 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-376)))) (-654 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4505 . T) (-4504 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4506 . T) (-4505 . T)) NIL (-655 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))}."))) +((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) #1="failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL NIL (-656 R) -((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),x,a,\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") 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(((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) +((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),x,a,\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) NIL NIL (-657 |vars|) @@ -2563,18 +2563,18 @@ NIL (-658 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-1402 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) +((-3045 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) (-659 K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) -((-4505 . T) (-4504 . T)) -((-12 (|HasCategory| (-657 |#2|) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133))))) +((-4506 . T) (-4505 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| (-657 |#2|) (QUOTE (-1133))))) (-660 R) ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) NIL NIL (-661 K B) ((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}."))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) NIL (-662 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) @@ -2582,8 +2582,8 @@ NIL NIL (-663 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} is the empty list."))) -((-4511 . T) (-4510 . T)) -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4512 . T) (-4511 . T)) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4043 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-664 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) NIL @@ -2606,8 +2606,8 @@ NIL NIL (-669 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-670 R) ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) NIL @@ -2619,30 +2619,30 @@ NIL (-672 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} := \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4511))) +((|HasAttribute| |#1| (QUOTE -4512))) (-673 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} := \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL (-674 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}."))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-814)))) -(-675 R -4187 L) +(-675 R -3581 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 -(-676 A -4291) +(-676 A -2902) ((|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}}"))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) (-677 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}}"))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) (-678 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) (-679 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2650,9 +2650,9 @@ NIL ((|HasCategory| |#2| (QUOTE (-376)))) (-680 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}."))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) NIL -(-681 -4187 UP) +(-681 -3581 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)))) @@ -2674,7 +2674,7 @@ NIL NIL (-686 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4505 . T) (-4504 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4506 . T) (-4505 . T)) ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-175)))) (-687 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}."))) @@ -2682,14 +2682,14 @@ NIL NIL (-688 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}."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) NIL -(-689 -4187 |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}."))) +(-689 -3581 |Row| |Col| M) +((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-690 -4187) -((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package's existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "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}."))) +(-690 -3581) +((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package's existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) #1="failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL (-691 R E OV P) @@ -2698,8 +2698,8 @@ NIL NIL (-692 |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."))) -((-4507 . T) (-4510 . T) (-4504 . T) (-4505 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4128 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-4128 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((-4508 . T) (-4511 . T) (-4505 . T) (-4506 . T)) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4513 #1="*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4043 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-4043 (|HasAttribute| |#2| (QUOTE (-4513 #1#))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-693) ((|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 @@ -2719,7 +2719,7 @@ NIL (-697 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 -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-698) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2759,10 +2759,10 @@ NIL (-707 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571)))) +((|HasAttribute| |#2| (QUOTE (-4513 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571)))) (-708 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4510 . T) (-4511 . T)) +((-4511 . T) (-4512 . T)) NIL (-709 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) @@ -2774,8 +2774,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571)))) (-711 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."))) -((-4510 . T) (-4511 . T)) -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4511 . T) (-4512 . T)) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4513 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-712 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} ** \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2784,7 +2784,7 @@ 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 `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) NIL NIL -(-714 S -4187 FLAF FLAS) +(-714 S -3581 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,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{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}."))) 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T)) -((|HasCategory| (-721) (QUOTE (-149))) (|HasCategory| (-721) (QUOTE (-147))) (|HasCategory| (-721) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-381))) (|HasCategory| (-721) (QUOTE (-376))) (-4128 (|HasCategory| (-721) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-239))) (-4128 (-12 (|HasCategory| (-721) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (|%list| (QUOTE -930) (QUOTE (-1209))))) (-4128 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (|%list| (QUOTE -298) (QUOTE (-721)) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -321) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-721) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-721) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-721) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-4128 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-721) (QUOTE (-1052))) (|HasCategory| (-721) (QUOTE (-1235))) (-12 (|HasCategory| (-721) (QUOTE (-1034))) (|HasCategory| (-721) (QUOTE (-1235)))) (-4128 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-376))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-940))))) (-4128 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (-12 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-940)))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-940))))) (|HasCategory| (-721) (QUOTE (-559))) (-12 (|HasCategory| (-721) (QUOTE (-1092))) (|HasCategory| (-721) (QUOTE (-1235)))) (|HasCategory| (-721) (QUOTE (-1092))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940))) (-4128 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-376)))) (-4128 (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (QUOTE (-239)))) (-4128 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-571)))) (-12 (|HasCategory| (-721) (QUOTE (-239))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-571))) (|HasAttribute| (-721) (QUOTE -4509)) (|HasAttribute| (-721) (QUOTE -4506)) (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (|%list| (QUOTE -930) (QUOTE (-1209)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-147)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-363))))) +((-4504 . 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T)) +((|HasCategory| (-721) (QUOTE (-149))) (|HasCategory| (-721) (QUOTE (-147))) (|HasCategory| (-721) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-381))) (|HasCategory| (-721) (QUOTE (-376))) (-4043 (|HasCategory| (-721) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-239))) (-4043 (-12 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (|%list| (QUOTE -928) (QUOTE (-1209))))) (|HasCategory| (-721) (|%list| (QUOTE -930) (QUOTE (-1209))))) (-4043 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (|%list| (QUOTE -298) (QUOTE (-721)) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -321) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-721) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-721) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-721) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-4043 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-721) (QUOTE (-1052))) (|HasCategory| (-721) (QUOTE (-1235))) (-12 (|HasCategory| (-721) (QUOTE (-1034))) (|HasCategory| (-721) (QUOTE (-1235)))) (-4043 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-376)))) (-4043 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (-12 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-940)))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-940))))) (|HasCategory| (-721) (QUOTE (-559))) (-12 (|HasCategory| (-721) (QUOTE (-1092))) (|HasCategory| (-721) (QUOTE (-1235)))) (|HasCategory| (-721) (QUOTE (-1092))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940))) (-4043 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-376)))) (-4043 (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (QUOTE (-239)))) (-4043 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-571)))) (-12 (|HasCategory| (-721) (QUOTE (-239))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (|%list| (QUOTE -928) (QUOTE (-1209))))) (|HasCategory| (-721) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-571))) (|HasAttribute| (-721) (QUOTE -4510)) (|HasAttribute| (-721) (QUOTE -4507)) (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (|%list| (QUOTE -930) (QUOTE (-1209)))) (-4043 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-147)))) (-4043 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-940)))) (|HasCategory| (-721) (QUOTE (-363))))) (-717 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}."))) -((-4511 . T)) +((-4512 . T)) NIL (-718 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the gcd of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) NIL NIL (-719) -((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "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"))) +((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1="undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-720 OV E -4187 PG) +(-720 OV E -3581 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 (-721) ((|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}"))) -((-2859 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4286 . T) (-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-722 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."))) @@ -2822,7 +2822,7 @@ NIL NIL (-723) ((|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}"))) -((-4509 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4510 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-724 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"))) @@ -2840,7 +2840,7 @@ 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 \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) NIL NIL -(-728 S -1601 I) +(-728 S -3156 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 @@ -2850,7 +2850,7 @@ NIL NIL (-730 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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) NIL (-731 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) @@ -2860,25 +2860,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) 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T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-734 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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T) (-4505 . T) (-4508 . T)) +((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1114) (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4043 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4043 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4043 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4509)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) (-735 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-736 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) +((-4506 |has| |#1| (-175)) (-4505 |has| |#1| (-175)) (-4508 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-737 R |Mod| -2235 -4337 |exactQuo|) +(-737 R |Mod| -2261 -4024 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4507 . T)) +((-4508 . T)) NIL (-738 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2886,11 +2886,11 @@ NIL NIL (-739 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) NIL -(-740 -4187) +(-740 -3581) ((|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]]}."))) -((-4507 . T)) +((-4508 . T)) NIL (-741 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."))) @@ -2914,7 +2914,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-381)))) (-746 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."))) -((-4503 |has| |#1| (-376)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 |has| |#1| (-376)) (-4509 |has| |#1| (-376)) (-4503 |has| |#1| (-376)) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-747 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."))) @@ -2924,7 +2924,7 @@ 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 -(-749 -4187 UP) +(-749 -3581 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 @@ -2942,8 +2942,8 @@ NIL NIL (-753 |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."))) -(((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (-4128 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4128 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4128 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4128 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4128 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +(((-4513 "*") |has| |#2| (-175)) (-4504 |has| |#2| (-571)) (-4509 |has| |#2| (-6 -4509)) (-4506 . T) (-4505 . T) (-4508 . T)) +((|HasCategory| |#2| (QUOTE (-940))) (-4043 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4043 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4043 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4043 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4043 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4509)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4043 (-12 (|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) (-754 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2958,15 +2958,15 @@ NIL NIL (-757 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) +((-4506 |has| |#1| (-175)) (-4505 |has| |#1| (-175)) (-4508 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-872)))) (-758 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}."))) -((-4510 . T) (-4500 . T) (-4511 . T)) +((-4511 . T) (-4501 . T) (-4512 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-759 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4500 . T) (-4511 . T)) +((-4501 . T) (-4512 . T)) NIL (-760) ((|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."))) @@ -2978,7 +2978,7 @@ NIL NIL (-762 |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}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4506 . T) (-4505 . T) (-4508 . T)) NIL (-763 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"))) @@ -2994,7 +2994,7 @@ NIL NIL (-766 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) NIL (-767) ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{\\spad{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'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's Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) @@ -3076,11 +3076,11 @@ 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 -(-787 -4187) +(-787 -3581) ((|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 -(-788 P -4187) +(-788 P -3581) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''."))) NIL NIL @@ -3088,7 +3088,7 @@ NIL NIL NIL NIL -(-790 UP -4187) +(-790 UP -3581) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3102,9 +3102,9 @@ NIL NIL (-793) ((|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."))) -(((-4512 "*") . T)) +(((-4513 "*") . T)) NIL -(-794 R -4187) +(-794 R -3581) ((|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 @@ -3124,7 +3124,7 @@ 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 gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}ts)} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}ts)} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-799 -4187 |ExtF| |SUEx| |ExtP| |n|) +(-799 -3581 |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 @@ -3138,12 +3138,12 @@ NIL NIL (-802 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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(|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{R^(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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T) (-4505 . T) (-4508 . T)) +((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1114) (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4043 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4043 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4043 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4509)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) (-804 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3154,7 +3154,7 @@ NIL ((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-806 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) NIL (-807 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}."))) @@ -3210,7 +3210,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-381)))) (-820 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) NIL (-821) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) @@ -3218,9 +3218,9 @@ NIL NIL (-822 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-4128 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4128 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) -(-823 -4128 R OS S) +((-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-4043 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4043 (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) +(-823 -4043 R OS S) ((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL @@ -3228,19 +3228,19 @@ NIL ((|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 -(-825 R -4187 L) +(-825 R -3581 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-826 R -4187) -((|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."))) +(-826 R -3581) +((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| #1="failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| #1#) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2="failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2#) (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL (-827) ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE'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 -(-828 R -4187) +(-828 R -3581) ((|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 @@ -3248,11 +3248,11 @@ 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'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'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'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'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'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'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'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's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-830 -4187 UP UPUP R) +(-830 -3581 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 -(-831 -4187 UP L LQ) +(-831 -3581 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3260,41 +3260,41 @@ 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 -(-833 -4187 UP L LQ) +(-833 -3581 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'s such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of pj. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {gcd(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-834 -4187 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}'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}'s form a basis for the rational solutions of the homogeneous equation."))) +(-834 -3581 UP) +((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1="failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1#)) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-835 -4187 L UP A LO) +(-835 -3581 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 -(-836 -4187 UP) +(-836 -3581 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-837 -4187 LO) +(-837 -3581 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 -(-838 -4187 LODO) +(-838 -3581 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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T) (-4505 . T) (-4504 . T)) +(((-4513 "*") |has| |#2| (-376)) (-4504 |has| |#2| (-376)) (-4509 |has| |#2| (-376)) (-4503 |has| |#2| (-376)) (-4508 . T) (-4506 . T) (-4505 . T)) ((|HasCategory| |#2| (QUOTE (-376)))) (-842 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}))."))) @@ -3306,7 +3306,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-872)))) (-844) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-845) ((|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 XML encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath XML encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath XML encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) @@ -3338,7 +3338,7 @@ NIL NIL (-852 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-240)))) (-853) ((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from CD \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the CDs supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM."))) @@ -3346,7 +3346,7 @@ NIL NIL (-854 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4510 . T) (-4500 . T) (-4511 . T)) +((-4511 . T) (-4501 . T) (-4512 . T)) NIL (-855) ((|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."))) @@ -3354,15 +3354,15 @@ NIL NIL (-856 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."))) -((-4507 |has| |#1| (-871))) -((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-4128 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4128 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((-4508 |has| |#1| (-871))) +((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-4043 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4043 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-857 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL NIL (-858 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) +((-4506 |has| |#1| (-175)) (-4505 |has| |#1| (-175)) (-4508 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) (-859 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) @@ -3394,8 +3394,8 @@ NIL NIL (-866 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4507 |has| |#1| (-871))) -((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-4128 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4128 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((-4508 |has| |#1| (-871))) +((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-4043 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4043 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-867 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL @@ -3404,7 +3404,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-869 -3258 S) +(-869 -3106 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 @@ -3414,7 +3414,7 @@ NIL NIL (-871) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) -((-4507 . T)) +((-4508 . T)) NIL (-872) ((|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}."))) @@ -3438,19 +3438,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175)))) (-877 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) NIL (-878 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) -(-879 R |sigma| -4369) +(-879 R |sigma| -3748) ((|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."))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) -(-880 |x| R |sigma| -4369) +(-880 |x| R |sigma| -3748) ((|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}."))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376)))) (-881 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..)}."))) @@ -3494,7 +3494,7 @@ NIL NIL (-891 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) +((-4506 |has| |#1| (-175)) (-4505 |has| |#1| (-175)) (-4508 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (-892 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)."))) @@ -3506,24 +3506,24 @@ NIL NIL (-894 |p|) ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-895 |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}."))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-896 |p|) ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-894 |#1|) (QUOTE (-940))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-894 |#1|) (QUOTE (-1052))) (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872))) (-4128 (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-1184))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -894) (|devaluate| |#1|)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| (-894 |#1|) (QUOTE (-940))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-894 |#1|) (QUOTE (-1052))) (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872))) (-4043 (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-1184))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -894) (|devaluate| |#1|)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (-4043 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))))) (-897 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of Qp.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872))) (-4128 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872))) (-4043 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4043 (-12 (|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) (-898 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of `s' and `t'."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-899) ((|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's highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it's lowest value."))) NIL @@ -3583,7 +3583,7 @@ NIL (-913 |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 (-1402 (|HasCategory| |#2| (QUOTE (-1081)))) (-1402 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (-1402 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) +((-12 (-3045 (|HasCategory| |#2| (QUOTE (-1081)))) (-3045 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (-3045 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) (-914 R S) ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don't,{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}\\spad{e1}),{}...,{}(vn,{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL @@ -3596,7 +3596,7 @@ NIL ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-917 R -1601) +(-917 R -3156) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and fn to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3624,7 +3624,7 @@ 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 -(-924 UP -4187) +(-924 UP -3581) ((|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 @@ -3638,11 +3638,11 @@ NIL NIL (-927 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) NIL (-928 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4507 . T)) +((-4508 . T)) NIL (-929 A S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) @@ -3655,18 +3655,18 @@ NIL (-931 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-932 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4507 . T)) -((-4128 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) +((-4508 . T)) +((-4043 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (-933 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL NIL (-934 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4507 . T)) +((-4508 . T)) NIL (-935 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3674,7 +3674,7 @@ NIL NIL (-936 |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."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) ((|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-381)))) (-937 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) @@ -3690,9 +3690,9 @@ NIL ((|HasCategory| |#1| (QUOTE (-147)))) (-940) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL -(-941 R0 -4187 UP UPUP R) +(-941 R0 -3581 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 @@ -3706,7 +3706,7 @@ NIL NIL (-944 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact'' form has only one fractional term per prime in the denominator,{} while the ``p-adic'' form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} ``p-adically'' in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-945 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."))) @@ -3720,13 +3720,13 @@ 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's group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik's Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-948 -4187) +(-948 -3581) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any gcd domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL (-949) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = y*x")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4512 "*") . T)) +(((-4513 "*") . T)) NIL (-950 R) ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) @@ -3734,13 +3734,13 @@ NIL NIL (-951) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL -(-952 |xx| -4187) +(-952 |xx| -3581) ((|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 -(-953 -4187 P) +(-953 -3581 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL @@ -3768,7 +3768,7 @@ NIL ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-960 R -4187) +(-960 R -3581) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3776,7 +3776,7 @@ 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 -(-962 S R -4187) +(-962 S R -3581) ((|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 @@ -3796,11 +3796,11 @@ 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 -912) (|devaluate| |#1|)))) -(-967 -1601) +(-967 -3156) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-968 R -4187 -1601) +(-968 R -3581 -3156) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL @@ -3822,8 +3822,8 @@ NIL NIL (-973 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4511 . T) (-4510 . T)) -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4512 . T) (-4511 . T)) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4043 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-974 |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 @@ -3834,8 +3834,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-871)))) (-976 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}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4128 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4128 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-6 -4509)) (-4506 . T) (-4505 . T) (-4508 . T)) +((|HasCategory| |#1| (QUOTE (-940))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4043 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4043 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1209) (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4043 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4509)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) (-977 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL @@ -3847,12 +3847,12 @@ NIL (-979 S R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-940))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#4| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#4| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) +((|HasCategory| |#2| (QUOTE (-940))) (|HasAttribute| |#2| (QUOTE -4509)) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#4| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#4| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (-980 R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-6 -4509)) (-4506 . T) (-4505 . T) (-4508 . T)) NIL -(-981 E V R P -4187) +(-981 E V R P -3581) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}mn] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3860,7 +3860,7 @@ NIL ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-983 E V R P -4187) +(-983 E V R P -3581) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-466)))) @@ -3874,16 +3874,16 @@ NIL NIL (-986 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4508))) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-6 -4509)) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4043 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4509))) (-987 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL NIL (-988 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4511 . T) (-4510 . T)) -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4512 . T) (-4511 . T)) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4043 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-989 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -3892,7 +3892,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) NIL NIL -(-991 -4187) +(-991 -3581) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3906,8 +3906,8 @@ NIL NIL (-994 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"))) -((-4507 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) +((-4508 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-995) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3930,7 +3930,7 @@ NIL NIL (-1000 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4510 . T) (-4511 . T)) +((-4511 . T) (-4512 . T)) NIL (-1001 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean1}}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean2}}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.fr}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{\\spad{nextsousResultant2}(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{S_{\\spad{e}-1}} where \\axiom{\\spad{P} ~ S_d,{} \\spad{Q} = S_{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = lc(S_d)}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{\\spad{Lazard2}(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)**(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{gcd(\\spad{P},{} \\spad{Q})} returns the gcd of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{\\spad{coef1} * \\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the gcd of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{\\spad{coef1}.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) @@ -3950,7 +3950,7 @@ NIL NIL (-1005 |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}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1006) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the x-,{} y-,{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) @@ -3962,7 +3962,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-571)))) (-1008 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#3| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4510 . T)) +((-4511 . T)) NIL (-1009 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(lp,{}lq)} returns the same as \\axiom{irreducibleFactors(concat(lp,{}lq))} assuming that \\axiom{irreducibleFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of gcd techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{lp}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(lp,{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(lp)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(lp)} returns \\axiom{lg} where \\axiom{lg} is a list of the gcds of every pair in \\axiom{lp} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(lp,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} and \\axiom{lp} generate the same ideal in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{lq} has rank not higher than the one of \\axiom{lp}. Moreover,{} \\axiom{lq} is computed by reducing \\axiom{lp} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{lp}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(lp,{}pred?,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(lp)} returns \\axiom{lq} such that \\axiom{lp} and and \\axiom{lq} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{lq}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(lp)} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{lp}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(lp)} returns \\axiom{lq} such that \\axiom{lp} and \\axiom{lq} generate the same ideal and no polynomial in \\axiom{lq} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}lf)} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}lf,{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf,{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(lp)} returns \\axiom{bps,{}nbps} where \\axiom{bps} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(lp)} returns \\axiom{lps,{}nlps} where \\axiom{lps} is a list of the linear polynomials in lp,{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(lp)} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(lp)} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{lp} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{bps} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(lp)} returns \\spad{true} iff the number of polynomials in \\axiom{lp} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}llp)} returns \\spad{true} iff for every \\axiom{lp} in \\axiom{llp} certainlySubVariety?(newlp,{}lp) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}lp)} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{lp} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is gcd-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(lp)} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in lp]} if \\axiom{\\spad{R}} is gcd-domain else returns \\axiom{lp}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(lp,{}lq,{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(lp,{}lq)),{}lq)} assuming that \\axiom{remOp(lq)} returns \\axiom{lq} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp,{}lq)} returns the same as \\axiom{removeRedundantFactors(concat(lp,{}lq))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(lp,{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}lp))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp)} returns \\axiom{lq} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lq = [\\spad{q1},{}...,{}qm]} then the product \\axiom{p1*p2*...*pn} vanishes iff the product \\axiom{q1*q2*...*qm} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{pj},{} and no polynomial in \\axiom{lq} divides another polynomial in \\axiom{lq}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{lq} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is gcd-domain,{} the polynomials in \\axiom{lq} are pairwise without common non trivial factor."))) @@ -3978,7 +3978,7 @@ NIL NIL (-1012 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}."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) NIL (-1013 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) @@ -3996,12 +3996,12 @@ 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 -(-1017 K R UP -4187) +(-1017 K R UP -3581) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL (-1018 R |Var| |Expon| |Dpoly|) -((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger's algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don't know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} ~= 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) +((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger's algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) #1="failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don't know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} ~= 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-319))))) (-1019 |vl| |nv|) @@ -4022,7 +4022,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1184)))) (-1023 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}."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1024 A B R S) ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) @@ -4038,19 +4038,19 @@ NIL NIL (-1027 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\#q}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4510 . T) (-4511 . T)) +((-4511 . T) (-4512 . T)) NIL (-1028 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.}"))) -((-4503 |has| |#1| (-302)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-4128 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559)))) +((-4504 |has| |#1| (-302)) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-4043 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-4043 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559)))) (-1029 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL ((|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-302)))) (-1030 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-4503 |has| |#1| (-302)) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 |has| |#1| (-302)) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1031 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) @@ -4058,8 +4058,8 @@ NIL NIL (-1032 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1033 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4068,14 +4068,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1035 -4187 UP UPUP |radicnd| |n|) +(-1035 -3581 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-4128 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-4128 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4128 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4128 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-4128 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-4128 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +((-4504 |has| (-421 |#2|) (-376)) (-4509 |has| (-421 |#2|) (-376)) (-4503 |has| (-421 |#2|) (-376)) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-4043 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-4043 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4043 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4043 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-363))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-4043 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-4043 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-1036 |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."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4128 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4043 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4043 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-1037) ((|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 @@ -4095,7 +4095,7 @@ NIL (-1041 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4511)) (|HasCategory| |#2| (QUOTE (-1133)))) +((|HasAttribute| |#1| (QUOTE -4512)) (|HasCategory| |#2| (QUOTE (-1133)))) (-1042 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL @@ -4106,21 +4106,21 @@ NIL NIL (-1044) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) -((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) +((-4504 . T) (-4509 . T) (-4503 . T) (-4506 . T) (-4505 . T) ((-4513 "*") . T) (-4508 . T)) NIL -(-1045 R -4187) +(-1045 R -3581) ((|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 -(-1046 R -4187) +(-1046 R -3581) ((|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 -(-1047 -4187 UP) +(-1047 -3581 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 -(-1048 -4187 UP) +(-1048 -3581 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 @@ -4154,9 +4154,9 @@ NIL NIL (-1056 |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"))) -((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) -((-4128 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560))))) -(-1057 -4187 L) +((-4504 . T) (-4509 . T) (-4503 . T) (-4506 . T) (-4505 . T) ((-4513 "*") . T) (-4508 . T)) +((-4043 (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560))))) +(-1057 -3581 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4166,7 +4166,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1133)))) (-1059 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#4| (QUOTE (-102)))) (-1060) ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) @@ -4175,7 +4175,7 @@ NIL (-1061 R) ((|constructor| (NIL "\\spad{RepresentationPackage1} provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 <= \\spad{i} <= \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 <= \\spad{i} <= \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4512 "*")))) +((|HasAttribute| |#1| (QUOTE (-4513 "*")))) (-1062 R) ((|constructor| (NIL "\\spad{RepresentationPackage2} provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker's fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker's fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker's fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton's irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL @@ -4192,14 +4192,14 @@ 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 -(-1066 -4187 |Expon| |VarSet| |FPol| |LFPol|) +(-1066 -3581 |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"))) -(((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1067) ((|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.}"))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2654) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -1356) (QUOTE (-51))))))) (-4128 (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-4128 (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4128 (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4376) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -2300) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-1133)))) (-4043 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-1133)))) (-4043 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-1133)))) (-4043 (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-4043 (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4043 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-102)))) (-1068) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4242,7 +4242,7 @@ NIL NIL (-1078 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a Gcd-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) ((-12 (|HasCategory| (-802 |#1| (-889 |#2|)) (QUOTE (-1133))) (|HasCategory| (-802 |#1| (-889 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -802) (|devaluate| |#1|) (|%list| (QUOTE -889) (|devaluate| |#2|)))))) (|HasCategory| (-802 |#1| (-889 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-802 |#1| (-889 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| (-889 |#2|) (QUOTE (-381))) (|HasCategory| (-802 |#1| (-889 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-802 |#1| (-889 |#2|)) (QUOTE (-102)))) (-1079) ((|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"))) @@ -4254,9 +4254,9 @@ NIL NIL (-1081) ((|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."))) -((-4507 . T)) +((-4508 . T)) NIL -(-1082 |xx| -4187) +(-1082 |xx| -3581) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4270,12 +4270,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-376))) (|HasCategory| |#4| (QUOTE (-571))) (|HasCategory| |#4| (QUOTE (-175)))) (-1085 |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"))) -((-4510 . T) (-4505 . T) (-4504 . T)) +((-4511 . T) (-4506 . T) (-4505 . T)) NIL (-1086 |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}."))) -((-4510 . T) (-4505 . T) (-4504 . T)) -((|HasCategory| |#3| (QUOTE (-175))) (-4128 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888))))) +((-4511 . T) (-4506 . T) (-4505 . T)) +((|HasCategory| |#3| (QUOTE (-175))) (-4043 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4043 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888))))) (-1087 |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 @@ -4298,7 +4298,7 @@ NIL NIL (-1092) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1093 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4306,19 +4306,19 @@ NIL NIL (-1094) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4498 . T) (-4502 . T) (-4497 . T) (-4508 . T) (-4509 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4499 . T) (-4503 . T) (-4498 . T) (-4509 . T) (-4510 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1095) ((|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| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE's")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE's")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2654) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -1356) (QUOTE (-51))))))) (-4128 (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-4128 (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4128 (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 (-1209)) (|:| -1356 (-51))) (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4376) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -2300) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-1133)))) (-4043 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-1133)))) (-4043 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-1133)))) (-4043 (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-4043 (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4043 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 (-1209)) (|:| -2300 (-51))) (QUOTE (-102)))) (-1096 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (|%list| (QUOTE -38) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1023) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-1209))))) (-1097 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-6 -4509)) (-4506 . T) (-4505 . T) (-4508 . T)) NIL (-1098) ((|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'."))) @@ -4342,7 +4342,7 @@ NIL NIL (-1103 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) NIL (-1104 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}ts)} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts,{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) @@ -4356,7 +4356,7 @@ NIL ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1107 |Base| R -4187) +(-1107 |Base| R -3581) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}fn are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL @@ -4364,7 +4364,7 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1109 |Base| R -4187) +(-1109 |Base| R -3581) ((|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 @@ -4374,8 +4374,8 @@ NIL NIL (-1111 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."))) -((-4503 |has| |#1| (-376)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-4128 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) +((-4504 |has| |#1| (-376)) (-4509 |has| |#1| (-376)) (-4503 |has| |#1| (-376)) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . 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(|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4406,8 +4406,8 @@ NIL NIL (-1119 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"))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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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 @@ -4446,15 +4446,15 @@ NIL NIL (-1129 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)}}"))) -((-4510 . T) (-4500 . T) (-4511 . T)) -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4511 . T) (-4501 . T) (-4512 . T)) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-1130 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL (-1131 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4500 . T)) +((-4501 . T)) NIL (-1132 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}."))) @@ -4465,7 +4465,7 @@ NIL NIL NIL (-1134 |m| |n|) -((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the k^{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {\\spad{a_1},{}...,{}a_m}. Error if {\\spad{a_1},{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the k^{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the k^{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) +((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the k^{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {\\spad{a_1},{}...,{}a_m}. Error if {\\spad{a_1},{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ #1="failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the k^{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ #1#) $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the k^{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL (-1135) @@ -4494,7 +4494,7 @@ NIL NIL (-1141 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the gcd of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(ts,{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) NIL (-1142) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4510,8 +4510,8 @@ NIL NIL (-1145 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4504 |has| |#3| (-1081)) (-4505 |has| |#3| (-1081)) (-4507 |has| |#3| (-6 -4507)) (-4510 . 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(QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (-1146 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4524,12 +4524,12 @@ 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 `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) NIL NIL -(-1149 R -4187) -((|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."))) +(-1149 R -3581) +((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) #1#) |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL (-1150 R) -((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) +((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL (-1151) @@ -4538,19 +4538,19 @@ NIL NIL (-1152) ((|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}.")) (|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."))) -((-4498 . T) (-4502 . T) (-4497 . T) (-4508 . T) (-4509 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4499 . T) (-4503 . T) (-4498 . T) (-4509 . T) (-4510 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1153 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\#s}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4510 . T) (-4511 . T)) +((-4511 . T) (-4512 . T)) NIL (-1154 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-376))) (|HasAttribute| |#3| (QUOTE (-4512 "*"))) (|HasCategory| |#3| (QUOTE (-175)))) +((|HasCategory| |#3| (QUOTE (-376))) (|HasAttribute| |#3| (QUOTE (-4513 "*"))) (|HasCategory| |#3| (QUOTE (-175)))) (-1155 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) -((-4510 . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4511 . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1156 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}."))) @@ -4558,17 +4558,17 @@ NIL NIL (-1157 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."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4128 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4128 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4128 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-6 -4509)) (-4506 . T) (-4505 . T) (-4508 . T)) +((|HasCategory| |#1| (QUOTE (-940))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4043 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4043 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4043 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4509)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1158 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4506 . T) (-4505 . T) (-4508 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1159 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}"))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) NIL -(-1160 UP -4187) +(-1160 UP -3581) ((|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 @@ -4622,19 +4622,19 @@ NIL NIL (-1173 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in ls]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}lt)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}ls)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))) (-4128 (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (-4128 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))))) (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))) (-4043 (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102)))) (-1174 |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}."))) -((-4507 . T) (-4499 |has| |#2| (-6 (-4512 "*"))) (-4510 . T) (-4504 . T) (-4505 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4128 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (-4128 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((-4508 . T) (-4500 |has| |#2| (-6 (-4513 "*"))) (-4511 . T) (-4505 . T) (-4506 . T)) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4513 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4043 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (-4043 (|HasAttribute| |#2| (QUOTE (-4513 "*"))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-1175 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1176) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) NIL (-1177 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4642,7 +4642,7 @@ NIL NIL (-1178 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#4| (QUOTE (-102)))) (-1179) ((|constructor| (NIL "The category of all semiring structures,{} \\spadignore{e.g.} triples (\\spad{D},{}+,{}*) such that (\\spad{D},{}+) is an Abelian monoid and (\\spad{D},{}*) is a monoid with the following laws:"))) @@ -4650,8 +4650,8 @@ NIL NIL (-1180 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}."))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1181 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4662,8 +4662,8 @@ NIL NIL (-1183 |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."))) -((-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2654) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1356) (|devaluate| |#2|)))))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-872))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133)))) +((-4512 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2300) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-872))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102)))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-1184) ((|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}'s are never \\spad{nothing}.}")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4678,8 +4678,8 @@ NIL NIL (-1187 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."))) -((-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4512 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1188 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) NIL @@ -4694,12 +4694,12 @@ NIL NIL (-1191) ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) -((-4511 . T) (-4510 . T)) -((-4128 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4128 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-4128 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-4512 . T) (-4511 . 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(|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by r: \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4730,9 +4730,9 @@ NIL NIL (-1200 |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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(|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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T) (-4505 . T) (-4508 . T)) +((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1114) (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4043 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4043 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4043 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4509)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1204 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -4754,12 +4754,12 @@ NIL NIL (-1206 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . 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We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . 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T) (-4506 . T) (-4508 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -4462) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4328) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3570) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1208) ((|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 @@ -4774,10 +4774,10 @@ NIL NIL (-1211 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4128 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1003) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4508))) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-6 -4509)) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4043 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| (-1003) (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4509))) (-1212) -((|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."))) +((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL NIL (-1213) @@ -4814,8 +4814,8 @@ NIL NIL (-1221 |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}"))) -((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2654) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1356) (|devaluate| |#2|)))))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4128 (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (QUOTE (-102)))) +((-4511 . T) (-4512 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2300) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4043 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4043 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (QUOTE (-102)))) (-1222 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL @@ -4834,7 +4834,7 @@ NIL NIL (-1226 |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{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4511 . T)) +((-4512 . T)) NIL (-1227 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key -> Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) @@ -4874,8 +4874,8 @@ NIL NIL (-1236 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4511 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4512 . T) (-4511 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1237 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4884,7 +4884,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1239 R -4187) +(-1239 R -3581) ((|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 @@ -4892,21 +4892,21 @@ 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 -(-1241 R -4187) +(-1241 R -3581) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on f:\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on f:\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (|devaluate| |#1|))))) (-1242 |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}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4506 . T) (-4505 . T) (-4508 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1243 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL ((|HasCategory| |#4| (QUOTE (-381)))) (-1244 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#4|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) NIL (-1245 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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}."))) @@ -4920,7 +4920,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) -(-1248 -4187) +(-1248 -3581) ((|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 @@ -4946,7 +4946,7 @@ NIL NIL (-1254) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1255) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4966,15 +4966,15 @@ NIL NIL (-1259 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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(-1289 |#1| |#2| |#3|) (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1260 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL (-1261 |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{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."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-376)) (-4503 |has| |#1| (-376)) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1262 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)}."))) @@ -4982,12 +4982,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-376)))) (-1263 |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)}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-376)) (-4503 |has| |#1| (-376)) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1264 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are 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)}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . 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T)) +((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4043 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1114) (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4043 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4043 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4043 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4043 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4509)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4043 (-12 (|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) (-1269 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -5030,7 +5030,7 @@ NIL ((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-1184)))) (-1275 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4509 |has| |#1| (-6 -4509)) (-4506 . T) (-4505 . T) (-4508 . T)) NIL (-1276 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."))) @@ -5039,26 +5039,26 @@ NIL (-1277 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1144))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -4457) (|%list| (|devaluate| |#2|) (QUOTE (-1209)))))) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1144))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -4462) (|%list| (|devaluate| |#2|) (QUOTE (-1209)))))) (-1278 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1279 RC P) -((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) +((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL (-1280 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4128 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -4457) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4128 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2243) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -1647) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-376)) (-4503 |has| |#1| (-376)) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4043 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -4462) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4328) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3570) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1281 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL (-1282 |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."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-376)) (-4503 |has| |#1| (-376)) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1283 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)}."))) @@ -5066,28 +5066,28 @@ NIL NIL (-1284 |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)}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-376)) (-4503 |has| |#1| (-376)) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1285 |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)}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4128 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -4457) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4128 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2243) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -1647) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4509 |has| |#1| (-376)) (-4503 |has| |#1| (-376)) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4043 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -4462) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4328) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3570) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-1286 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))}."))) -(((-4512 "*") |has| (-1280 |#2| |#3| |#4|) (-175)) (-4503 |has| (-1280 |#2| |#3| |#4|) (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-175))) (-4128 (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-571)))) +(((-4513 "*") |has| (-1280 |#2| |#3| |#4|) (-175)) (-4504 |has| (-1280 |#2| |#3| |#4|) (-571)) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-175))) (-4043 (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-571)))) (-1287 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4511))) +((|HasAttribute| |#1| (QUOTE -4512))) (-1288 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL (-1289 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . 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T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4128 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -4457) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-4128 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2243) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -1647) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4505 . T) (-4506 . T) (-4508 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4043 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -4462) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4328) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3570) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1290 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL @@ -5095,16 +5095,16 @@ NIL (-1291 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 (-560)))) (|HasCategory| |#2| (QUOTE (-990))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasSignature| |#2| (|%list| (QUOTE -1647) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -2243) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) +((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-990))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasSignature| |#2| (|%list| (QUOTE -3570) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -4328) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) (-1292 |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."))) -(((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") |has| |#1| (-175)) (-4504 |has| |#1| (-571)) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1293 |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 -(-1294 -4187 UP L UTS) +(-1294 -3581 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 (-571)))) @@ -5122,12 +5122,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1298 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) NIL (-1299 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4511 . T) (-4510 . T)) -((-4128 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4128 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4128 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4128 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4512 . T) (-4511 . T)) +((-4043 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4043 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4043 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4043 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-1300 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL @@ -5158,13 +5158,13 @@ NIL NIL (-1307 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}."))) -((-4505 . T) (-4504 . T)) +((-4506 . T) (-4505 . T)) NIL (-1308 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*v + A[2]\\spad{*v**2} + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1309 K R UP -4187) +(-1309 K R UP -3581) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -5178,56 +5178,56 @@ NIL NIL (-1312 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) +((-4506 |has| |#1| (-175)) (-4505 |has| |#1| (-175)) (-4508 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (-1313 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{ps} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{bs} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}."))) -((-4511 . T) (-4510 . T)) +((-4512 . T) (-4511 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#4| (QUOTE (-102)))) (-1314 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.fr)"))) -((-4504 . T) (-4505 . T) (-4507 . T)) +((-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1315 |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."))) -((-4507 . T) (-4503 |has| |#2| (-6 -4503)) (-4505 . T) (-4504 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4503))) +((-4508 . T) (-4504 |has| |#2| (-6 -4504)) (-4506 . T) (-4505 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4504))) (-1316 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1317 S -4187) +(-1317 S -3581) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1318 -4187) +(-1318 -3581) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) -((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 . T) (-4509 . T) (-4504 . T) ((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL (-1319 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4503 |has| |#2| (-6 -4503)) (-4505 . T) (-4504 . T) (-4507 . T)) +((-4504 |has| |#2| (-6 -4504)) (-4506 . T) (-4505 . T) (-4508 . T)) NIL (-1320 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-4503 |has| |#2| (-6 -4503)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -739) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasAttribute| |#2| (QUOTE -4503))) +((-4504 |has| |#2| (-6 -4504)) (-4506 . T) (-4505 . T) (-4508 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -739) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasAttribute| |#2| (QUOTE -4504))) (-1321 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."))) -((-4503 |has| |#1| (-6 -4503)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4503))) +((-4504 |has| |#1| (-6 -4504)) (-4506 . T) (-4505 . T) (-4508 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4504))) (-1322 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4503 |has| |#2| (-6 -4503)) (-4505 . T) (-4504 . T) (-4507 . T)) +((-4504 |has| |#2| (-6 -4504)) (-4506 . T) (-4505 . T) (-4508 . T)) NIL (-1323 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4507 . T) (-4508 |has| |#1| (-6 -4508)) (-4503 |has| |#1| (-6 -4503)) (-4505 . T) (-4504 . T)) -((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4503))) +((-4508 . T) (-4509 |has| |#1| (-6 -4509)) (-4504 |has| |#1| (-6 -4504)) (-4506 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4509)) (|HasAttribute| |#1| (QUOTE -4504))) (-1324 |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."))) -((-4503 |has| |#2| (-6 -4503)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4503))) +((-4504 |has| |#2| (-6 -4504)) (-4506 . T) (-4505 . T) (-4508 . T)) +((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4504))) (-1325) ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) NIL @@ -5246,7 +5246,7 @@ NIL NIL (-1329 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +(((-4513 "*") . T) (-4505 . T) (-4506 . T) (-4508 . T)) NIL NIL NIL @@ -5264,4 +5264,4 @@ NIL NIL NIL NIL -((-3 NIL 2294535 2294540 2294545 2294550) (-2 NIL 2294515 2294520 2294525 2294530) (-1 NIL 2294495 2294500 2294505 2294510) (0 NIL 2294475 2294480 2294485 2294490) (-1329 "ZMOD.spad" 2294284 2294297 2294413 2294470) (-1328 "ZLINDEP.spad" 2293382 2293393 2294274 2294279) (-1327 "ZDSOLVE.spad" 2283342 2283364 2293372 2293377) (-1326 "YSTREAM.spad" 2282837 2282848 2283332 2283337) (-1325 "YDIAGRAM.spad" 2282471 2282480 2282827 2282832) (-1324 "XRPOLY.spad" 2281691 2281711 2282327 2282396) (-1323 "XPR.spad" 2279486 2279499 2281409 2281508) (-1322 "XPOLYC.spad" 2278805 2278821 2279412 2279481) (-1321 "XPOLY.spad" 2278360 2278371 2278661 2278730) (-1320 "XPBWPOLY.spad" 2276799 2276819 2278134 2278203) (-1319 "XFALG.spad" 2273847 2273863 2276725 2276794) (-1318 "XF.spad" 2272310 2272325 2273749 2273842) (-1317 "XF.spad" 2270753 2270770 2272194 2272199) (-1316 "XEXPPKG.spad" 2270012 2270038 2270743 2270748) (-1315 "XDPOLY.spad" 2269626 2269642 2269868 2269937) (-1314 "XALG.spad" 2269294 2269305 2269582 2269621) (-1313 "WUTSET.spad" 2265264 2265281 2268895 2268922) (-1312 "WP.spad" 2264471 2264515 2265122 2265189) (-1311 "WHILEAST.spad" 2264269 2264278 2264461 2264466) (-1310 "WHEREAST.spad" 2263940 2263949 2264259 2264264) (-1309 "WFFINTBS.spad" 2261603 2261625 2263930 2263935) (-1308 "WEIER.spad" 2259825 2259836 2261593 2261598) (-1307 "VSPACE.spad" 2259498 2259509 2259793 2259820) (-1306 "VSPACE.spad" 2259191 2259204 2259488 2259493) (-1305 "VOID.spad" 2258868 2258877 2259181 2259186) (-1304 "VIEWDEF.spad" 2254069 2254078 2258858 2258863) (-1303 "VIEW3D.spad" 2238030 2238039 2254059 2254064) (-1302 "VIEW2D.spad" 2225929 2225938 2238020 2238025) (-1301 "VIEW.spad" 2223649 2223658 2225919 2225924) (-1300 "VECTOR2.spad" 2222288 2222301 2223639 2223644) (-1299 "VECTOR.spad" 2220788 2220799 2221039 2221066) (-1298 "VECTCAT.spad" 2218700 2218711 2220756 2220783) (-1297 "VECTCAT.spad" 2216419 2216432 2218477 2218482) (-1296 "VARIABLE.spad" 2216199 2216214 2216409 2216414) (-1295 "UTYPE.spad" 2215843 2215852 2216189 2216194) (-1294 "UTSODETL.spad" 2215138 2215162 2215799 2215804) (-1293 "UTSODE.spad" 2213354 2213374 2215128 2215133) (-1292 "UTSCAT.spad" 2210833 2210849 2213252 2213349) (-1291 "UTSCAT.spad" 2207932 2207950 2210353 2210358) (-1290 "UTS2.spad" 2207527 2207562 2207922 2207927) (-1289 "UTS.spad" 2202405 2202433 2205925 2206022) (-1288 "URAGG.spad" 2197126 2197137 2202395 2202400) (-1287 "URAGG.spad" 2191811 2191824 2197082 2197087) (-1286 "UPXSSING.spad" 2189429 2189455 2190865 2190998) (-1285 "UPXSCONS.spad" 2187107 2187127 2187480 2187629) (-1284 "UPXSCCA.spad" 2185678 2185698 2186953 2187102) (-1283 "UPXSCCA.spad" 2184391 2184413 2185668 2185673) (-1282 "UPXSCAT.spad" 2182980 2182996 2184237 2184386) (-1281 "UPXS2.spad" 2182523 2182576 2182970 2182975) (-1280 "UPXS.spad" 2179738 2179766 2180574 2180723) (-1279 "UPSQFREE.spad" 2178152 2178166 2179728 2179733) (-1278 "UPSCAT.spad" 2175947 2175971 2178050 2178147) (-1277 "UPSCAT.spad" 2173427 2173453 2175532 2175537) (-1276 "UPOLYC2.spad" 2172898 2172917 2173417 2173422) (-1275 "UPOLYC.spad" 2167978 2167989 2172740 2172893) (-1274 "UPOLYC.spad" 2162944 2162957 2167708 2167713) (-1273 "UPMP.spad" 2161876 2161889 2162934 2162939) (-1272 "UPDIVP.spad" 2161441 2161455 2161866 2161871) (-1271 "UPDECOMP.spad" 2159702 2159716 2161431 2161436) (-1270 "UPCDEN.spad" 2158919 2158935 2159692 2159697) (-1269 "UP2.spad" 2158283 2158304 2158909 2158914) (-1268 "UP.spad" 2155311 2155326 2155698 2155851) (-1267 "UNISEG2.spad" 2154808 2154821 2155267 2155272) (-1266 "UNISEG.spad" 2154161 2154172 2154727 2154732) (-1265 "UNIFACT.spad" 2153264 2153276 2154151 2154156) (-1264 "ULSCONS.spad" 2144176 2144196 2144546 2144695) (-1263 "ULSCCAT.spad" 2141913 2141933 2144022 2144171) (-1262 "ULSCCAT.spad" 2139758 2139780 2141869 2141874) (-1261 "ULSCAT.spad" 2137998 2138014 2139604 2139753) (-1260 "ULS2.spad" 2137512 2137565 2137988 2137993) (-1259 "ULS.spad" 2127083 2127111 2128028 2128457) (-1258 "UINT8.spad" 2126960 2126969 2127073 2127078) (-1257 "UINT64.spad" 2126836 2126845 2126950 2126955) (-1256 "UINT32.spad" 2126712 2126721 2126826 2126831) (-1255 "UINT16.spad" 2126588 2126597 2126702 2126707) (-1254 "UFD.spad" 2125653 2125662 2126514 2126583) (-1253 "UFD.spad" 2124780 2124791 2125643 2125648) (-1252 "UDVO.spad" 2123661 2123670 2124770 2124775) (-1251 "UDPO.spad" 2121242 2121253 2123617 2123622) (-1250 "TYPEAST.spad" 2121161 2121170 2121232 2121237) (-1249 "TYPE.spad" 2121093 2121102 2121151 2121156) (-1248 "TWOFACT.spad" 2119745 2119760 2121083 2121088) (-1247 "TUPLE.spad" 2119236 2119247 2119641 2119646) (-1246 "TUBETOOL.spad" 2116103 2116112 2119226 2119231) (-1245 "TUBE.spad" 2114750 2114767 2116093 2116098) (-1244 "TSETCAT.spad" 2102821 2102838 2114718 2114745) (-1243 "TSETCAT.spad" 2090878 2090897 2102777 2102782) (-1242 "TS.spad" 2089471 2089487 2090437 2090534) (-1241 "TRMANIP.spad" 2083835 2083852 2089159 2089164) (-1240 "TRIMAT.spad" 2082798 2082823 2083825 2083830) (-1239 "TRIGMNIP.spad" 2081325 2081342 2082788 2082793) (-1238 "TRIGCAT.spad" 2080837 2080846 2081315 2081320) (-1237 "TRIGCAT.spad" 2080347 2080358 2080827 2080832) (-1236 "TREE.spad" 2078793 2078804 2079825 2079852) (-1235 "TRANFUN.spad" 2078632 2078641 2078783 2078788) (-1234 "TRANFUN.spad" 2078469 2078480 2078622 2078627) (-1233 "TOPSP.spad" 2078143 2078152 2078459 2078464) (-1232 "TOOLSIGN.spad" 2077806 2077817 2078133 2078138) (-1231 "TEXTFILE.spad" 2076367 2076376 2077796 2077801) (-1230 "TEX1.spad" 2075923 2075934 2076357 2076362) (-1229 "TEX.spad" 2073117 2073126 2075913 2075918) (-1228 "TEMUTL.spad" 2072672 2072681 2073107 2073112) (-1227 "TBCMPPK.spad" 2070773 2070796 2072662 2072667) (-1226 "TBAGG.spad" 2069831 2069854 2070753 2070768) (-1225 "TBAGG.spad" 2068897 2068922 2069821 2069826) (-1224 "TANEXP.spad" 2068305 2068316 2068887 2068892) (-1223 "TALGOP.spad" 2068029 2068040 2068295 2068300) (-1222 "TABLEAU.spad" 2067510 2067521 2068019 2068024) (-1221 "TABLE.spad" 2065443 2065466 2065713 2065740) (-1220 "TABLBUMP.spad" 2062222 2062233 2065433 2065438) (-1219 "SYSTEM.spad" 2061450 2061459 2062212 2062217) (-1218 "SYSSOLP.spad" 2058933 2058944 2061440 2061445) (-1217 "SYSPTR.spad" 2058832 2058841 2058923 2058928) (-1216 "SYSNNI.spad" 2058055 2058066 2058822 2058827) (-1215 "SYSINT.spad" 2057459 2057470 2058045 2058050) (-1214 "SYNTAX.spad" 2053793 2053802 2057449 2057454) (-1213 "SYMTAB.spad" 2051861 2051870 2053783 2053788) (-1212 "SYMS.spad" 2047884 2047893 2051851 2051856) (-1211 "SYMPOLY.spad" 2046863 2046874 2046945 2047072) (-1210 "SYMFUNC.spad" 2046364 2046375 2046853 2046858) (-1209 "SYMBOL.spad" 2043859 2043868 2046354 2046359) (-1208 "SWITCH.spad" 2040630 2040639 2043849 2043854) (-1207 "SUTS.spad" 2037609 2037637 2039028 2039125) (-1206 "SUPXS.spad" 2034811 2034839 2035660 2035809) (-1205 "SUPFRACF.spad" 2033916 2033934 2034801 2034806) (-1204 "SUP2.spad" 2033308 2033321 2033906 2033911) (-1203 "SUP.spad" 2029950 2029961 2030723 2030876) (-1202 "SUMRF.spad" 2028924 2028935 2029940 2029945) (-1201 "SUMFS.spad" 2028553 2028570 2028914 2028919) (-1200 "SULS.spad" 2018111 2018139 2019069 2019498) (-1199 "SUCHTAST.spad" 2017880 2017889 2018101 2018106) (-1198 "SUCH.spad" 2017570 2017585 2017870 2017875) (-1197 "SUBSPACE.spad" 2009701 2009716 2017560 2017565) (-1196 "SUBRESP.spad" 2008871 2008885 2009657 2009662) (-1195 "STTFNC.spad" 2005339 2005355 2008861 2008866) (-1194 "STTF.spad" 2001438 2001454 2005329 2005334) (-1193 "STTAYLOR.spad" 1994083 1994094 2001313 2001318) (-1192 "STRTBL.spad" 1992098 1992115 1992247 1992274) (-1191 "STRING.spad" 1990864 1990873 1991085 1991112) (-1190 "STREAM3.spad" 1990437 1990452 1990854 1990859) (-1189 "STREAM2.spad" 1989565 1989578 1990427 1990432) (-1188 "STREAM1.spad" 1989271 1989282 1989555 1989560) (-1187 "STREAM.spad" 1986057 1986068 1988664 1988679) (-1186 "STINPROD.spad" 1984993 1985009 1986047 1986052) (-1185 "STEPAST.spad" 1984227 1984236 1984983 1984988) (-1184 "STEP.spad" 1983436 1983445 1984217 1984222) (-1183 "STBL.spad" 1981484 1981512 1981651 1981666) (-1182 "STAGG.spad" 1980183 1980194 1981474 1981479) (-1181 "STAGG.spad" 1978880 1978893 1980173 1980178) (-1180 "STACK.spad" 1978108 1978119 1978358 1978385) (-1179 "SRING.spad" 1977868 1977877 1978098 1978103) (-1178 "SREGSET.spad" 1975567 1975584 1977469 1977496) (-1177 "SRDCMPK.spad" 1974144 1974164 1975557 1975562) (-1176 "SRAGG.spad" 1969327 1969336 1974112 1974139) (-1175 "SRAGG.spad" 1964530 1964541 1969317 1969322) (-1174 "SQMATRIX.spad" 1962025 1962043 1962941 1963028) (-1173 "SPLTREE.spad" 1956491 1956504 1961287 1961314) (-1172 "SPLNODE.spad" 1953111 1953124 1956481 1956486) (-1171 "SPFCAT.spad" 1951920 1951929 1953101 1953106) (-1170 "SPECOUT.spad" 1950472 1950481 1951910 1951915) (-1169 "SPADXPT.spad" 1942563 1942572 1950462 1950467) (-1168 "spad-parser.spad" 1942028 1942037 1942553 1942558) (-1167 "SPADAST.spad" 1941729 1941738 1942018 1942023) (-1166 "SPACEC.spad" 1925944 1925955 1941719 1941724) (-1165 "SPACE3.spad" 1925720 1925731 1925934 1925939) (-1164 "SORTPAK.spad" 1925269 1925282 1925676 1925681) (-1163 "SOLVETRA.spad" 1923032 1923043 1925259 1925264) (-1162 "SOLVESER.spad" 1921488 1921499 1923022 1923027) (-1161 "SOLVERAD.spad" 1917514 1917525 1921478 1921483) (-1160 "SOLVEFOR.spad" 1915976 1915994 1917504 1917509) (-1159 "SNTSCAT.spad" 1915576 1915593 1915944 1915971) (-1158 "SMTS.spad" 1913858 1913884 1915135 1915232) (-1157 "SMP.spad" 1911261 1911281 1911651 1911778) (-1156 "SMITH.spad" 1910106 1910131 1911251 1911256) (-1155 "SMATCAT.spad" 1908224 1908254 1910050 1910101) (-1154 "SMATCAT.spad" 1906274 1906306 1908102 1908107) (-1153 "SKAGG.spad" 1905243 1905254 1906242 1906269) (-1152 "SINT.spad" 1904183 1904192 1905109 1905238) (-1151 "SIMPAN.spad" 1903911 1903920 1904173 1904178) (-1150 "SIGNRF.spad" 1903029 1903040 1903901 1903906) (-1149 "SIGNEF.spad" 1902308 1902325 1903019 1903024) (-1148 "SIGAST.spad" 1901725 1901734 1902298 1902303) (-1147 "SIG.spad" 1901087 1901096 1901715 1901720) (-1146 "SHP.spad" 1899031 1899046 1901043 1901048) (-1145 "SHDP.spad" 1886386 1886413 1886903 1887002) (-1144 "SGROUP.spad" 1885994 1886003 1886376 1886381) (-1143 "SGROUP.spad" 1885600 1885611 1885984 1885989) (-1142 "SGCF.spad" 1878739 1878748 1885590 1885595) (-1141 "SFRTCAT.spad" 1877685 1877702 1878707 1878734) (-1140 "SFRGCD.spad" 1876748 1876768 1877675 1877680) (-1139 "SFQCMPK.spad" 1871561 1871581 1876738 1876743) (-1138 "SFORT.spad" 1871000 1871014 1871551 1871556) (-1137 "SEXOF.spad" 1870843 1870883 1870990 1870995) (-1136 "SEXCAT.spad" 1868671 1868711 1870833 1870838) (-1135 "SEX.spad" 1868563 1868572 1868661 1868666) (-1134 "SETMN.spad" 1867021 1867038 1868553 1868558) (-1133 "SETCAT.spad" 1866506 1866515 1867011 1867016) (-1132 "SETCAT.spad" 1865989 1866000 1866496 1866501) (-1131 "SETAGG.spad" 1862538 1862549 1865969 1865984) (-1130 "SETAGG.spad" 1859095 1859108 1862528 1862533) (-1129 "SET.spad" 1857368 1857379 1858465 1858504) (-1128 "SEQAST.spad" 1857071 1857080 1857358 1857363) (-1127 "SEGXCAT.spad" 1856227 1856240 1857061 1857066) (-1126 "SEGCAT.spad" 1855152 1855163 1856217 1856222) (-1125 "SEGBIND2.spad" 1854850 1854863 1855142 1855147) (-1124 "SEGBIND.spad" 1854608 1854619 1854797 1854802) (-1123 "SEGAST.spad" 1854338 1854347 1854598 1854603) (-1122 "SEG2.spad" 1853773 1853786 1854294 1854299) (-1121 "SEG.spad" 1853586 1853597 1853692 1853697) (-1120 "SDVAR.spad" 1852862 1852873 1853576 1853581) (-1119 "SDPOL.spad" 1850117 1850128 1850408 1850535) (-1118 "SCPKG.spad" 1848206 1848217 1850107 1850112) (-1117 "SCOPE.spad" 1847383 1847392 1848196 1848201) (-1116 "SCACHE.spad" 1846079 1846090 1847373 1847378) (-1115 "SASTCAT.spad" 1845988 1845997 1846069 1846074) (-1114 "SAOS.spad" 1845860 1845869 1845978 1845983) (-1113 "SAERFFC.spad" 1845573 1845593 1845850 1845855) (-1112 "SAEFACT.spad" 1845274 1845294 1845563 1845568) (-1111 "SAE.spad" 1842708 1842724 1843319 1843454) (-1110 "RURPK.spad" 1840367 1840383 1842698 1842703) (-1109 "RULESET.spad" 1839820 1839844 1840357 1840362) (-1108 "RULECOLD.spad" 1839672 1839685 1839810 1839815) (-1107 "RULE.spad" 1837920 1837944 1839662 1839667) (-1106 "RTVALUE.spad" 1837655 1837664 1837910 1837915) (-1105 "RSTRCAST.spad" 1837372 1837381 1837645 1837650) (-1104 "RSETGCD.spad" 1833814 1833834 1837362 1837367) (-1103 "RSETCAT.spad" 1823782 1823799 1833782 1833809) (-1102 "RSETCAT.spad" 1813770 1813789 1823772 1823777) (-1101 "RSDCMPK.spad" 1812270 1812290 1813760 1813765) (-1100 "RRCC.spad" 1810654 1810684 1812260 1812265) (-1099 "RRCC.spad" 1809036 1809068 1810644 1810649) (-1098 "RPTAST.spad" 1808738 1808747 1809026 1809031) (-1097 "RPOLCAT.spad" 1788242 1788257 1808606 1808733) (-1096 "RPOLCAT.spad" 1767441 1767458 1787807 1787812) (-1095 "ROUTINE.spad" 1762842 1762851 1765590 1765617) (-1094 "ROMAN.spad" 1762170 1762179 1762708 1762837) (-1093 "ROIRC.spad" 1761250 1761282 1762160 1762165) (-1092 "RNS.spad" 1760226 1760235 1761152 1761245) (-1091 "RNS.spad" 1759288 1759299 1760216 1760221) (-1090 "RNGBIND.spad" 1758448 1758462 1759243 1759248) (-1089 "RNG.spad" 1758183 1758192 1758438 1758443) (-1088 "RMODULE.spad" 1757964 1757975 1758173 1758178) (-1087 "RMCAT2.spad" 1757384 1757441 1757954 1757959) (-1086 "RMATRIX.spad" 1756154 1756173 1756497 1756536) (-1085 "RMATCAT.spad" 1751733 1751764 1756110 1756149) (-1084 "RMATCAT.spad" 1747202 1747235 1751581 1751586) (-1083 "RLINSET.spad" 1746906 1746917 1747192 1747197) (-1082 "RINTERP.spad" 1746794 1746814 1746896 1746901) (-1081 "RING.spad" 1746264 1746273 1746774 1746789) (-1080 "RING.spad" 1745742 1745753 1746254 1746259) (-1079 "RIDIST.spad" 1745134 1745143 1745732 1745737) (-1078 "RGCHAIN.spad" 1743655 1743671 1744549 1744576) (-1077 "RGBCSPC.spad" 1743444 1743456 1743645 1743650) (-1076 "RGBCMDL.spad" 1743006 1743018 1743434 1743439) (-1075 "RFFACTOR.spad" 1742468 1742479 1742996 1743001) (-1074 "RFFACT.spad" 1742203 1742215 1742458 1742463) (-1073 "RFDIST.spad" 1741199 1741208 1742193 1742198) (-1072 "RF.spad" 1738873 1738884 1741189 1741194) (-1071 "RETSOL.spad" 1738292 1738305 1738863 1738868) (-1070 "RETRACT.spad" 1737720 1737731 1738282 1738287) (-1069 "RETRACT.spad" 1737146 1737159 1737710 1737715) (-1068 "RETAST.spad" 1736958 1736967 1737136 1737141) (-1067 "RESULT.spad" 1734520 1734529 1735107 1735134) (-1066 "RESRING.spad" 1733867 1733914 1734458 1734515) (-1065 "RESLATC.spad" 1733191 1733202 1733857 1733862) (-1064 "REPSQ.spad" 1732922 1732933 1733181 1733186) (-1063 "REPDB.spad" 1732629 1732640 1732912 1732917) (-1062 "REP2.spad" 1722343 1722354 1732471 1732476) (-1061 "REP1.spad" 1716563 1716574 1722293 1722298) (-1060 "REP.spad" 1714117 1714126 1716553 1716558) (-1059 "REGSET.spad" 1711909 1711926 1713718 1713745) (-1058 "REF.spad" 1711244 1711255 1711864 1711869) (-1057 "REDORDER.spad" 1710450 1710467 1711234 1711239) (-1056 "RECLOS.spad" 1709209 1709229 1709913 1710006) (-1055 "REALSOLV.spad" 1708349 1708358 1709199 1709204) (-1054 "REAL0Q.spad" 1705647 1705662 1708339 1708344) (-1053 "REAL0.spad" 1702491 1702506 1705637 1705642) (-1052 "REAL.spad" 1702363 1702372 1702481 1702486) (-1051 "RDUCEAST.spad" 1702084 1702093 1702353 1702358) (-1050 "RDIV.spad" 1701739 1701764 1702074 1702079) (-1049 "RDIST.spad" 1701306 1701317 1701729 1701734) (-1048 "RDETRS.spad" 1700170 1700188 1701296 1701301) (-1047 "RDETR.spad" 1698309 1698327 1700160 1700165) (-1046 "RDEEFS.spad" 1697408 1697425 1698299 1698304) (-1045 "RDEEF.spad" 1696418 1696435 1697398 1697403) (-1044 "RCFIELD.spad" 1693636 1693645 1696320 1696413) (-1043 "RCFIELD.spad" 1690940 1690951 1693626 1693631) (-1042 "RCAGG.spad" 1688876 1688887 1690930 1690935) (-1041 "RCAGG.spad" 1686739 1686752 1688795 1688800) (-1040 "RATRET.spad" 1686099 1686110 1686729 1686734) (-1039 "RATFACT.spad" 1685791 1685803 1686089 1686094) (-1038 "RANDSRC.spad" 1685110 1685119 1685781 1685786) (-1037 "RADUTIL.spad" 1684866 1684875 1685100 1685105) (-1036 "RADIX.spad" 1681645 1681659 1683191 1683284) (-1035 "RADFF.spad" 1679348 1679385 1679467 1679623) (-1034 "RADCAT.spad" 1678943 1678952 1679338 1679343) (-1033 "RADCAT.spad" 1678536 1678547 1678933 1678938) (-1032 "QUEUE.spad" 1677755 1677766 1678014 1678041) (-1031 "QUATCT2.spad" 1677375 1677394 1677745 1677750) (-1030 "QUATCAT.spad" 1675545 1675556 1677305 1677370) (-1029 "QUATCAT.spad" 1673463 1673476 1675225 1675230) (-1028 "QUAT.spad" 1671915 1671926 1672258 1672323) (-1027 "QUAGG.spad" 1670748 1670759 1671883 1671910) (-1026 "QQUTAST.spad" 1670516 1670525 1670738 1670743) (-1025 "QFORM.spad" 1670134 1670149 1670506 1670511) (-1024 "QFCAT2.spad" 1669826 1669843 1670124 1670129) (-1023 "QFCAT.spad" 1668528 1668539 1669728 1669821) (-1022 "QFCAT.spad" 1666812 1666825 1668014 1668019) (-1021 "QEQUAT.spad" 1666370 1666379 1666802 1666807) (-1020 "QCMPACK.spad" 1661284 1661304 1666360 1666365) (-1019 "QALGSET2.spad" 1659279 1659298 1661274 1661279) (-1018 "QALGSET.spad" 1655381 1655414 1659193 1659198) (-1017 "PWFFINTB.spad" 1652796 1652818 1655371 1655376) (-1016 "PUSHVAR.spad" 1652134 1652154 1652786 1652791) (-1015 "PTRANFN.spad" 1648269 1648280 1652124 1652129) (-1014 "PTPACK.spad" 1645356 1645367 1648259 1648264) (-1013 "PTFUNC2.spad" 1645178 1645193 1645346 1645351) (-1012 "PTCAT.spad" 1644432 1644443 1645146 1645173) (-1011 "PSQFR.spad" 1643746 1643771 1644422 1644427) (-1010 "PSEUDLIN.spad" 1642631 1642642 1643736 1643741) (-1009 "PSETPK.spad" 1629335 1629352 1642509 1642514) (-1008 "PSETCAT.spad" 1623734 1623758 1629315 1629330) (-1007 "PSETCAT.spad" 1618107 1618133 1623690 1623695) (-1006 "PSCURVE.spad" 1617105 1617114 1618097 1618102) (-1005 "PSCAT.spad" 1615887 1615917 1617003 1617100) (-1004 "PSCAT.spad" 1614759 1614791 1615877 1615882) (-1003 "PRTITION.spad" 1613456 1613465 1614749 1614754) (-1002 "PRTDAST.spad" 1613174 1613183 1613446 1613451) (-1001 "PRS.spad" 1602791 1602809 1613130 1613135) 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1584799 1585501 1585506) (-981 "POLYCATQ.spad" 1582902 1582924 1584766 1584771) (-980 "POLYCAT.spad" 1576404 1576425 1582770 1582897) (-979 "POLYCAT.spad" 1569202 1569225 1575570 1575575) (-978 "POLY2UP.spad" 1568654 1568668 1569192 1569197) (-977 "POLY2.spad" 1568251 1568263 1568644 1568649) (-976 "POLY.spad" 1565514 1565524 1566029 1566156) (-975 "POLUTIL.spad" 1564479 1564508 1565470 1565475) (-974 "POLTOPOL.spad" 1563227 1563242 1564469 1564474) (-973 "POINT.spad" 1561891 1561901 1561978 1562005) (-972 "PNTHEORY.spad" 1558593 1558601 1561881 1561886) (-971 "PMTOOLS.spad" 1557368 1557382 1558583 1558588) (-970 "PMSYM.spad" 1556917 1556927 1557358 1557363) (-969 "PMQFCAT.spad" 1556508 1556522 1556907 1556912) (-968 "PMPREDFS.spad" 1555970 1555992 1556498 1556503) (-967 "PMPRED.spad" 1555457 1555471 1555960 1555965) (-966 "PMPLCAT.spad" 1554534 1554552 1555386 1555391) (-965 "PMLSAGG.spad" 1554119 1554133 1554524 1554529) (-964 "PMKERNEL.spad" 1553698 1553710 1554109 1554114) (-963 "PMINS.spad" 1553278 1553288 1553688 1553693) (-962 "PMFS.spad" 1552855 1552873 1553268 1553273) (-961 "PMDOWN.spad" 1552145 1552159 1552845 1552850) (-960 "PMASSFS.spad" 1551120 1551136 1552135 1552140) (-959 "PMASS.spad" 1550138 1550146 1551110 1551115) (-958 "PLOTTOOL.spad" 1549918 1549926 1550128 1550133) (-957 "PLOT3D.spad" 1546382 1546390 1549908 1549913) (-956 "PLOT1.spad" 1545555 1545565 1546372 1546377) (-955 "PLOT.spad" 1540478 1540486 1545545 1545550) (-954 "PLEQN.spad" 1527880 1527907 1540468 1540473) (-953 "PINTERPA.spad" 1527664 1527680 1527870 1527875) (-952 "PINTERP.spad" 1527286 1527305 1527654 1527659) (-951 "PID.spad" 1526260 1526268 1527212 1527281) (-950 "PICOERCE.spad" 1525917 1525927 1526250 1526255) (-949 "PI.spad" 1525534 1525542 1525891 1525912) (-948 "PGROEB.spad" 1524143 1524157 1525524 1525529) (-947 "PGE.spad" 1515816 1515824 1524133 1524138) (-946 "PGCD.spad" 1514770 1514787 1515806 1515811) (-945 "PFRPAC.spad" 1513919 1513929 1514760 1514765) (-944 "PFR.spad" 1510622 1510632 1513821 1513914) (-943 "PFOTOOLS.spad" 1509880 1509896 1510612 1510617) (-942 "PFOQ.spad" 1509250 1509268 1509870 1509875) (-941 "PFO.spad" 1508669 1508696 1509240 1509245) (-940 "PFECAT.spad" 1506379 1506387 1508595 1508664) (-939 "PFECAT.spad" 1504117 1504127 1506335 1506340) (-938 "PFBRU.spad" 1502005 1502017 1504107 1504112) (-937 "PFBR.spad" 1499565 1499588 1501995 1502000) (-936 "PF.spad" 1499139 1499151 1499370 1499463) (-935 "PERMGRP.spad" 1493909 1493919 1499129 1499134) (-934 "PERMCAT.spad" 1492570 1492580 1493889 1493904) (-933 "PERMAN.spad" 1491126 1491140 1492560 1492565) (-932 "PERM.spad" 1486933 1486943 1490956 1490971) (-931 "PENDTREE.spad" 1486153 1486163 1486433 1486438) (-930 "PDSPC.spad" 1484966 1484976 1486143 1486148) (-929 "PDSPC.spad" 1483777 1483789 1484956 1484961) (-928 "PDRING.spad" 1483619 1483629 1483757 1483772) (-927 "PDMOD.spad" 1483435 1483447 1483587 1483614) (-926 "PDEPROB.spad" 1482450 1482458 1483425 1483430) (-925 "PDEPACK.spad" 1476586 1476594 1482440 1482445) (-924 "PDECOMP.spad" 1476056 1476073 1476576 1476581) (-923 "PDECAT.spad" 1474412 1474420 1476046 1476051) (-922 "PDDOM.spad" 1473850 1473863 1474402 1474407) (-921 "PDDOM.spad" 1473286 1473301 1473840 1473845) (-920 "PCOMP.spad" 1473139 1473152 1473276 1473281) (-919 "PBWLB.spad" 1471735 1471752 1473129 1473134) (-918 "PATTERN2.spad" 1471473 1471485 1471725 1471730) (-917 "PATTERN1.spad" 1469817 1469833 1471463 1471468) (-916 "PATTERN.spad" 1464388 1464398 1469807 1469812) (-915 "PATRES2.spad" 1464060 1464074 1464378 1464383) (-914 "PATRES.spad" 1461643 1461655 1464050 1464055) (-913 "PATMATCH.spad" 1459831 1459862 1461342 1461347) (-912 "PATMAB.spad" 1459260 1459270 1459821 1459826) (-911 "PATLRES.spad" 1458346 1458360 1459250 1459255) (-910 "PATAB.spad" 1458110 1458120 1458336 1458341) (-909 "PARTPERM.spad" 1456166 1456174 1458100 1458105) (-908 "PARSURF.spad" 1455600 1455628 1456156 1456161) (-907 "PARSU2.spad" 1455397 1455413 1455590 1455595) (-906 "script-parser.spad" 1454917 1454925 1455387 1455392) (-905 "PARSCURV.spad" 1454351 1454379 1454907 1454912) (-904 "PARSC2.spad" 1454142 1454158 1454341 1454346) (-903 "PARPCURV.spad" 1453604 1453632 1454132 1454137) (-902 "PARPC2.spad" 1453395 1453411 1453594 1453599) (-901 "PARAMAST.spad" 1452523 1452531 1453385 1453390) (-900 "PAN2EXPR.spad" 1451935 1451943 1452513 1452518) (-899 "PALETTE.spad" 1450921 1450929 1451925 1451930) (-898 "PAIR.spad" 1449928 1449941 1450497 1450502) (-897 "PADICRC.spad" 1447132 1447150 1448295 1448388) (-896 "PADICRAT.spad" 1444991 1445003 1445204 1445297) (-895 "PADICCT.spad" 1443540 1443552 1444917 1444986) (-894 "PADIC.spad" 1443243 1443255 1443466 1443535) (-893 "PADEPAC.spad" 1441932 1441951 1443233 1443238) (-892 "PADE.spad" 1440684 1440700 1441922 1441927) (-891 "OWP.spad" 1439932 1439962 1440542 1440609) (-890 "OVERSET.spad" 1439505 1439513 1439922 1439927) (-889 "OVAR.spad" 1439286 1439309 1439495 1439500) (-888 "OUTFORM.spad" 1428694 1428702 1439276 1439281) (-887 "OUTBFILE.spad" 1428128 1428136 1428684 1428689) (-886 "OUTBCON.spad" 1427198 1427206 1428118 1428123) (-885 "OUTBCON.spad" 1426266 1426276 1427188 1427193) (-884 "OUT.spad" 1425384 1425392 1426256 1426261) (-883 "OSI.spad" 1424859 1424867 1425374 1425379) (-882 "OSGROUP.spad" 1424777 1424785 1424849 1424854) (-881 "ORTHPOL.spad" 1423256 1423266 1424688 1424693) (-880 "OREUP.spad" 1422700 1422728 1422927 1422966) (-879 "ORESUP.spad" 1421992 1422016 1422371 1422410) (-878 "OREPCTO.spad" 1419881 1419893 1421912 1421917) (-877 "OREPCAT.spad" 1414068 1414078 1419837 1419876) (-876 "OREPCAT.spad" 1408145 1408157 1413916 1413921) (-875 "ORDTYPE.spad" 1407382 1407390 1408135 1408140) (-874 "ORDTYPE.spad" 1406617 1406627 1407372 1407377) (-873 "ORDSTRCT.spad" 1406387 1406402 1406550 1406555) (-872 "ORDSET.spad" 1406087 1406095 1406377 1406382) (-871 "ORDRING.spad" 1405904 1405912 1406067 1406082) (-870 "ORDMON.spad" 1405759 1405767 1405894 1405899) (-869 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1384109) (-850 "OMERRK.spad" 1382998 1383006 1383938 1383943) (-849 "OMERR.spad" 1382543 1382551 1382988 1382993) (-848 "OMENC.spad" 1381895 1381903 1382533 1382538) (-847 "OMDEV.spad" 1376228 1376236 1381885 1381890) (-846 "OMCONN.spad" 1375637 1375645 1376218 1376223) (-845 "OM.spad" 1374634 1374642 1375627 1375632) (-844 "OINTDOM.spad" 1374397 1374405 1374560 1374629) (-843 "OFMONOID.spad" 1372536 1372546 1374353 1374358) (-842 "ODVAR.spad" 1371797 1371807 1372526 1372531) (-841 "ODR.spad" 1371441 1371467 1371609 1371758) (-840 "ODPOL.spad" 1368652 1368662 1368992 1369119) (-839 "ODP.spad" 1356151 1356171 1356524 1356623) (-838 "ODETOOLS.spad" 1354800 1354819 1356141 1356146) (-837 "ODESYS.spad" 1352494 1352511 1354790 1354795) (-836 "ODERTRIC.spad" 1348527 1348544 1352451 1352456) (-835 "ODERED.spad" 1347926 1347950 1348517 1348522) (-834 "ODERAT.spad" 1345557 1345574 1347916 1347921) (-833 "ODEPRRIC.spad" 1342650 1342672 1345547 1345552) (-832 "ODEPROB.spad" 1341907 1341915 1342640 1342645) (-831 "ODEPRIM.spad" 1339305 1339327 1341897 1341902) (-830 "ODEPAL.spad" 1338691 1338715 1339295 1339300) (-829 "ODEPACK.spad" 1325421 1325429 1338681 1338686) (-828 "ODEINT.spad" 1324856 1324872 1325411 1325416) (-827 "ODEIFTBL.spad" 1322259 1322267 1324846 1324851) (-826 "ODEEF.spad" 1317750 1317766 1322249 1322254) (-825 "ODECONST.spad" 1317295 1317313 1317740 1317745) (-824 "ODECAT.spad" 1315893 1315901 1317285 1317290) (-823 "OCTCT2.spad" 1315531 1315552 1315883 1315888) (-822 "OCT.spad" 1313619 1313629 1314333 1314372) (-821 "OCAMON.spad" 1313467 1313475 1313609 1313614) (-820 "OC.spad" 1311263 1311273 1313423 1313462) (-819 "OC.spad" 1308781 1308793 1310943 1310948) (-818 "OASGP.spad" 1308596 1308604 1308771 1308776) (-817 "OAMONS.spad" 1308118 1308126 1308586 1308591) (-816 "OAMON.spad" 1307876 1307884 1308108 1308113) (-815 "OAMON.spad" 1307632 1307642 1307866 1307871) (-814 "OAGROUP.spad" 1307170 1307178 1307622 1307627) (-813 "OAGROUP.spad" 1306706 1306716 1307160 1307165) (-812 "NUMTUBE.spad" 1306297 1306313 1306696 1306701) (-811 "NUMQUAD.spad" 1294273 1294281 1306287 1306292) (-810 "NUMODE.spad" 1285625 1285633 1294263 1294268) (-809 "NUMINT.spad" 1283191 1283199 1285615 1285620) (-808 "NUMFMT.spad" 1282031 1282039 1283181 1283186) (-807 "NUMERIC.spad" 1274145 1274155 1281836 1281841) (-806 "NTSCAT.spad" 1272653 1272669 1274113 1274140) (-805 "NTPOLFN.spad" 1272198 1272208 1272564 1272569) (-804 "NSUP2.spad" 1271590 1271602 1272188 1272193) (-803 "NSUP.spad" 1264585 1264595 1269005 1269158) (-802 "NSMP.spad" 1260684 1260703 1260976 1261103) (-801 "NREP.spad" 1259086 1259100 1260674 1260679) (-800 "NPCOEF.spad" 1258332 1258352 1259076 1259081) (-799 "NORMRETR.spad" 1257930 1257969 1258322 1258327) (-798 "NORMPK.spad" 1255872 1255891 1257920 1257925) (-797 "NORMMA.spad" 1255560 1255586 1255862 1255867) (-796 "NONE1.spad" 1255236 1255246 1255550 1255555) (-795 "NONE.spad" 1254977 1254985 1255226 1255231) (-794 "NODE1.spad" 1254464 1254480 1254967 1254972) (-793 "NNI.spad" 1253359 1253367 1254438 1254459) (-792 "NLINSOL.spad" 1251985 1251995 1253349 1253354) (-791 "NIPROB.spad" 1250526 1250534 1251975 1251980) (-790 "NFINTBAS.spad" 1248086 1248103 1250516 1250521) (-789 "NETCLT.spad" 1248060 1248071 1248076 1248081) (-788 "NCODIV.spad" 1246284 1246300 1248050 1248055) (-787 "NCNTFRAC.spad" 1245926 1245940 1246274 1246279) (-786 "NCEP.spad" 1244092 1244106 1245916 1245921) (-785 "NASRING.spad" 1243696 1243704 1244082 1244087) (-784 "NASRING.spad" 1243298 1243308 1243686 1243691) (-783 "NARNG.spad" 1242698 1242706 1243288 1243293) (-782 "NARNG.spad" 1242096 1242106 1242688 1242693) (-781 "NAGSP.spad" 1241173 1241181 1242086 1242091) (-780 "NAGS.spad" 1230890 1230898 1241163 1241168) (-779 "NAGF07.spad" 1229321 1229329 1230880 1230885) (-778 "NAGF04.spad" 1223723 1223731 1229311 1229316) (-777 "NAGF02.spad" 1217816 1217824 1223713 1223718) (-776 "NAGF01.spad" 1213585 1213593 1217806 1217811) (-775 "NAGE04.spad" 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"FAMR.spad" 488969 488983 490725 490730) (-336 "FAMONOID.spad" 488653 488663 488923 488928) (-335 "FAMONC.spad" 486973 486985 488643 488648) (-334 "FAGROUP.spad" 486613 486623 486869 486896) (-333 "FACUTIL.spad" 484825 484842 486603 486608) (-332 "FACTFUNC.spad" 484027 484037 484815 484820) (-331 "EXPUPXS.spad" 480779 480802 482078 482227) (-330 "EXPRTUBE.spad" 478067 478075 480769 480774) (-329 "EXPRODE.spad" 475235 475251 478057 478062) (-328 "EXPR2UPS.spad" 471357 471370 475225 475230) (-327 "EXPR2.spad" 471062 471074 471347 471352) (-326 "EXPR.spad" 466147 466157 466861 467156) (-325 "EXPEXPAN.spad" 462891 462916 463523 463616) (-324 "EXITAST.spad" 462627 462635 462881 462886) (-323 "EXIT.spad" 462298 462306 462617 462622) (-322 "EVALCYC.spad" 461758 461772 462288 462293) (-321 "EVALAB.spad" 461338 461348 461748 461753) (-320 "EVALAB.spad" 460916 460928 461328 461333) (-319 "EUCDOM.spad" 458506 458514 460842 460911) (-318 "EUCDOM.spad" 456158 456168 458496 458501) (-317 "ESTOOLS2.spad" 455753 455767 456148 456153) (-316 "ESTOOLS1.spad" 455430 455441 455743 455748) (-315 "ESTOOLS.spad" 447308 447316 455420 455425) (-314 "ESCONT1.spad" 447049 447061 447298 447303) (-313 "ESCONT.spad" 443842 443850 447039 447044) (-312 "ES2.spad" 443355 443371 443832 443837) (-311 "ES1.spad" 442925 442941 443345 443350) (-310 "ES.spad" 435796 435804 442915 442920) (-309 "ES.spad" 428570 428580 435691 435696) (-308 "ERROR.spad" 425897 425905 428560 428565) (-307 "EQTBL.spad" 423891 423913 424100 424127) (-306 "EQ2.spad" 423609 423621 423881 423886) (-305 "EQ.spad" 418385 418395 421180 421292) (-304 "EP.spad" 414711 414721 418375 418380) (-303 "ENV.spad" 413389 413397 414701 414706) (-302 "ENTIRER.spad" 413057 413065 413333 413384) (-301 "EMR.spad" 412345 412386 412983 413052) (-300 "ELTAGG.spad" 410599 410618 412335 412340) (-299 "ELTAGG.spad" 408817 408838 410555 410560) (-298 "ELTAB.spad" 408292 408305 408807 408812) (-297 "ELFUTS.spad" 407727 407746 408282 408287) (-296 "ELEMFUN.spad" 407416 407424 407717 407722) (-295 "ELEMFUN.spad" 407103 407113 407406 407411) (-294 "ELAGG.spad" 405074 405084 407083 407098) (-293 "ELAGG.spad" 402982 402994 404993 404998) (-292 "ELABOR.spad" 402328 402336 402972 402977) (-291 "ELABEXPR.spad" 401260 401268 402318 402323) (-290 "EFUPXS.spad" 398036 398066 401216 401221) (-289 "EFULS.spad" 394872 394895 397992 397997) (-288 "EFSTRUC.spad" 392887 392903 394862 394867) (-287 "EF.spad" 387663 387679 392877 392882) (-286 "EAB.spad" 385963 385971 387653 387658) (-285 "E04UCFA.spad" 385499 385507 385953 385958) (-284 "E04NAFA.spad" 385076 385084 385489 385494) (-283 "E04MBFA.spad" 384656 384664 385066 385071) (-282 "E04JAFA.spad" 384192 384200 384646 384651) (-281 "E04GCFA.spad" 383728 383736 384182 384187) (-280 "E04FDFA.spad" 383264 383272 383718 383723) (-279 "E04DGFA.spad" 382800 382808 383254 383259) (-278 "E04AGNT.spad" 378674 378682 382790 382795) (-277 "DVARCAT.spad" 375564 375574 378664 378669) (-276 "DVARCAT.spad" 372452 372464 375554 375559) (-275 "DSMP.spad" 369748 369762 370053 370180) (-274 "DSEXT.spad" 369050 369060 369738 369743) (-273 "DSEXT.spad" 368256 368268 368946 368951) (-272 "DROPT1.spad" 367921 367931 368246 368251) (-271 "DROPT0.spad" 362786 362794 367911 367916) (-270 "DROPT.spad" 356745 356753 362776 362781) (-269 "DRAWPT.spad" 354918 354926 356735 356740) (-268 "DRAWHACK.spad" 354226 354236 354908 354913) (-267 "DRAWCX.spad" 351704 351712 354216 354221) (-266 "DRAWCURV.spad" 351251 351266 351694 351699) (-265 "DRAWCFUN.spad" 340783 340791 351241 351246) (-264 "DRAW.spad" 333659 333672 340773 340778) (-263 "DQAGG.spad" 331837 331847 333627 333654) (-262 "DPOLCAT.spad" 327194 327210 331705 331832) (-261 "DPOLCAT.spad" 322637 322655 327150 327155) (-260 "DPMO.spad" 314160 314176 314298 314511) (-259 "DPMM.spad" 305696 305714 305821 306034) (-258 "DOMTMPLT.spad" 305467 305475 305686 305691) (-257 "DOMCTOR.spad" 305222 305230 305457 305462) (-256 "DOMAIN.spad" 304333 304341 305212 305217) (-255 "DMP.spad" 301521 301536 302091 302218) (-254 "DMEXT.spad" 301388 301398 301489 301516) (-253 "DLP.spad" 300748 300758 301378 301383) (-252 "DLIST.spad" 299153 299163 299757 299784) (-251 "DLAGG.spad" 297570 297580 299143 299148) (-250 "DIVRING.spad" 297112 297120 297514 297565) (-249 "DIVRING.spad" 296698 296708 297102 297107) (-248 "DISPLAY.spad" 294888 294896 296688 296693) (-247 "DIRPROD2.spad" 293706 293724 294878 294883) (-246 "DIRPROD.spad" 280938 280954 281578 281677) (-245 "DIRPCAT.spad" 280131 280147 280834 280933) (-244 "DIRPCAT.spad" 278951 278969 279656 279661) (-243 "DIOSP.spad" 277776 277784 278941 278946) (-242 "DIOPS.spad" 276772 276782 277756 277771) (-241 "DIOPS.spad" 275742 275754 276728 276733) (-240 "DIFRING.spad" 275580 275588 275722 275737) (-239 "DIFFSPC.spad" 275159 275167 275570 275575) (-238 "DIFFSPC.spad" 274736 274746 275149 275154) (-237 "DIFFMOD.spad" 274225 274235 274704 274731) (-236 "DIFFDOM.spad" 273390 273401 274215 274220) (-235 "DIFFDOM.spad" 272553 272566 273380 273385) (-234 "DIFEXT.spad" 272372 272382 272533 272548) (-233 "DIAGG.spad" 272002 272012 272352 272367) (-232 "DIAGG.spad" 271640 271652 271992 271997) (-231 "DHMATRIX.spad" 269823 269833 270968 270995) (-230 "DFSFUN.spad" 263463 263471 269813 269818) (-229 "DFLOAT.spad" 260194 260202 263353 263458) (-228 "DFINTTLS.spad" 258425 258441 260184 260189) (-227 "DERHAM.spad" 256339 256371 258405 258420) (-226 "DEQUEUE.spad" 255534 255544 255817 255844) (-225 "DEGRED.spad" 255151 255165 255524 255529) (-224 "DEFINTRF.spad" 252688 252698 255141 255146) (-223 "DEFINTEF.spad" 251198 251214 252678 252683) (-222 "DEFAST.spad" 250582 250590 251188 251193) (-221 "DECIMAL.spad" 248546 248554 248907 249000) (-220 "DDFACT.spad" 246367 246384 248536 248541) (-219 "DBLRESP.spad" 245967 245991 246357 246362) (-218 "DBASIS.spad" 245593 245608 245957 245962) (-217 "DBASE.spad" 244257 244267 245583 245588) (-216 "DATAARY.spad" 243743 243756 244247 244252) (-215 "D03FAFA.spad" 243571 243579 243733 243738) (-214 "D03EEFA.spad" 243391 243399 243561 243566) (-213 "D03AGNT.spad" 242477 242485 243381 243386) (-212 "D02EJFA.spad" 241939 241947 242467 242472) (-211 "D02CJFA.spad" 241417 241425 241929 241934) (-210 "D02BHFA.spad" 240907 240915 241407 241412) (-209 "D02BBFA.spad" 240397 240405 240897 240902) (-208 "D02AGNT.spad" 235267 235275 240387 240392) (-207 "D01WGTS.spad" 233586 233594 235257 235262) (-206 "D01TRNS.spad" 233563 233571 233576 233581) (-205 "D01GBFA.spad" 233085 233093 233553 233558) (-204 "D01FCFA.spad" 232607 232615 233075 233080) (-203 "D01ASFA.spad" 232075 232083 232597 232602) (-202 "D01AQFA.spad" 231529 231537 232065 232070) (-201 "D01APFA.spad" 230969 230977 231519 231524) (-200 "D01ANFA.spad" 230463 230471 230959 230964) (-199 "D01AMFA.spad" 229973 229981 230453 230458) (-198 "D01ALFA.spad" 229513 229521 229963 229968) (-197 "D01AKFA.spad" 229039 229047 229503 229508) (-196 "D01AJFA.spad" 228562 228570 229029 229034) (-195 "D01AGNT.spad" 224629 224637 228552 228557) (-194 "CYCLOTOM.spad" 224135 224143 224619 224624) (-193 "CYCLES.spad" 220927 220935 224125 224130) (-192 "CVMP.spad" 220344 220354 220917 220922) (-191 "CTRIGMNP.spad" 218844 218860 220334 220339) (-190 "CTORKIND.spad" 218447 218455 218834 218839) (-189 "CTORCAT.spad" 217688 217696 218437 218442) (-188 "CTORCAT.spad" 216927 216937 217678 217683) (-187 "CTORCALL.spad" 216516 216526 216917 216922) (-186 "CTOR.spad" 216207 216215 216506 216511) (-185 "CSTTOOLS.spad" 215452 215465 216197 216202) (-184 "CRFP.spad" 209224 209237 215442 215447) (-183 "CRCEAST.spad" 208944 208952 209214 209219) (-182 "CRAPACK.spad" 208011 208021 208934 208939) (-181 "CPMATCH.spad" 207512 207527 207933 207938) (-180 "CPIMA.spad" 207217 207236 207502 207507) (-179 "COORDSYS.spad" 202226 202236 207207 207212) (-178 "CONTOUR.spad" 201653 201661 202216 202221) (-177 "CONTFRAC.spad" 197403 197413 201555 201648) (-176 "CONDUIT.spad" 197161 197169 197393 197398) (-175 "COMRING.spad" 196835 196843 197099 197156) (-174 "COMPPROP.spad" 196353 196361 196825 196830) (-173 "COMPLPAT.spad" 196120 196135 196343 196348) (-172 "COMPLEX2.spad" 195835 195847 196110 196115) (-171 "COMPLEX.spad" 191146 191156 191390 191651) (-170 "COMPILER.spad" 190695 190703 191136 191141) (-169 "COMPFACT.spad" 190297 190311 190685 190690) (-168 "COMPCAT.spad" 188369 188379 190031 190292) (-167 "COMPCAT.spad" 186166 186178 187830 187835) (-166 "COMMUPC.spad" 185914 185932 186156 186161) (-165 "COMMONOP.spad" 185447 185455 185904 185909) (-164 "COMMAAST.spad" 185210 185218 185437 185442) (-163 "COMM.spad" 185021 185029 185200 185205) (-162 "COMBOPC.spad" 183944 183952 185011 185016) (-161 "COMBINAT.spad" 182711 182721 183934 183939) (-160 "COMBF.spad" 180133 180149 182701 182706) (-159 "COLOR.spad" 178970 178978 180123 180128) (-158 "COLONAST.spad" 178636 178644 178960 178965) (-157 "CMPLXRT.spad" 178347 178364 178626 178631) (-156 "CLLCTAST.spad" 178009 178017 178337 178342) (-155 "CLIP.spad" 174117 174125 177999 178004) (-154 "CLIF.spad" 172772 172788 174073 174112) (-153 "CLAGG.spad" 169309 169319 172762 172767) (-152 "CLAGG.spad" 165714 165726 169169 169174) (-151 "CINTSLPE.spad" 165069 165082 165704 165709) (-150 "CHVAR.spad" 163207 163229 165059 165064) (-149 "CHARZ.spad" 163122 163130 163187 163202) (-148 "CHARPOL.spad" 162648 162658 163112 163117) (-147 "CHARNZ.spad" 162410 162418 162628 162643) (-146 "CHAR.spad" 159778 159786 162400 162405) (-145 "CFCAT.spad" 159106 159114 159768 159773) (-144 "CDEN.spad" 158326 158340 159096 159101) (-143 "CCLASS.spad" 156422 156430 157684 157723) (-142 "CATEGORY.spad" 155496 155504 156412 156417) (-141 "CATCTOR.spad" 155387 155395 155486 155491) (-140 "CATAST.spad" 155013 155021 155377 155382) (-139 "CASEAST.spad" 154727 154735 155003 155008) (-138 "CARTEN2.spad" 154117 154144 154717 154722) (-137 "CARTEN.spad" 149484 149508 154107 154112) (-136 "CARD.spad" 146779 146787 149458 149479) (-135 "CAPSLAST.spad" 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(-114 "BOOLEAN.spad" 122051 122059 122603 122608) (-113 "BOOLE.spad" 121701 121709 122041 122046) (-112 "BOOLE.spad" 121349 121359 121691 121696) (-111 "BMODULE.spad" 121061 121073 121317 121344) (-110 "BITS.spad" 120435 120443 120650 120677) (-109 "BINDING.spad" 119856 119864 120425 120430) (-108 "BINARY.spad" 117825 117833 118181 118274) (-107 "BGAGG.spad" 117030 117040 117805 117820) (-106 "BGAGG.spad" 116243 116255 117020 117025) (-105 "BFUNCT.spad" 115807 115815 116223 116238) (-104 "BEZOUT.spad" 114947 114974 115757 115762) (-103 "BBTREE.spad" 111695 111705 114425 114452) (-102 "BASTYPE.spad" 111194 111202 111685 111690) (-101 "BASTYPE.spad" 110691 110701 111184 111189) (-100 "BALFACT.spad" 110150 110163 110681 110686) (-99 "AUTOMOR.spad" 109601 109610 110130 110145) (-98 "ATTREG.spad" 106324 106331 109353 109596) (-97 "ATTRBUT.spad" 102347 102354 106304 106319) (-96 "ATTRAST.spad" 102064 102071 102337 102342) (-95 "ATRIG.spad" 101534 101541 102054 102059) (-94 "ATRIG.spad" 101002 101011 101524 101529) (-93 "ASTCAT.spad" 100906 100913 100992 100997) (-92 "ASTCAT.spad" 100808 100817 100896 100901) (-91 "ASTACK.spad" 100018 100027 100286 100313) (-90 "ASSOCEQ.spad" 98852 98863 99974 99979) (-89 "ASP9.spad" 97933 97946 98842 98847) (-88 "ASP80.spad" 97255 97268 97923 97928) (-87 "ASP8.spad" 96298 96311 97245 97250) (-86 "ASP78.spad" 95749 95762 96288 96293) (-85 "ASP77.spad" 95118 95131 95739 95744) (-84 "ASP74.spad" 94210 94223 95108 95113) (-83 "ASP73.spad" 93481 93494 94200 94205) (-82 "ASP7.spad" 92641 92654 93471 93476) (-81 "ASP6.spad" 91508 91521 92631 92636) (-80 "ASP55.spad" 90017 90030 91498 91503) (-79 "ASP50.spad" 87834 87847 90007 90012) (-78 "ASP49.spad" 86833 86846 87824 87829) (-77 "ASP42.spad" 85248 85287 86823 86828) (-76 "ASP41.spad" 83835 83874 85238 85243) (-75 "ASP4.spad" 83130 83143 83825 83830) (-74 "ASP35.spad" 82118 82131 83120 83125) (-73 "ASP34.spad" 81419 81432 82108 82113) (-72 "ASP33.spad" 80979 80992 81409 81414) (-71 "ASP31.spad" 80119 80132 80969 80974) (-70 "ASP30.spad" 79011 79024 80109 80114) (-69 "ASP29.spad" 78477 78490 79001 79006) (-68 "ASP28.spad" 69750 69763 78467 78472) (-67 "ASP27.spad" 68647 68660 69740 69745) (-66 "ASP24.spad" 67734 67747 68637 68642) (-65 "ASP20.spad" 67198 67211 67724 67729) (-64 "ASP19.spad" 61884 61897 67188 67193) (-63 "ASP12.spad" 61298 61311 61874 61879) (-62 "ASP10.spad" 60569 60582 61288 61293) (-61 "ASP1.spad" 59950 59963 60559 60564) (-60 "ARRAY2.spad" 59189 59198 59428 59455) (-59 "ARRAY12.spad" 57902 57913 59179 59184) (-58 "ARRAY1.spad" 56565 56574 56911 56938) (-57 "ARR2CAT.spad" 52347 52368 56533 56560) (-56 "ARR2CAT.spad" 48149 48172 52337 52342) (-55 "ARITY.spad" 47521 47528 48139 48144) (-54 "APPRULE.spad" 46805 46827 47511 47516) (-53 "APPLYORE.spad" 46424 46437 46795 46800) (-52 "ANY1.spad" 45495 45504 46414 46419) (-51 "ANY.spad" 44346 44353 45485 45490) (-50 "ANTISYM.spad" 42791 42807 44326 44341) (-49 "ANON.spad" 42500 42507 42781 42786) (-48 "AN.spad" 40806 40813 42313 42406) (-47 "AMR.spad" 38991 39002 40704 40801) (-46 "AMR.spad" 37007 37020 38722 38727) (-45 "ALIST.spad" 33847 33868 34197 34224) (-44 "ALGSC.spad" 32982 33008 33719 33772) (-43 "ALGPKG.spad" 28765 28776 32938 32943) (-42 "ALGMFACT.spad" 27958 27972 28755 28760) (-41 "ALGMANIP.spad" 25442 25457 27785 27790) (-40 "ALGFF.spad" 23047 23074 23264 23420) (-39 "ALGFACT.spad" 22166 22176 23037 23042) (-38 "ALGEBRA.spad" 21999 22008 22122 22161) (-37 "ALGEBRA.spad" 21864 21875 21989 21994) (-36 "ALAGG.spad" 21376 21397 21832 21859) (-35 "AHYP.spad" 20757 20764 21366 21371) (-34 "AGG.spad" 19466 19473 20747 20752) (-33 "AGG.spad" 18139 18148 19422 19427) (-32 "AF.spad" 16567 16582 18071 18076) (-31 "ADDAST.spad" 16253 16260 16557 16562) (-30 "ACPLOT.spad" 14844 14851 16243 16248) (-29 "ACFS.spad" 12701 12710 14746 14839) (-28 "ACFS.spad" 10644 10655 12691 12696) (-27 "ACF.spad" 7398 7405 10546 10639) (-26 "ACF.spad" 4238 4247 7388 7393) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2292987 2292992 2292997 2293002) (-2 NIL 2292967 2292972 2292977 2292982) (-1 NIL 2292947 2292952 2292957 2292962) (0 NIL 2292927 2292932 2292937 2292942) (-1329 "ZMOD.spad" 2292736 2292749 2292865 2292922) (-1328 "ZLINDEP.spad" 2291834 2291845 2292726 2292731) (-1327 "ZDSOLVE.spad" 2281794 2281816 2291824 2291829) (-1326 "YSTREAM.spad" 2281289 2281300 2281784 2281789) (-1325 "YDIAGRAM.spad" 2280923 2280932 2281279 2281284) (-1324 "XRPOLY.spad" 2280143 2280163 2280779 2280848) (-1323 "XPR.spad" 2277938 2277951 2279861 2279960) (-1322 "XPOLYC.spad" 2277257 2277273 2277864 2277933) (-1321 "XPOLY.spad" 2276812 2276823 2277113 2277182) (-1320 "XPBWPOLY.spad" 2275251 2275271 2276586 2276655) (-1319 "XFALG.spad" 2272299 2272315 2275177 2275246) (-1318 "XF.spad" 2270762 2270777 2272201 2272294) (-1317 "XF.spad" 2269205 2269222 2270646 2270651) (-1316 "XEXPPKG.spad" 2268464 2268490 2269195 2269200) (-1315 "XDPOLY.spad" 2268078 2268094 2268320 2268389) (-1314 "XALG.spad" 2267746 2267757 2268034 2268073) (-1313 "WUTSET.spad" 2263716 2263733 2267347 2267374) (-1312 "WP.spad" 2262923 2262967 2263574 2263641) (-1311 "WHILEAST.spad" 2262721 2262730 2262913 2262918) (-1310 "WHEREAST.spad" 2262392 2262401 2262711 2262716) (-1309 "WFFINTBS.spad" 2260055 2260077 2262382 2262387) (-1308 "WEIER.spad" 2258277 2258288 2260045 2260050) (-1307 "VSPACE.spad" 2257950 2257961 2258245 2258272) (-1306 "VSPACE.spad" 2257643 2257656 2257940 2257945) (-1305 "VOID.spad" 2257320 2257329 2257633 2257638) (-1304 "VIEWDEF.spad" 2252521 2252530 2257310 2257315) (-1303 "VIEW3D.spad" 2236482 2236491 2252511 2252516) (-1302 "VIEW2D.spad" 2224381 2224390 2236472 2236477) (-1301 "VIEW.spad" 2222101 2222110 2224371 2224376) (-1300 "VECTOR2.spad" 2220740 2220753 2222091 2222096) (-1299 "VECTOR.spad" 2219240 2219251 2219491 2219518) (-1298 "VECTCAT.spad" 2217152 2217163 2219208 2219235) (-1297 "VECTCAT.spad" 2214871 2214884 2216929 2216934) (-1296 "VARIABLE.spad" 2214651 2214666 2214861 2214866) (-1295 "UTYPE.spad" 2214295 2214304 2214641 2214646) (-1294 "UTSODETL.spad" 2213590 2213614 2214251 2214256) (-1293 "UTSODE.spad" 2211806 2211826 2213580 2213585) (-1292 "UTSCAT.spad" 2209285 2209301 2211704 2211801) (-1291 "UTSCAT.spad" 2206384 2206402 2208805 2208810) (-1290 "UTS2.spad" 2205979 2206014 2206374 2206379) (-1289 "UTS.spad" 2200857 2200885 2204377 2204474) (-1288 "URAGG.spad" 2195578 2195589 2200847 2200852) (-1287 "URAGG.spad" 2190263 2190276 2195534 2195539) (-1286 "UPXSSING.spad" 2187881 2187907 2189317 2189450) (-1285 "UPXSCONS.spad" 2185559 2185579 2185932 2186081) (-1284 "UPXSCCA.spad" 2184130 2184150 2185405 2185554) (-1283 "UPXSCCA.spad" 2182843 2182865 2184120 2184125) (-1282 "UPXSCAT.spad" 2181432 2181448 2182689 2182838) (-1281 "UPXS2.spad" 2180975 2181028 2181422 2181427) (-1280 "UPXS.spad" 2178190 2178218 2179026 2179175) (-1279 "UPSQFREE.spad" 2176605 2176619 2178180 2178185) (-1278 "UPSCAT.spad" 2174400 2174424 2176503 2176600) (-1277 "UPSCAT.spad" 2171880 2171906 2173985 2173990) (-1276 "UPOLYC2.spad" 2171351 2171370 2171870 2171875) (-1275 "UPOLYC.spad" 2166431 2166442 2171193 2171346) (-1274 "UPOLYC.spad" 2161397 2161410 2166161 2166166) (-1273 "UPMP.spad" 2160329 2160342 2161387 2161392) (-1272 "UPDIVP.spad" 2159894 2159908 2160319 2160324) (-1271 "UPDECOMP.spad" 2158155 2158169 2159884 2159889) (-1270 "UPCDEN.spad" 2157372 2157388 2158145 2158150) (-1269 "UP2.spad" 2156736 2156757 2157362 2157367) (-1268 "UP.spad" 2153764 2153779 2154151 2154304) (-1267 "UNISEG2.spad" 2153261 2153274 2153720 2153725) (-1266 "UNISEG.spad" 2152614 2152625 2153180 2153185) (-1265 "UNIFACT.spad" 2151717 2151729 2152604 2152609) (-1264 "ULSCONS.spad" 2142629 2142649 2142999 2143148) (-1263 "ULSCCAT.spad" 2140366 2140386 2142475 2142624) (-1262 "ULSCCAT.spad" 2138211 2138233 2140322 2140327) (-1261 "ULSCAT.spad" 2136451 2136467 2138057 2138206) (-1260 "ULS2.spad" 2135965 2136018 2136441 2136446) (-1259 "ULS.spad" 2125536 2125564 2126481 2126910) (-1258 "UINT8.spad" 2125413 2125422 2125526 2125531) (-1257 "UINT64.spad" 2125289 2125298 2125403 2125408) (-1256 "UINT32.spad" 2125165 2125174 2125279 2125284) (-1255 "UINT16.spad" 2125041 2125050 2125155 2125160) (-1254 "UFD.spad" 2124106 2124115 2124967 2125036) (-1253 "UFD.spad" 2123233 2123244 2124096 2124101) (-1252 "UDVO.spad" 2122114 2122123 2123223 2123228) (-1251 "UDPO.spad" 2119695 2119706 2122070 2122075) (-1250 "TYPEAST.spad" 2119614 2119623 2119685 2119690) (-1249 "TYPE.spad" 2119546 2119555 2119604 2119609) (-1248 "TWOFACT.spad" 2118198 2118213 2119536 2119541) (-1247 "TUPLE.spad" 2117689 2117700 2118094 2118099) (-1246 "TUBETOOL.spad" 2114556 2114565 2117679 2117684) (-1245 "TUBE.spad" 2113203 2113220 2114546 2114551) (-1244 "TSETCAT.spad" 2101274 2101291 2113171 2113198) (-1243 "TSETCAT.spad" 2089331 2089350 2101230 2101235) (-1242 "TS.spad" 2087924 2087940 2088890 2088987) (-1241 "TRMANIP.spad" 2082288 2082305 2087612 2087617) (-1240 "TRIMAT.spad" 2081251 2081276 2082278 2082283) (-1239 "TRIGMNIP.spad" 2079778 2079795 2081241 2081246) (-1238 "TRIGCAT.spad" 2079290 2079299 2079768 2079773) (-1237 "TRIGCAT.spad" 2078800 2078811 2079280 2079285) (-1236 "TREE.spad" 2077246 2077257 2078278 2078305) (-1235 "TRANFUN.spad" 2077085 2077094 2077236 2077241) (-1234 "TRANFUN.spad" 2076922 2076933 2077075 2077080) (-1233 "TOPSP.spad" 2076596 2076605 2076912 2076917) (-1232 "TOOLSIGN.spad" 2076259 2076270 2076586 2076591) (-1231 "TEXTFILE.spad" 2074820 2074829 2076249 2076254) (-1230 "TEX1.spad" 2074376 2074387 2074810 2074815) (-1229 "TEX.spad" 2071570 2071579 2074366 2074371) (-1228 "TEMUTL.spad" 2071125 2071134 2071560 2071565) (-1227 "TBCMPPK.spad" 2069226 2069249 2071115 2071120) (-1226 "TBAGG.spad" 2068284 2068307 2069206 2069221) (-1225 "TBAGG.spad" 2067350 2067375 2068274 2068279) (-1224 "TANEXP.spad" 2066758 2066769 2067340 2067345) (-1223 "TALGOP.spad" 2066482 2066493 2066748 2066753) (-1222 "TABLEAU.spad" 2065963 2065974 2066472 2066477) (-1221 "TABLE.spad" 2063896 2063919 2064166 2064193) (-1220 "TABLBUMP.spad" 2060675 2060686 2063886 2063891) (-1219 "SYSTEM.spad" 2059903 2059912 2060665 2060670) (-1218 "SYSSOLP.spad" 2057386 2057397 2059893 2059898) (-1217 "SYSPTR.spad" 2057285 2057294 2057376 2057381) (-1216 "SYSNNI.spad" 2056508 2056519 2057275 2057280) (-1215 "SYSINT.spad" 2055912 2055923 2056498 2056503) (-1214 "SYNTAX.spad" 2052246 2052255 2055902 2055907) (-1213 "SYMTAB.spad" 2050314 2050323 2052236 2052241) (-1212 "SYMS.spad" 2046343 2046352 2050304 2050309) (-1211 "SYMPOLY.spad" 2045322 2045333 2045404 2045531) (-1210 "SYMFUNC.spad" 2044823 2044834 2045312 2045317) (-1209 "SYMBOL.spad" 2042318 2042327 2044813 2044818) (-1208 "SWITCH.spad" 2039089 2039098 2042308 2042313) (-1207 "SUTS.spad" 2036068 2036096 2037487 2037584) (-1206 "SUPXS.spad" 2033270 2033298 2034119 2034268) (-1205 "SUPFRACF.spad" 2032375 2032393 2033260 2033265) (-1204 "SUP2.spad" 2031767 2031780 2032365 2032370) (-1203 "SUP.spad" 2028409 2028420 2029182 2029335) (-1202 "SUMRF.spad" 2027383 2027394 2028399 2028404) (-1201 "SUMFS.spad" 2027012 2027029 2027373 2027378) (-1200 "SULS.spad" 2016570 2016598 2017528 2017957) (-1199 "SUCHTAST.spad" 2016339 2016348 2016560 2016565) (-1198 "SUCH.spad" 2016029 2016044 2016329 2016334) (-1197 "SUBSPACE.spad" 2008160 2008175 2016019 2016024) (-1196 "SUBRESP.spad" 2007330 2007344 2008116 2008121) (-1195 "STTFNC.spad" 2003798 2003814 2007320 2007325) (-1194 "STTF.spad" 1999897 1999913 2003788 2003793) (-1193 "STTAYLOR.spad" 1992542 1992553 1999772 1999777) (-1192 "STRTBL.spad" 1990557 1990574 1990706 1990733) (-1191 "STRING.spad" 1989323 1989332 1989544 1989571) (-1190 "STREAM3.spad" 1988896 1988911 1989313 1989318) (-1189 "STREAM2.spad" 1988024 1988037 1988886 1988891) (-1188 "STREAM1.spad" 1987730 1987741 1988014 1988019) (-1187 "STREAM.spad" 1984516 1984527 1987123 1987138) (-1186 "STINPROD.spad" 1983452 1983468 1984506 1984511) (-1185 "STEPAST.spad" 1982686 1982695 1983442 1983447) (-1184 "STEP.spad" 1981895 1981904 1982676 1982681) (-1183 "STBL.spad" 1979943 1979971 1980110 1980125) (-1182 "STAGG.spad" 1978642 1978653 1979933 1979938) (-1181 "STAGG.spad" 1977339 1977352 1978632 1978637) (-1180 "STACK.spad" 1976567 1976578 1976817 1976844) (-1179 "SRING.spad" 1976327 1976336 1976557 1976562) (-1178 "SREGSET.spad" 1974026 1974043 1975928 1975955) (-1177 "SRDCMPK.spad" 1972603 1972623 1974016 1974021) (-1176 "SRAGG.spad" 1967786 1967795 1972571 1972598) (-1175 "SRAGG.spad" 1962989 1963000 1967776 1967781) (-1174 "SQMATRIX.spad" 1960484 1960502 1961400 1961487) (-1173 "SPLTREE.spad" 1954950 1954963 1959746 1959773) (-1172 "SPLNODE.spad" 1951570 1951583 1954940 1954945) (-1171 "SPFCAT.spad" 1950379 1950388 1951560 1951565) (-1170 "SPECOUT.spad" 1948931 1948940 1950369 1950374) (-1169 "SPADXPT.spad" 1941022 1941031 1948921 1948926) (-1168 "spad-parser.spad" 1940487 1940496 1941012 1941017) (-1167 "SPADAST.spad" 1940188 1940197 1940477 1940482) (-1166 "SPACEC.spad" 1924403 1924414 1940178 1940183) (-1165 "SPACE3.spad" 1924179 1924190 1924393 1924398) (-1164 "SORTPAK.spad" 1923728 1923741 1924135 1924140) (-1163 "SOLVETRA.spad" 1921491 1921502 1923718 1923723) (-1162 "SOLVESER.spad" 1919947 1919958 1921481 1921486) (-1161 "SOLVERAD.spad" 1915973 1915984 1919937 1919942) (-1160 "SOLVEFOR.spad" 1914435 1914453 1915963 1915968) (-1159 "SNTSCAT.spad" 1914035 1914052 1914403 1914430) (-1158 "SMTS.spad" 1912317 1912343 1913594 1913691) (-1157 "SMP.spad" 1909720 1909740 1910110 1910237) (-1156 "SMITH.spad" 1908565 1908590 1909710 1909715) (-1155 "SMATCAT.spad" 1906683 1906713 1908509 1908560) (-1154 "SMATCAT.spad" 1904733 1904765 1906561 1906566) (-1153 "SKAGG.spad" 1903702 1903713 1904701 1904728) (-1152 "SINT.spad" 1902642 1902651 1903568 1903697) (-1151 "SIMPAN.spad" 1902370 1902379 1902632 1902637) (-1150 "SIGNRF.spad" 1901495 1901506 1902360 1902365) (-1149 "SIGNEF.spad" 1900781 1900798 1901485 1901490) (-1148 "SIGAST.spad" 1900198 1900207 1900771 1900776) (-1147 "SIG.spad" 1899560 1899569 1900188 1900193) (-1146 "SHP.spad" 1897504 1897519 1899516 1899521) (-1145 "SHDP.spad" 1884859 1884886 1885376 1885475) (-1144 "SGROUP.spad" 1884467 1884476 1884849 1884854) (-1143 "SGROUP.spad" 1884073 1884084 1884457 1884462) (-1142 "SGCF.spad" 1877212 1877221 1884063 1884068) (-1141 "SFRTCAT.spad" 1876158 1876175 1877180 1877207) (-1140 "SFRGCD.spad" 1875221 1875241 1876148 1876153) (-1139 "SFQCMPK.spad" 1870034 1870054 1875211 1875216) (-1138 "SFORT.spad" 1869473 1869487 1870024 1870029) (-1137 "SEXOF.spad" 1869316 1869356 1869463 1869468) (-1136 "SEXCAT.spad" 1867144 1867184 1869306 1869311) (-1135 "SEX.spad" 1867036 1867045 1867134 1867139) (-1134 "SETMN.spad" 1865496 1865513 1867026 1867031) (-1133 "SETCAT.spad" 1864981 1864990 1865486 1865491) (-1132 "SETCAT.spad" 1864464 1864475 1864971 1864976) (-1131 "SETAGG.spad" 1861013 1861024 1864444 1864459) (-1130 "SETAGG.spad" 1857570 1857583 1861003 1861008) (-1129 "SET.spad" 1855843 1855854 1856940 1856979) (-1128 "SEQAST.spad" 1855546 1855555 1855833 1855838) (-1127 "SEGXCAT.spad" 1854702 1854715 1855536 1855541) (-1126 "SEGCAT.spad" 1853627 1853638 1854692 1854697) (-1125 "SEGBIND2.spad" 1853325 1853338 1853617 1853622) (-1124 "SEGBIND.spad" 1853083 1853094 1853272 1853277) (-1123 "SEGAST.spad" 1852813 1852822 1853073 1853078) (-1122 "SEG2.spad" 1852248 1852261 1852769 1852774) (-1121 "SEG.spad" 1852061 1852072 1852167 1852172) (-1120 "SDVAR.spad" 1851337 1851348 1852051 1852056) (-1119 "SDPOL.spad" 1848592 1848603 1848883 1849010) (-1118 "SCPKG.spad" 1846681 1846692 1848582 1848587) (-1117 "SCOPE.spad" 1845858 1845867 1846671 1846676) (-1116 "SCACHE.spad" 1844554 1844565 1845848 1845853) (-1115 "SASTCAT.spad" 1844463 1844472 1844544 1844549) (-1114 "SAOS.spad" 1844335 1844344 1844453 1844458) (-1113 "SAERFFC.spad" 1844048 1844068 1844325 1844330) (-1112 "SAEFACT.spad" 1843749 1843769 1844038 1844043) (-1111 "SAE.spad" 1841183 1841199 1841794 1841929) (-1110 "RURPK.spad" 1838842 1838858 1841173 1841178) (-1109 "RULESET.spad" 1838295 1838319 1838832 1838837) (-1108 "RULECOLD.spad" 1838147 1838160 1838285 1838290) (-1107 "RULE.spad" 1836395 1836419 1838137 1838142) (-1106 "RTVALUE.spad" 1836130 1836139 1836385 1836390) (-1105 "RSTRCAST.spad" 1835847 1835856 1836120 1836125) (-1104 "RSETGCD.spad" 1832289 1832309 1835837 1835842) (-1103 "RSETCAT.spad" 1822257 1822274 1832257 1832284) (-1102 "RSETCAT.spad" 1812245 1812264 1822247 1822252) (-1101 "RSDCMPK.spad" 1810745 1810765 1812235 1812240) (-1100 "RRCC.spad" 1809129 1809159 1810735 1810740) (-1099 "RRCC.spad" 1807511 1807543 1809119 1809124) (-1098 "RPTAST.spad" 1807213 1807222 1807501 1807506) (-1097 "RPOLCAT.spad" 1786717 1786732 1807081 1807208) (-1096 "RPOLCAT.spad" 1765916 1765933 1786282 1786287) (-1095 "ROUTINE.spad" 1761317 1761326 1764065 1764092) (-1094 "ROMAN.spad" 1760645 1760654 1761183 1761312) (-1093 "ROIRC.spad" 1759725 1759757 1760635 1760640) (-1092 "RNS.spad" 1758701 1758710 1759627 1759720) (-1091 "RNS.spad" 1757763 1757774 1758691 1758696) (-1090 "RNGBIND.spad" 1756923 1756937 1757718 1757723) (-1089 "RNG.spad" 1756658 1756667 1756913 1756918) (-1088 "RMODULE.spad" 1756439 1756450 1756648 1756653) (-1087 "RMCAT2.spad" 1755859 1755916 1756429 1756434) (-1086 "RMATRIX.spad" 1754629 1754648 1754972 1755011) (-1085 "RMATCAT.spad" 1750208 1750239 1754585 1754624) (-1084 "RMATCAT.spad" 1745677 1745710 1750056 1750061) (-1083 "RLINSET.spad" 1745381 1745392 1745667 1745672) (-1082 "RINTERP.spad" 1745269 1745289 1745371 1745376) (-1081 "RING.spad" 1744739 1744748 1745249 1745264) (-1080 "RING.spad" 1744217 1744228 1744729 1744734) (-1079 "RIDIST.spad" 1743609 1743618 1744207 1744212) (-1078 "RGCHAIN.spad" 1742130 1742146 1743024 1743051) (-1077 "RGBCSPC.spad" 1741919 1741931 1742120 1742125) (-1076 "RGBCMDL.spad" 1741481 1741493 1741909 1741914) (-1075 "RFFACTOR.spad" 1740943 1740954 1741471 1741476) (-1074 "RFFACT.spad" 1740678 1740690 1740933 1740938) (-1073 "RFDIST.spad" 1739674 1739683 1740668 1740673) (-1072 "RF.spad" 1737348 1737359 1739664 1739669) (-1071 "RETSOL.spad" 1736767 1736780 1737338 1737343) (-1070 "RETRACT.spad" 1736195 1736206 1736757 1736762) (-1069 "RETRACT.spad" 1735621 1735634 1736185 1736190) (-1068 "RETAST.spad" 1735433 1735442 1735611 1735616) (-1067 "RESULT.spad" 1732995 1733004 1733582 1733609) (-1066 "RESRING.spad" 1732342 1732389 1732933 1732990) (-1065 "RESLATC.spad" 1731666 1731677 1732332 1732337) (-1064 "REPSQ.spad" 1731397 1731408 1731656 1731661) (-1063 "REPDB.spad" 1731104 1731115 1731387 1731392) (-1062 "REP2.spad" 1720818 1720829 1730946 1730951) (-1061 "REP1.spad" 1715038 1715049 1720768 1720773) (-1060 "REP.spad" 1712592 1712601 1715028 1715033) (-1059 "REGSET.spad" 1710384 1710401 1712193 1712220) (-1058 "REF.spad" 1709719 1709730 1710339 1710344) (-1057 "REDORDER.spad" 1708925 1708942 1709709 1709714) (-1056 "RECLOS.spad" 1707684 1707704 1708388 1708481) (-1055 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. -1133) T) ((-530 . -19) 194483) ((-510 . -19) 194467) ((-58 . -618) 194444) ((-1035 . -239) 194381) ((-931 . -102) 194331) ((-879 . -748) T) ((-803 . -1133) T) ((-530 . -618) 194308) ((-510 . -618) 194285) ((-802 . -1133) T) ((-802 . -1097) 194252) ((-475 . -1133) T) ((-468 . -1133) T) ((-597 . -739) 194227) ((-671 . -1133) T) ((-1289 . -47) 194204) ((-1286 . -102) T) ((-1280 . -47) 194174) ((-1259 . -47) 194151) ((-1242 . -175) 194102) ((-1206 . -319) 194081) ((-1200 . -319) 194060) ((-1128 . -635) 194041) ((-1123 . -635) 194022) ((-1111 . -571) 193973) ((-1111 . -1254) 193924) ((-1105 . -635) 193905) ((-1036 . -928) NIL) ((-1098 . -635) 193886) ((-692 . -133) T) ((-646 . -1144) T) ((-1068 . -635) 193867) ((-1051 . -635) 193848) ((-736 . -1088) 193818) ((-734 . -922) 193721) ((-721 . -668) 193671) ((-286 . -1133) T) ((-86 . -455) T) ((-86 . -410) T) ((-733 . -175) T) ((-659 . -1088) 193655) ((-50 . -1133) T) ((-609 . -47) 193632) ((-229 . -670) 193597) ((-595 . -1133) T) ((-532 . -1133) T) ((-501 . -844) T) ((-501 . -951) T) ((-372 . -1254) T) ((-367 . -1254) T) ((-359 . -1254) T) ((-331 . -1144) T) ((-326 . -1083) 193507) ((-325 . -1083) 193436) ((-108 . -1254) T) ((-645 . -635) 193417) ((-372 . -571) T) ((-221 . -951) T) ((-221 . -844) T) ((-326 . -662) 193327) ((-325 . -662) 193256) ((-367 . -571) T) ((-359 . -571) T) ((-659 . -111) 193235) ((-497 . -635) 193216) ((-108 . -571) T) ((-1200 . -1052) NIL) ((-676 . -739) 193186) ((-496 . -875) 193137) ((-222 . -635) 193118) ((-331 . -23) T) ((-67 . -1249) T) ((-1032 . -632) 193050) ((-1329 . -1184) T) ((-716 . -274) 193032) ((-716 . -234) 193014) ((-1324 . -21) T) ((-736 . -111) 192979) ((-1324 . -25) T) ((-663 . -34) T) ((-252 . -503) 192963) ((-1321 . -133) T) ((-1320 . -133) T) ((-1313 . -102) T) ((-1296 . -632) 192929) ((-1129 . -1131) 192913) ((-174 . -1133) T) ((-1289 . -1249) T) ((-1280 . -1249) T) ((-1280 . -1070) 192848) ((-1259 . -1249) T) ((-1259 . -912) NIL) ((-976 . -940) 192827) ((-1259 . -910) 192779) ((-1259 . -1070) 192745) ((-1242 . -528) 192712) ((-529 . -635) 192696) ((-1221 . -633) NIL) ((-1221 . -632) 192678) ((-1174 . -1155) 192623) ((-495 . -940) 192602) ((-1119 . -739) 192451) ((-1094 . -670) 192423) ((-976 . -670) 192312) ((-842 . -875) T) ((-803 . -739) 192141) ((-611 . -504) 192122) ((-600 . -504) 192103) ((-611 . -632) 192069) ((-600 . -632) 192035) ((-549 . -632) 192017) ((-593 . -1249) T) ((-549 . -633) 191998) ((-802 . -739) 191847) ((-1109 . -102) T) ((-642 . -668) 191819) ((-395 . -25) T) ((-395 . -21) T) ((-495 . -670) 191708) ((-475 . -739) 191679) ((-468 . -739) 191528) ((-1018 . -102) T) ((-1078 . -1244) 191457) ((-931 . -321) 191395) ((-758 . -102) T) ((-659 . -635) 191372) ((-119 . -668) 191302) ((-901 . -93) T) ((-736 . -635) 191256) ((-703 . -93) T) ((-545 . -25) T) ((-698 . -93) T) ((-686 . -632) 191238) ((-667 . -504) 191219) ((-667 . -632) 191172) ((-143 . -102) T) ((-44 . -133) T) ((-610 . -1249) T) ((-609 . -1249) T) ((-357 . -1089) T) ((-301 . -1144) T) ((-492 . -93) T) ((-421 . -239) 191123) ((-368 . -632) 191105) ((-366 . -632) 191087) ((-358 . -632) 191069) ((-275 . -633) 190817) ((-275 . -632) 190799) ((-255 . -632) 190781) ((-255 . -633) 190642) ((-140 . -93) T) ((-139 . -93) T) ((-135 . -93) T) ((-1173 . -632) 190624) ((-1152 . -662) 190611) ((-1152 . -1083) 190598) ((-843 . -748) T) ((-843 . -882) T) ((-616 . -300) 190575) ((-595 . -739) 190540) ((-493 . -633) NIL) ((-493 . -632) 190522) ((-532 . -739) 190467) ((-326 . -102) T) ((-325 . -102) T) ((-301 . -23) T) ((-154 . -133) T) ((-936 . -632) 190449) ((-936 . -633) 190431) ((-400 . -748) T) ((-897 . -1088) 190383) ((-897 . -111) 190321) ((-736 . -1081) T) ((-734 . -1275) 190305) ((-716 . -363) NIL) ((-115 . -102) T) ((-141 . -102) T) ((-137 . -102) T) ((-533 . -632) 190237) ((-391 . -821) T) ((-170 . -1249) T) ((-227 . -1133) T) ((-391 . -816) T) ((-58 . -633) 190198) ((-229 . -818) T) ((-229 . -814) T) ((-58 . -632) 190110) ((-229 . -748) T) ((-530 . -633) 190071) ((-530 . -632) 189983) ((-511 . -632) 189915) ((-510 . -633) 189876) ((-510 . -632) 189788) ((-1111 . -376) 189739) ((-40 . -426) 189716) ((-78 . -1249) T) ((-896 . -940) NIL) ((-372 . -341) 189700) ((-372 . -376) T) ((-367 . -341) 189684) ((-367 . -376) T) ((-359 . -341) 189668) ((-359 . -376) T) ((-326 . -296) 189647) ((-108 . -376) T) ((-70 . -1249) T) ((-661 . -1133) T) ((-1259 . -351) 189599) ((-896 . -670) 189544) ((-1259 . -390) 189496) ((-994 . -133) 189351) ((-839 . -133) 189222) ((-45 . -875) NIL) ((-988 . -673) 189206) ((-1258 . -684) T) ((-1119 . -175) 189117) ((-988 . -385) 189101) ((-1094 . -818) T) ((-1094 . -814) T) ((-897 . -635) 188999) ((-803 . -175) 188890) ((-802 . -175) 188801) ((-840 . -47) 188763) ((-1094 . -748) T) ((-339 . -503) 188747) ((-976 . -748) T) ((-1313 . -321) 188685) ((-1289 . -928) 188598) ((-468 . -175) 188509) ((-252 . -298) 188461) ((-1285 . -1088) 188296) ((-1280 . -928) 188202) ((-1264 . -1088) 188010) ((-495 . -748) T) ((-1259 . -928) 187843) ((-1242 . -302) 187822) ((-1219 . -1249) T) ((-1216 . -381) T) ((-1215 . -381) T) ((-1178 . -153) 187806) ((-1152 . -102) T) ((-1147 . -1133) T) ((-1111 . -23) T) ((-1111 . -1144) T) ((-1108 . -102) T) ((-1090 . -632) 187773) ((-1035 . -424) 187745) ((-955 . -985) T) ((-758 . -321) 187683) ((-76 . -1249) T) ((-686 . -397) 187655) ((-171 . -940) 187608) ((-30 . -985) T) ((-114 . -868) T) ((-1 . -632) 187590) ((-1028 . -922) 187511) ((-131 . -673) 187493) ((-50 . -640) 187477) ((-716 . -668) 187412) ((-609 . -928) 187325) ((-452 . -102) T) ((-143 . -321) NIL) ((-131 . -385) 187307) ((-897 . -1081) T) ((-856 . -872) 187286) ((-81 . -1249) T) ((-733 . -302) T) ((-40 . -1089) T) ((-595 . -175) T) ((-532 . -175) T) ((-526 . -632) 187268) ((-171 . -670) 187142) ((-521 . -632) 187124) ((-365 . -149) 187106) ((-365 . -147) T) ((-372 . -1144) T) ((-367 . -1144) T) ((-359 . -1144) T) ((-1036 . -319) T) ((-944 . -319) T) ((-897 . -250) T) ((-108 . -1144) T) ((-897 . -240) 187085) ((-1285 . -111) 186906) ((-1264 . -111) 186695) ((-252 . -1288) 186679) ((-560 . -871) T) ((-372 . -23) T) ((-353 . -363) T) ((-326 . -321) 186666) ((-325 . -321) 186607) ((-367 . -23) T) ((-331 . -133) T) ((-359 . -23) T) ((-1036 . -1052) T) ((-31 . -635) 186588) ((-108 . -23) T) ((-678 . -1083) 186572) ((-252 . -618) 186549) ((-661 . -739) 186533) ((-345 . -1133) T) ((-678 . -662) 186503) ((-1286 . -38) 186395) ((-1268 . -940) 186374) ((-114 . -1133) T) ((-840 . -1249) T) ((-427 . -1249) T) ((-1067 . -102) T) ((-1268 . -670) 186263) ((-896 . -818) NIL) ((-880 . -670) 186237) ((-896 . -814) NIL) ((-840 . -912) NIL) ((-896 . -748) T) ((-1119 . -528) 186104) ((-803 . -528) 186051) ((-802 . -528) 186003) ((-585 . -670) 185990) ((-840 . -1070) 185818) ((-468 . -528) 185761) ((-402 . -403) T) ((-1285 . -635) 185574) ((-1264 . -635) 185322) ((-60 . -1249) T) ((-638 . -872) 185301) ((-514 . -684) T) ((-1178 . -1008) 185270) ((-1056 . -668) 185207) ((-1035 . -466) T) ((-721 . -871) T) ((-525 . -816) T) ((-488 . -1088) 185042) ((-514 . -113) T) ((-357 . -1133) T) ((-325 . -1184) NIL) ((-301 . -133) T) ((-407 . -1133) T) ((-894 . -1089) T) ((-716 . -383) 185009) ((-353 . -668) 184939) ((-227 . -640) 184916) ((-339 . -298) 184868) ((-488 . -111) 184689) ((-1285 . -1081) T) ((-1264 . -1081) T) ((-840 . -390) 184673) ((-850 . -1249) T) ((-171 . -748) T) ((-1315 . -1249) T) ((-678 . -102) T) ((-1285 . -250) 184652) ((-1285 . -240) 184604) ((-1264 . -240) 184509) ((-1264 . -250) 184488) ((-1035 . -416) NIL) ((-692 . -660) 184436) ((-326 . -38) 184346) ((-325 . -38) 184275) ((-69 . -632) 184257) ((-331 . -507) 184223) ((-48 . -668) 184173) ((-1221 . -300) 184152) ((-1258 . -872) T) ((-1145 . -1144) 184130) ((-84 . -1249) T) ((-62 . -632) 184112) ((-889 . -875) T) ((-493 . -300) 184091) ((-1315 . -1070) 184068) ((-1197 . -1133) T) ((-1145 . -23) 183920) ((-840 . -928) 183856) ((-1268 . -748) T) ((-1129 . -1249) T) ((-488 . -635) 183682) ((-365 . -239) T) ((-1119 . -302) 183613) ((-996 . -1133) T) ((-919 . -102) T) ((-803 . -302) 183524) ((-339 . -19) 183508) ((-58 . -300) 183485) ((-802 . -302) 183416) ((-880 . -748) T) ((-119 . -871) NIL) ((-530 . -300) 183393) ((-339 . -618) 183370) ((-510 . -300) 183347) ((-468 . -302) 183278) ((-1067 . -321) 183129) ((-901 . -504) 183110) ((-901 . -632) 183076) ((-703 . -504) 183057) ((-585 . -748) T) ((-698 . -504) 183038) ((-703 . -632) 182988) ((-698 . -632) 182954) ((-674 . -632) 182936) ((-492 . -504) 182917) ((-492 . -632) 182883) ((-252 . -633) 182844) ((-252 . -504) 182821) ((-140 . -504) 182802) ((-139 . -504) 182783) ((-135 . -504) 182764) ((-252 . -632) 182656) ((-216 . -102) T) ((-140 . -632) 182622) ((-139 . -632) 182588) ((-135 . -632) 182554) ((-1180 . -34) T) ((-973 . -1249) T) ((-357 . -739) 182499) ((-692 . -25) T) ((-692 . -21) T) ((-1209 . -635) 182480) ((-343 . -1249) T) ((-488 . -1081) T) ((-652 . -432) 182445) ((-620 . -432) 182410) ((-1152 . -1184) T) ((-1280 . -319) 182389) ((-734 . -1083) 182212) ((-595 . -302) T) ((-532 . -302) T) ((-1259 . -319) 182191) ((-488 . -240) 182143) ((-488 . -250) 182122) ((-453 . -1249) T) ((-734 . -662) 181951) ((-1259 . -1052) NIL) ((-1111 . -133) T) ((-897 . -821) 181930) ((-146 . -102) T) ((-40 . -1133) T) ((-897 . -816) 181909) ((-663 . -1042) 181893) ((-594 . -1089) T) ((-560 . -1089) T) ((-509 . -1089) T) ((-421 . -466) T) ((-372 . -133) T) ((-326 . -414) 181877) ((-325 . -414) 181838) ((-367 . -133) T) ((-359 . -133) T) ((-1214 . -1133) T) ((-1152 . -38) 181825) ((-1121 . -632) 181792) ((-108 . -133) T) ((-984 . -1133) T) ((-949 . -1133) T) ((-793 . -1133) T) ((-694 . -1133) T) ((-723 . -149) T) ((-623 . -102) T) ((-118 . -149) T) ((-1321 . -21) T) ((-1321 . -25) T) ((-1320 . -21) T) ((-1320 . -25) T) ((-686 . -1088) 181776) ((-545 . -872) T) ((-514 . -872) T) ((-377 . -1249) T) ((-368 . -1088) 181728) ((-366 . -1088) 181680) ((-358 . -1088) 181632) ((-260 . -1249) T) ((-259 . -1249) T) ((-275 . -1088) 181475) ((-255 . -1088) 181318) ((-686 . -111) 181297) ((-841 . -1254) 181276) ((-562 . -868) T) ((-326 . -930) 181242) ((-368 . -111) 181180) ((-366 . -111) 181118) ((-358 . -111) 181056) ((-275 . -111) 180885) ((-255 . -111) 180714) ((-325 . -930) NIL) ((-642 . -426) 180698) ((-44 . -21) T) ((-44 . -25) T) ((-932 . -875) 180649) ((-130 . -684) T) ((-839 . -660) 180555) ((-841 . -571) 180534) ((-501 . -875) T) ((-260 . -1070) 180361) ((-259 . -1070) 180188) ((-128 . -121) 180172) ((-221 . -875) T) ((-936 . -1088) 180137) ((-734 . -102) T) ((-721 . -1089) T) ((-611 . -635) 180118) ((-600 . -635) 180099) ((-549 . -637) 180002) ((-357 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-87 . -632) 179984) ((-936 . -111) 179940) ((-40 . -739) 179885) ((-894 . -1133) T) ((-686 . -635) 179862) ((-667 . -635) 179843) ((-368 . -635) 179780) ((-366 . -635) 179717) ((-358 . -635) 179654) ((-562 . -1133) T) ((-339 . -633) 179615) ((-339 . -632) 179527) ((-275 . -635) 179280) ((-255 . -635) 179065) ((-190 . -1249) T) ((-1264 . -816) 179018) ((-1264 . -821) 178971) ((-260 . -390) 178940) ((-259 . -390) 178909) ((-564 . -875) T) ((-678 . -38) 178879) ((-627 . -34) T) ((-496 . -1144) 178857) ((-489 . -34) T) ((-1145 . -133) 178728) ((-994 . -25) 178539) ((-936 . -635) 178489) ((-899 . -632) 178471) ((-218 . -868) T) ((-994 . -21) 178426) ((-839 . -25) 178259) ((-839 . -21) 178170) ((-1256 . -381) T) ((-642 . -1089) T) ((-1211 . -571) 178149) ((-1203 . -47) 178126) ((-368 . -1081) T) ((-366 . -1081) T) ((-496 . -23) 177978) ((-358 . -1081) T) ((-275 . -1081) T) ((-255 . -1081) T) ((-1157 . -47) 177950) ((-119 . -1089) T) ((-1066 . -670) 177924) ((-988 . -34) T) ((-368 . -240) 177903) ((-368 . -250) T) ((-366 . -240) 177882) ((-366 . -250) T) ((-358 . -240) 177861) ((-358 . -250) T) ((-275 . -338) 177833) ((-255 . -338) 177790) ((-275 . -240) 177769) ((-1187 . -153) 177753) ((-260 . -928) 177685) ((-259 . -928) 177617) ((-1174 . -922) 177538) ((-1114 . -872) T) ((-1266 . -1249) 177516) ((-429 . -1144) T) ((-1242 . -1034) 177482) ((-1086 . -23) T) ((-1056 . -871) T) ((-936 . -1081) T) ((-334 . -670) 177464) ((-723 . -239) T) ((-692 . -236) 177409) ((-1206 . -951) 177388) ((-1200 . -951) 177367) ((-1200 . -844) NIL) ((-1028 . -1083) 177263) ((-997 . -1249) T) ((-936 . -250) T) ((-841 . -376) 177242) ((-218 . -1133) T) ((-394 . -23) T) ((-129 . -1133) 177220) ((-123 . -1133) 177198) ((-936 . -240) T) ((-131 . -34) T) ((-391 . -670) 177163) ((-1028 . -662) 177111) ((-894 . -739) 177098) ((-1329 . -668) 177070) ((-1078 . -153) 177035) ((-1025 . -1249) T) ((-888 . -1249) T) ((-40 . -175) T) ((-716 . -426) 177017) ((-734 . -321) 177004) ((-858 . -670) 176964) ((-852 . -670) 176938) ((-331 . -25) T) ((-331 . -21) T) ((-676 . -298) 176917) ((-594 . -1133) T) ((-560 . -1133) T) ((-509 . -1133) T) ((-1203 . -1249) T) ((-252 . -300) 176894) ((-1157 . -1249) T) ((-879 . -1249) T) ((-325 . -274) 176855) ((-325 . -234) 176816) ((-1255 . -875) T) ((-1203 . -912) NIL) ((-55 . -1133) T) ((-1157 . -912) 176675) ((-130 . -872) T) ((-1203 . -1070) 176555) ((-1157 . -1070) 176438) ((-187 . -632) 176420) ((-879 . -1070) 176316) ((-803 . -298) 176243) ((-841 . -1144) T) ((-1066 . -748) T) ((-1078 . -1008) 176172) ((-616 . -673) 176156) ((-1035 . -922) 176063) ((-1028 . -102) T) ((-841 . -23) T) ((-734 . -1184) 176041) ((-716 . -1089) T) ((-616 . -385) 176025) ((-365 . -466) T) ((-357 . -302) T) ((-1302 . -1133) T) ((-256 . -1133) T) ((-413 . -102) T) ((-301 . -21) T) ((-301 . -25) T) ((-374 . -748) T) ((-732 . -1133) T) ((-721 . -1133) T) ((-374 . -487) T) ((-1242 . -632) 176007) ((-1203 . -390) 175991) ((-1157 . -390) 175975) ((-1056 . -426) 175937) ((-143 . -233) 175919) ((-391 . -818) T) ((-391 . -814) T) ((-894 . -175) T) ((-391 . -748) T) ((-733 . -632) 175901) ((-734 . -38) 175730) ((-1299 . -1298) 175714) ((-365 . -416) T) ((-1299 . -1133) 175664) ((-1223 . -1133) T) ((-594 . -739) 175651) ((-560 . -739) 175638) ((-509 . -739) 175603) ((-1286 . -668) 175493) ((-326 . -649) 175472) ((-858 . -748) T) ((-852 . -748) T) ((-1148 . -1249) T) ((-663 . -1249) T) ((-1111 . -660) 175420) ((-1203 . -928) 175363) ((-1157 . -928) 175347) ((-839 . -236) 175238) ((-674 . -1088) 175222) ((-108 . -660) 175204) ((-496 . -133) 175075) ((-1211 . -1144) T) ((-843 . -1249) T) ((-976 . -47) 175044) ((-642 . -1133) T) ((-674 . -111) 175023) ((-505 . -632) 174989) ((-339 . -300) 174966) ((-400 . -1249) T) ((-336 . -1249) T) ((-495 . -47) 174923) ((-1211 . -23) T) ((-119 . -1133) T) ((-103 . -102) 174873) ((-1312 . -1144) T) ((-563 . -872) T) ((-229 . -1249) T) ((-1086 . -133) T) ((-1056 . -1089) T) ((-1312 . -23) T) ((-1229 . -632) 174855) ((-843 . -1070) 174839) ((-1152 . -845) T) ((-1035 . -746) 174811) ((-1137 . -1133) T) ((-721 . -739) 174776) ((-597 . -632) 174758) ((-400 . -1070) 174742) ((-353 . -1089) T) ((-394 . -133) T) ((-336 . -1070) 174726) ((-1111 . -21) T) ((-1111 . -25) T) ((-1036 . -844) T) ((-229 . -912) 174708) ((-1036 . -951) T) ((-91 . -34) T) ((-1028 . -321) 174673) ((-944 . -951) T) ((-901 . -635) 174654) ((-736 . -670) 174614) ((-501 . -1254) T) ((-703 . -635) 174595) ((-698 . -635) 174576) ((-659 . -670) 174560) ((-221 . -1254) T) ((-421 . -922) 174481) ((-229 . -1070) 174441) ((-40 . -302) T) ((-501 . -571) T) ((-492 . -635) 174422) ((-372 . -25) T) ((-326 . -668) 174077) ((-325 . -668) 173991) ((-372 . -21) T) ((-367 . -25) T) ((-367 . -21) T) ((-221 . -571) T) ((-359 . -25) T) ((-359 . -21) T) ((-331 . -236) 173937) ((-252 . -635) 173914) ((-140 . -635) 173895) ((-139 . -635) 173876) ((-135 . -635) 173857) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1089) T) ((-594 . -175) T) ((-560 . -175) T) ((-509 . -175) T) ((-1094 . -1249) T) ((-976 . -1249) T) ((-735 . -1249) T) ((-661 . -298) 173824) ((-676 . -632) 173806) ((-495 . -1249) T) ((-758 . -759) 173790) ((-346 . -632) 173772) ((-68 . -396) T) ((-68 . -410) T) ((-1129 . -107) 173756) ((-1094 . -912) 173738) ((-976 . -912) 173663) ((-677 . -1144) T) ((-642 . -739) 173650) ((-495 . -912) NIL) ((-1178 . -102) T) ((-1121 . -637) 173634) ((-1094 . -1070) 173616) ((-97 . -632) 173598) ((-491 . -149) T) ((-976 . -1070) 173478) ((-119 . -739) 173423) ((-734 . -930) 173330) ((-677 . -23) T) ((-495 . -1070) 173206) ((-1119 . -633) NIL) ((-1119 . -632) 173188) ((-803 . -633) NIL) ((-803 . -632) 173149) ((-802 . -633) 172783) ((-802 . -632) 172697) ((-1145 . -660) 172603) ((-822 . -875) 172582) ((-475 . -632) 172564) ((-468 . -632) 172546) ((-468 . -633) 172407) ((-1067 . -233) 172353) ((-897 . -940) 172332) ((-128 . -34) T) ((-841 . -133) T) ((-671 . -632) 172314) ((-592 . -102) T) ((-368 . -1318) 172298) ((-366 . -1318) 172282) ((-358 . -1318) 172266) ((-123 . -528) 172199) ((-129 . -528) 172132) ((-526 . -816) T) ((-526 . -821) T) ((-525 . -818) T) ((-103 . -321) 172070) ((-226 . -102) 172020) ((-721 . -175) T) ((-716 . -1133) T) ((-897 . -670) 171936) ((-65 . -398) T) ((-286 . -632) 171918) ((-65 . -410) T) ((-976 . -390) 171902) ((-894 . -302) T) ((-50 . -632) 171884) ((-1152 . -668) 171856) ((-1028 . -38) 171804) ((-626 . -1133) T) ((-621 . -1133) T) ((-595 . -632) 171786) ((-495 . -390) 171770) ((-595 . -633) 171752) ((-532 . -632) 171734) ((-936 . -1318) 171721) ((-896 . -1249) T) ((-723 . -466) T) ((-509 . -528) 171687) ((-1311 . -1249) T) ((-1310 . -1249) T) ((-501 . -376) T) ((-368 . -381) 171666) ((-366 . -381) 171645) ((-358 . -381) 171624) ((-736 . -748) T) ((-221 . -376) T) ((-118 . -466) T) ((-1323 . -1314) 171608) ((-896 . -910) 171585) ((-896 . -912) NIL) ((-994 . -872) 171484) ((-839 . -872) 171435) ((-1257 . -102) T) ((-678 . -680) 171419) ((-1236 . -34) T) ((-174 . -632) 171401) ((-1145 . -25) 171234) ((-1145 . -21) 171145) ((-896 . -1070) 171122) ((-976 . -928) 171103) ((-1268 . -47) 171080) ((-936 . -381) T) ((-607 . -875) T) ((-58 . -673) 171064) ((-530 . -673) 171048) ((-495 . -928) 171025) ((-71 . -455) T) ((-71 . -410) T) ((-510 . -673) 171009) ((-58 . -385) 170993) ((-642 . -175) T) ((-530 . -385) 170977) ((-510 . -385) 170961) ((-561 . -1249) T) 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169678) ((-359 . -236) 169651) ((-177 . -466) T) ((-82 . -455) T) ((-226 . -321) 169589) ((-82 . -410) T) ((-227 . -632) 169571) ((-108 . -236) 169558) ((-221 . -23) T) ((-1324 . -1319) 169537) ((-699 . -1070) 169521) ((-594 . -302) T) ((-560 . -302) T) ((-509 . -302) T) ((-1268 . -1249) T) ((-137 . -484) 169476) ((-880 . -1249) T) ((-678 . -668) 169435) ((-48 . -1133) T) ((-734 . -274) 169419) ((-734 . -234) 169403) ((-896 . -928) NIL) ((-585 . -1249) T) ((-1268 . -912) NIL) ((-914 . -102) T) ((-911 . -102) T) ((-661 . -632) 169385) ((-402 . -1133) T) ((-171 . -390) 169369) ((-171 . -351) 169353) ((-1268 . -1070) 169233) ((-880 . -1070) 169129) ((-1174 . -102) T) ((-1028 . -930) 169052) ((-677 . -133) T) ((-674 . -816) 169031) ((-674 . -821) 169010) ((-119 . -528) 168918) ((-585 . -1070) 168900) ((-305 . -1307) 168870) ((-1200 . -875) NIL) ((-891 . -102) T) ((-986 . -571) 168849) ((-1242 . -1088) 168732) ((-1035 . -1083) 168677) ((-496 . -660) 168583) ((-935 . -1133) T) ((-1056 . -739) 168520) ((-733 . -1088) 168485) ((-1035 . -662) 168430) ((-636 . -102) T) ((-616 . -34) T) ((-1180 . -1249) T) ((-1242 . -111) 168299) ((-488 . -670) 168196) ((-353 . -739) 168141) ((-171 . -928) 168100) ((-721 . -302) T) ((-716 . -175) T) ((-733 . -111) 168056) ((-1329 . -1089) T) ((-1268 . -390) 168040) ((-419 . -1254) 168018) ((-1147 . -632) 168000) ((-325 . -871) NIL) ((-419 . -571) T) ((-229 . -319) T) ((-1264 . -814) 167953) ((-1264 . -818) 167906) ((-1285 . -748) T) ((-1264 . -748) T) ((-48 . -739) 167871) ((-229 . -1052) T) ((-1286 . -426) 167837) ((-1268 . -928) 167780) ((-365 . -1307) 167757) ((-1242 . -635) 167639) ((-740 . -748) T) ((-345 . -632) 167621) ((-534 . -875) 167600) ((-1145 . -236) 167491) ((-114 . -632) 167473) ((-114 . -633) 167455) ((-740 . -487) T) ((-733 . -635) 167405) ((-1323 . -1083) 167389) ((-496 . -25) 167222) ((-129 . -503) 167206) ((-123 . -503) 167190) ((-496 . -21) 167101) ((-1323 . -662) 167071) ((-642 . -302) T) ((-597 . -1088) 167046) ((-450 . -1133) T) ((-1094 . -319) T) ((-119 . -302) T) ((-1135 . -102) T) ((-1035 . -102) T) ((-597 . -111) 167014) ((-1242 . -1081) T) ((-1174 . -321) 166952) ((-1094 . -1052) T) ((-1086 . -25) T) ((-66 . -1249) T) ((-916 . -1249) T) ((-1086 . -21) T) ((-733 . -1081) T) ((-394 . -21) T) ((-394 . -25) T) ((-716 . -528) NIL) ((-1056 . -175) T) ((-733 . -250) T) ((-1094 . -559) T) ((-734 . -668) 166862) ((-520 . -102) T) ((-516 . -102) T) ((-357 . -632) 166844) ((-353 . -175) T) ((-421 . -1083) 166796) ((-407 . -632) 166778) ((-1152 . -871) T) ((-488 . -748) T) ((-916 . -1070) 166746) ((-421 . -662) 166698) ((-108 . -872) T) ((-676 . -1088) 166682) ((-501 . -133) T) ((-1286 . -1089) T) ((-221 . -133) T) ((-1187 . -102) 166632) ((-99 . -1133) T) ((-246 . -875) 166583) ((-252 . -688) 166567) ((-252 . -673) 166551) ((-676 . -111) 166530) ((-597 . -635) 166514) ((-326 . -426) 166498) ((-252 . -385) 166482) ((-1192 . -242) 166429) ((-1028 . -274) 166413) ((-1028 . -234) 166397) ((-74 . -1249) T) ((-48 . -175) T) ((-723 . -401) T) ((-723 . -145) T) ((-1323 . -102) T) ((-1231 . -1249) T) ((-1229 . -635) 166379) ((-1120 . -1249) T) ((-1119 . -1088) 166222) ((-1107 . -1249) T) ((-275 . -940) 166201) ((-255 . -940) 166180) ((-803 . -1088) 166003) ((-802 . -1088) 165846) ((-627 . -1249) T) ((-1197 . -632) 165828) ((-1119 . -111) 165657) ((-1078 . -102) T) ((-489 . -1249) T) ((-475 . -1088) 165628) ((-468 . -1088) 165471) ((-686 . -670) 165455) ((-896 . -319) T) ((-803 . -111) 165264) ((-802 . -111) 165093) ((-368 . -670) 165045) ((-366 . -670) 164997) ((-358 . -670) 164949) ((-275 . -670) 164838) ((-255 . -670) 164727) ((-1191 . -872) T) ((-1120 . -1070) 164711) ((-1107 . -1070) 164688) ((-1036 . -875) T) ((-1032 . -34) T) ((-475 . -111) 164649) ((-468 . -111) 164478) ((-1003 . -875) T) ((-996 . -632) 164460) ((-988 . -1249) T) ((-986 . -1144) T) ((-128 . -1042) 164444) ((-873 . -1249) T) ((-896 . -1052) NIL) ((-757 . -1144) T) ((-737 . -1144) T) ((-676 . -635) 164362) ((-1299 . -503) 164346) ((-1217 . -1249) T) ((-1216 . -1249) T) ((-1174 . -38) 164306) ((-986 . -23) T) ((-936 . -670) 164271) ((-890 . -1133) T) ((-866 . -102) T) ((-841 . -21) T) ((-652 . -1083) 164255) ((-620 . -1083) 164239) ((-841 . -25) T) ((-757 . -23) T) ((-737 . -23) T) ((-652 . -662) 164223) ((-110 . -684) T) ((-620 . -662) 164207) ((-595 . -1088) 164172) ((-532 . -1088) 164117) ((-231 . -57) 164075) ((-467 . -23) T) ((-421 . -102) T) ((-1215 . -1249) T) ((-270 . -102) T) ((-110 . -113) T) ((-716 . -302) T) ((-891 . -38) 164045) ((-1119 . -635) 163781) ((-595 . -111) 163737) ((-532 . -111) 163666) ((-419 . -1144) T) ((-326 . -1089) 163556) ((-325 . -1089) T) ((-132 . -1249) T) ((-131 . -1249) T) ((-803 . -635) 163304) ((-802 . -635) 163070) ((-676 . -1081) T) ((-1329 . -1133) T) ((-468 . -635) 162855) ((-171 . -319) 162786) ((-419 . -23) T) ((-40 . -632) 162768) ((-40 . -633) 162752) ((-108 . -1023) 162734) ((-118 . -895) 162718) ((-671 . -635) 162702) ((-48 . -528) 162668) ((-1236 . -1042) 162652) ((-1214 . -632) 162619) ((-1221 . -34) T) ((-984 . -632) 162585) ((-949 . -632) 162567) ((-1145 . -872) 162518) ((-793 . -632) 162500) ((-694 . -632) 162482) ((-531 . -1249) T) ((-1268 . -319) 162461) ((-1187 . -321) 162399) ((-1173 . -34) T) ((-493 . -34) T) ((-1124 . -1249) T) ((-491 . -466) T) ((-1066 . -1249) T) ((-1119 . -1081) T) ((-50 . -635) 162368) ((-803 . -1081) T) ((-802 . -1081) T) ((-669 . -242) 162352) ((-651 . -242) 162298) ((-1211 . -21) T) ((-595 . -635) 162248) ((-532 . -635) 162178) ((-496 . -236) 162069) ((-1211 . -25) T) ((-1119 . -338) 162030) ((-468 . -1081) T) ((-1119 . -240) 162009) ((-803 . -338) 161986) ((-803 . -240) T) ((-802 . -338) 161958) ((-753 . -1254) 161937) ((-533 . -34) T) ((-339 . -673) 161921) ((-530 . -34) T) ((-58 . -34) T) ((-511 . -34) T) ((-510 . -34) T) ((-468 . -338) 161900) ((-339 . -385) 161884) ((-374 . -1249) T) ((-334 . -1249) T) ((-1035 . -1184) NIL) ((-753 . -571) 161815) ((-652 . -102) T) ((-620 . -102) T) ((-368 . -748) T) ((-366 . -748) T) ((-358 . -748) T) ((-275 . -748) T) ((-255 . -748) T) ((-391 . -1249) T) ((-1312 . -21) T) ((-1078 . -321) 161723) ((-1312 . -25) T) ((-931 . -1133) 161701) ((-842 . -236) 161688) ((-50 . -1081) T) ((-1207 . -571) 161667) ((-1206 . -1254) 161646) ((-1206 . -571) 161597) ((-1200 . -1254) 161576) ((-1200 . -571) 161527) ((-1056 . -302) T) ((-595 . -1081) T) ((-532 . -1081) T) ((-1035 . -38) 161472) ((-374 . -1070) 161456) ((-334 . -1070) 161440) ((-1028 . -668) 161363) ((-391 . -912) 161345) ((-858 . -1249) T) ((-852 . -1249) T) ((-849 . -1249) T) ((-822 . -1144) T) ((-936 . -748) T) ((-595 . -250) T) ((-595 . -240) T) ((-532 . -240) T) ((-532 . -250) T) ((-1158 . -571) 161324) ((-353 . -302) T) ((-669 . -717) 161308) ((-391 . -1070) 161268) ((-305 . -1083) 161189) ((-352 . -922) 161168) ((-1152 . -1089) T) ((-103 . -127) 161152) ((-305 . -662) 161094) ((-822 . -23) T) ((-1321 . -1319) 161070) ((-1320 . -1319) 161049) ((-1299 . -298) 161001) ((-1286 . -1133) T) ((-421 . -321) 160966) ((-1174 . -930) 160889) ((-894 . -632) 160871) ((-858 . -1070) 160840) ((-661 . -1088) 160824) ((-206 . -809) T) ((-205 . -809) T) ((-204 . -809) T) ((-203 . -809) T) ((-202 . -809) T) ((-201 . -809) T) ((-200 . -809) T) ((-199 . -809) T) ((-198 . -809) T) ((-197 . -809) T) ((-562 . -632) 160806) ((-509 . -1034) T) ((-285 . -863) T) ((-284 . -863) T) ((-283 . -863) T) ((-282 . -863) T) ((-48 . -302) T) ((-281 . -863) T) ((-280 . -863) T) ((-279 . -863) T) ((-196 . -809) T) ((-661 . -111) 160785) ((-630 . -872) T) ((-678 . -426) 160769) ((-692 . -239) 160720) ((-227 . -635) 160682) ((-110 . -872) T) ((-677 . -21) T) ((-677 . -25) T) ((-1323 . -38) 160652) ((-119 . -298) 160603) ((-1299 . -19) 160587) ((-1259 . -875) NIL) ((-1299 . -618) 160564) ((-1313 . -1133) T) ((-365 . -1083) 160509) ((-1109 . -1133) T) ((-1018 . -1133) T) ((-986 . -133) T) ((-841 . -236) 160496) ((-758 . -1133) T) ((-365 . -662) 160441) ((-757 . -133) T) ((-737 . -133) T) ((-526 . -817) T) ((-526 . -818) T) ((-467 . -133) T) ((-421 . -1184) 160419) ((-227 . -1081) T) ((-305 . -102) 160201) ((-143 . -1133) T) ((-721 . -1034) T) ((-1137 . -298) 160157) ((-91 . -1249) T) ((-218 . -632) 160139) ((-129 . -632) 160071) ((-123 . -632) 160003) ((-1329 . -175) T) ((-1206 . -376) 159982) ((-1200 . -376) 159961) ((-326 . -1133) T) ((-419 . -133) T) ((-325 . -1133) T) ((-421 . -38) 159913) ((-1165 . -102) T) ((-1286 . -739) 159805) ((-1167 . -1295) T) ((-1128 . -1249) T) ((-1123 . -1249) T) ((-678 . -1089) T) ((-1105 . -1249) T) ((-1098 . -1249) T) ((-1068 . -1249) T) ((-1051 . -1249) T) ((-331 . -147) 159784) ((-331 . -149) 159763) ((-141 . -1133) T) ((-137 . -1133) T) ((-115 . -1133) T) ((-883 . -102) T) ((-645 . -1249) T) ((-497 . -1249) T) ((-594 . -632) 159745) ((-560 . -633) 159644) ((-560 . -632) 159626) ((-509 . -632) 159608) ((-509 . -633) 159553) ((-499 . -23) T) ((-222 . -1249) T) ((-496 . -872) 159504) ((-501 . -660) 159486) ((-995 . -632) 159468) ((-1035 . -930) 159377) ((-221 . -660) 159359) ((-229 . -418) T) ((-674 . -670) 159343) ((-55 . -632) 159325) ((-1203 . -951) 159304) ((-753 . -1144) T) ((-657 . -102) T) ((-529 . -1249) T) ((-525 . -1249) T) ((-522 . -1249) T) ((-365 . -102) T) ((-1250 . -1115) T) ((-1152 . -868) T) ((-842 . -872) T) ((-753 . -23) T) ((-357 . -1088) 159249) ((-1180 . -107) 159233) ((-1302 . -632) 159215) ((-1207 . -23) T) ((-1207 . -1144) T) ((-1206 . -1144) T) ((-659 . -1249) T) ((-1206 . -23) T) ((-1200 . -1144) T) ((-1200 . -23) T) ((-1174 . -274) 159199) ((-529 . -1070) 159183) ((-1174 . -234) 159167) ((-1158 . -1144) T) ((-357 . -111) 159096) ((-1036 . -1254) T) ((-128 . -1249) T) ((-944 . -1254) T) ((-1158 . -23) T) ((-1108 . -1133) T) ((-716 . -298) NIL) ((-736 . -1249) T) ((-1036 . -571) T) ((-944 . -571) T) ((-839 . -239) 158993) ((-625 . -684) T) ((-624 . -684) T) ((-257 . -1249) T) ((-186 . -1249) T) ((-163 . -1249) T) ((-159 . -1249) T) ((-256 . -632) 158975) ((-622 . -684) T) ((-822 . -133) T) ((-732 . -632) 158957) ((-326 . -739) 158867) ((-325 . -739) 158796) ((-721 . -632) 158778) ((-721 . -633) 158723) ((-421 . -414) 158707) ((-452 . -1133) T) ((-501 . -25) T) ((-501 . -21) T) ((-1152 . -1133) T) ((-221 . -25) T) ((-221 . -21) T) ((-734 . -426) 158691) ((-736 . -1070) 158660) ((-1299 . -632) 158572) ((-1299 . -633) 158533) ((-1286 . -175) T) ((-1223 . -632) 158515) ((-252 . -34) T) ((-357 . -635) 158445) ((-407 . -635) 158427) ((-957 . -1006) T) ((-1236 . -1249) T) ((-674 . -814) 158406) ((-674 . -818) 158385) ((-412 . -410) T) ((-537 . -102) 158335) ((-1256 . -1249) T) ((-1067 . -1133) T) ((-421 . -930) 158258) ((-226 . -1027) 158242) ((-862 . -1249) T) ((-518 . -102) T) ((-642 . -632) 158224) ((-45 . -872) NIL) ((-642 . -633) 158201) ((-1067 . -629) 158176) ((-931 . -528) 158109) ((-331 . -239) 158061) ((-357 . -1081) T) ((-119 . -633) NIL) ((-119 . -632) 158043) ((-897 . -1249) T) ((-692 . -432) 158027) ((-692 . -1155) 157972) ((-514 . -153) 157954) ((-357 . -240) T) 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156858) ((-391 . -1052) T) ((-108 . -149) T) ((-108 . -147) NIL) ((-45 . -242) 156808) ((-678 . -1133) T) ((-627 . -107) 156755) ((-499 . -133) T) ((-489 . -107) 156705) ((-246 . -1144) 156683) ((-31 . -1249) T) ((-897 . -390) 156667) ((-897 . -351) 156651) ((-246 . -23) 156503) ((-40 . -635) 156433) ((-1313 . -528) 156366) ((-1094 . -951) T) ((-1094 . -844) T) ((-595 . -381) T) ((-532 . -381) T) ((-1289 . -571) 156345) ((-1285 . -1249) T) ((-1280 . -1254) 156324) ((-1280 . -571) 156275) ((-1264 . -1249) T) ((-365 . -1184) T) ((-339 . -34) T) ((-44 . -432) 156259) ((-1214 . -635) 156195) ((-898 . -1249) T) ((-404 . -766) 156179) ((-1264 . -912) 156052) ((-1264 . -910) 156022) ((-1174 . -668) 155981) ((-753 . -133) T) ((-694 . -635) 155965) ((-1259 . -1254) 155944) ((-1259 . -571) 155895) ((-1207 . -133) T) ((-1206 . -133) T) ((-1200 . -133) T) ((-1158 . -133) T) ((-324 . -1115) T) ((-1056 . -1034) T) ((-758 . -528) 155828) ((-1036 . -23) T) ((-1036 . -1144) T) ((-919 . -1133) T) ((-146 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. -133) T) ((-1135 . -1133) T) ((-1035 . -1133) T) ((-63 . -632) 142001) ((-1111 . -922) 141870) ((-1056 . -816) T) ((-1056 . -821) T) ((-1289 . -25) T) ((-1289 . -21) T) ((-1280 . -21) T) ((-1280 . -25) T) ((-894 . -670) 141857) ((-1259 . -21) T) ((-1259 . -25) T) ((-1059 . -153) 141841) ((-1036 . -236) 141828) ((-897 . -844) 141807) ((-897 . -951) T) ((-734 . -298) 141734) ((-610 . -21) T) ((-352 . -668) 141693) ((-108 . -922) NIL) ((-610 . -25) T) ((-609 . -21) T) ((-177 . -668) 141610) ((-40 . -748) T) ((-226 . -528) 141543) ((-609 . -25) T) ((-490 . -153) 141527) ((-477 . -153) 141511) ((-187 . -1249) T) ((-949 . -818) T) ((-949 . -748) T) ((-793 . -817) T) ((-793 . -818) T) ((-520 . -1133) T) ((-516 . -1133) T) ((-793 . -748) T) ((-229 . -376) T) ((-1321 . -1083) 141495) ((-1320 . -1083) 141479) ((-1321 . -662) 141449) ((-1187 . -1133) 141427) ((-896 . -1254) T) ((-1320 . -662) 141397) ((-1120 . -875) T) ((-678 . -632) 141379) ((-896 . -571) T) ((-716 . -381) NIL) ((-44 . -1083) 141363) ((-1329 . -635) 141345) ((-1323 . -1133) T) ((-692 . -102) T) ((-372 . -1307) 141329) ((-367 . -1307) 141313) ((-44 . -662) 141297) ((-359 . -1307) 141281) ((-563 . -102) T) ((-1242 . -1249) T) ((-534 . -872) 141260) ((-733 . -1249) T) ((-988 . -875) 141239) ((-873 . -875) T) ((-501 . -239) T) ((-221 . -239) T) ((-1078 . -1133) T) ((-841 . -466) 141218) ((-154 . -1083) 141202) ((-1078 . -1103) 141131) ((-1059 . -1008) 141100) ((-843 . -1144) T) ((-1035 . -739) 141045) ((-154 . -662) 141029) ((-400 . -1144) T) ((-490 . -1008) 140998) ((-477 . -1008) 140967) ((-1216 . -875) T) ((-110 . -153) 140949) ((-73 . -632) 140931) ((-919 . -632) 140913) ((-1215 . -875) T) ((-1111 . -746) 140892) ((-1329 . -1081) T) ((-840 . -660) 140840) ((-305 . -1089) 140782) ((-171 . -1254) 140687) ((-229 . -1144) T) ((-336 . -23) T) ((-1200 . -1023) 140639) ((-1286 . -1088) 140544) ((-866 . -1133) T) ((-131 . -875) T) ((-1158 . -762) 140523) ((-1285 . -951) 140502) ((-1264 . -951) 140481) ((-894 . 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137321) ((-1119 . -1249) T) ((-1067 . -300) 137296) ((-594 . -748) T) ((-560 . -818) T) ((-171 . -376) 137247) ((-560 . -814) T) ((-560 . -748) T) ((-509 . -748) T) ((-803 . -1249) T) ((-802 . -1249) T) ((-1178 . -503) 137231) ((-475 . -1249) T) ((-468 . -1249) T) ((-1321 . -1322) 137207) ((-1119 . -912) NIL) ((-896 . -1144) T) ((-119 . -940) NIL) ((-1320 . -1322) 137186) ((-671 . -1249) T) ((-803 . -912) NIL) ((-802 . -912) 137045) ((-1315 . -25) T) ((-1315 . -21) T) ((-1247 . -102) 137023) ((-1138 . -410) T) ((-642 . -670) 137010) ((-468 . -912) NIL) ((-697 . -102) 136960) ((-1119 . -1070) 136787) ((-896 . -23) T) ((-803 . -1070) 136646) ((-802 . -1070) 136503) ((-119 . -670) 136448) ((-468 . -1070) 136324) ((-286 . -1249) T) ((-326 . -635) 135888) ((-325 . -635) 135771) ((-50 . -1249) T) ((-404 . -668) 135740) ((-671 . -1070) 135724) ((-646 . -102) T) ((-595 . -1249) T) ((-532 . -1249) T) ((-226 . -503) 135708) ((-1299 . -34) T) ((-638 . -668) 135667) ((-301 . -1083) 135654) ((-137 . -635) 135638) ((-301 . -662) 135625) ((-652 . -739) 135609) ((-620 . -739) 135593) ((-692 . -38) 135553) ((-331 . -102) T) ((-1152 . -1088) 135540) ((-86 . -632) 135522) ((-50 . -1070) 135506) ((-1119 . -390) 135490) ((-803 . -390) 135474) ((-721 . -748) T) ((-721 . -818) T) ((-721 . -814) T) ((-60 . -57) 135436) ((-595 . -1070) 135423) ((-532 . -1070) 135400) ((-174 . -1249) T) ((-336 . -133) T) ((-326 . -1081) 135290) ((-325 . -1081) T) ((-171 . -1144) T) ((-802 . -390) 135274) ((-45 . -153) 135224) ((-1036 . -1023) 135206) ((-468 . -390) 135190) ((-421 . -175) T) ((-326 . -250) 135169) ((-325 . -250) T) ((-325 . -240) NIL) ((-305 . -1133) 134951) ((-229 . -133) T) ((-1152 . -111) 134936) ((-171 . -23) T) ((-822 . -149) 134915) ((-822 . -147) 134894) ((-260 . -660) 134800) ((-259 . -660) 134706) ((-331 . -296) 134672) ((-1187 . -528) 134605) ((-491 . -668) 134555) ((-657 . -868) T) ((-496 . -922) 134422) ((-1165 . -1133) T) ((-229 . -1092) T) ((-839 . -321) 134360) ((-1119 . -928) 134295) ((-803 . -928) 134238) ((-802 . -928) 134222) ((-1321 . -38) 134192) ((-1320 . -38) 134162) ((-1268 . -1144) T) ((-880 . -1144) T) ((-468 . -928) 134139) ((-883 . -1133) T) ((-1268 . -23) T) ((-1152 . -635) 134111) ((-1094 . -133) T) ((-880 . -23) T) ((-585 . -1144) T) ((-642 . -748) T) ((-525 . -875) T) ((-368 . -951) T) ((-366 . -951) T) ((-301 . -102) T) ((-358 . -951) T) ((-1002 . -1115) T) ((-976 . -133) T) ((-840 . -236) 134056) ((-119 . -818) NIL) ((-119 . -814) NIL) ((-119 . -748) T) ((-1078 . -528) 133957) ((-716 . -940) NIL) ((-585 . -23) T) ((-495 . -133) T) ((-419 . -239) 133908) ((-697 . -321) 133846) ((-227 . -1249) T) ((-657 . -1133) T) ((-652 . -783) T) ((-620 . -783) T) ((-1259 . -872) NIL) ((-1111 . -1083) 133756) ((-1035 . -302) T) ((-716 . -670) 133706) ((-260 . -25) T) ((-365 . -1133) T) ((-260 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-154 . -38) 133690) ((-2 . -102) T) ((-936 . -951) T) ((-1111 . -662) 133558) ((-496 . -1307) 133528) ((-1152 . -1081) T) ((-733 . -319) T) ((-723 . -1089) T) ((-372 . -1083) 133480) ((-367 . -1083) 133432) ((-359 . -1083) 133384) ((-372 . -662) 133336) ((-227 . -1070) 133313) ((-367 . -662) 133265) ((-108 . -1083) 133215) ((-359 . -662) 133167) ((-305 . -739) 133109) ((-661 . -1249) T) ((-501 . -466) T) ((-421 . -528) 133021) ((-108 . -662) 132971) ((-221 . -466) T) ((-1152 . -240) T) ((-307 . -153) 132921) ((-1028 . -633) 132882) ((-1028 . -632) 132864) ((-1021 . -632) 132846) ((-118 . -1089) T) ((-678 . -1088) 132830) ((-229 . -507) T) ((-413 . -632) 132812) ((-413 . -633) 132789) ((-1086 . -1307) 132759) ((-678 . -111) 132738) ((-692 . -930) 132661) ((-1174 . -503) 132645) ((-1324 . -668) 132604) ((-395 . -668) 132573) ((-64 . -455) T) ((-64 . -410) T) ((-1192 . -102) T) ((-896 . -133) T) ((-498 . -102) 132523) ((-1147 . -1249) T) ((-1256 . -875) T) ((-1329 . -381) T) ((-1111 . -102) T) ((-1093 . -102) T) ((-365 . -739) 132468) ((-897 . -875) 132419) ((-753 . -149) 132398) ((-753 . -147) 132377) 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-102) T) ((-204 . -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) ((-734 . -111) 129717) ((-353 . -748) T) ((-692 . -274) 129701) ((-692 . -234) 129685) ((-595 . -319) T) ((-532 . -319) T) ((-305 . -528) 129634) ((-1197 . -1249) T) ((-108 . -321) NIL) ((-72 . -410) T) ((-1145 . -102) 129366) ((-856 . -426) 129350) ((-1152 . -821) T) ((-1152 . -816) T) ((-723 . -1133) T) ((-592 . -632) 129332) ((-391 . -376) T) ((-171 . -507) 129310) ((-226 . -632) 129242) ((-136 . -1133) T) ((-118 . -1133) T) ((-996 . -1249) T) ((-48 . -748) T) ((-1078 . -503) 129207) ((-143 . -440) 129189) ((-143 . -381) T) ((-1059 . -102) T) ((-524 . -523) 129168) ((-734 . -635) 128924) ((-1257 . -632) 128906) ((-1214 . -1249) T) ((-1214 . -1070) 128842) ((-1207 . -239) 128801) ((-490 . -102) T) ((-477 . -102) T) ((-1206 . -239) 128753) ((-1200 . -239) 128576) ((-1066 . -1144) T) ((-331 . -930) 128482) ((-1209 . -875) T) ((-1207 . -35) 128448) ((-1207 . -95) 128414) ((-1207 . -1238) 128380) ((-1207 . -1235) 128346) ((-1206 . -1235) 128312) ((-1206 . -1238) 128278) ((-1206 . -95) 128244) ((-1206 . -35) 128210) ((-1200 . -1235) 128176) ((-1200 . -1238) 128142) ((-1191 . -321) NIL) ((-89 . -411) T) ((-89 . -410) T) ((-1111 . -1184) 128121) ((-40 . -1249) T) ((-1200 . -95) 128087) ((-1066 . -23) T) ((-1200 . -35) 128053) ((-585 . -507) T) ((-1158 . -35) 128019) ((-1158 . -95) 127985) ((-1158 . -1238) 127951) ((-1158 . -1235) 127917) ((-374 . -1144) T) ((-372 . -1184) 127896) ((-367 . -1184) 127875) ((-359 . -1184) 127854) ((-1135 . -298) 127810) ((-984 . -1249) T) ((-949 . -1249) T) ((-108 . -1184) T) ((-856 . -1089) 127789) ((-793 . -1249) T) ((-669 . -321) 127727) ((-651 . -321) 127578) ((-694 . -1249) T) ((-734 . -1081) T) ((-1094 . -660) 127560) ((-1111 . -38) 127428) ((-976 . -660) 127376) ((-1036 . -149) T) ((-1036 . -147) NIL) ((-391 . -1144) T) ((-336 . -25) T) ((-334 . -23) T) ((-973 . -872) 127355) ((-734 . -338) 127332) ((-495 . -660) 127280) ((-40 . -1070) 127168) ((-734 . -240) T) ((-723 . -739) 127155) ((-352 . -1133) T) ((-177 . -1133) T) ((-343 . -872) T) ((-419 . -466) 127105) ((-391 . -23) T) ((-372 . -38) 127070) ((-367 . -38) 127035) ((-359 . -38) 127000) ((-80 . -455) T) ((-80 . -410) T) ((-229 . -25) T) ((-229 . -21) T) ((-858 . -1144) T) ((-108 . -38) 126950) ((-852 . -1144) T) ((-795 . -1133) T) ((-118 . -739) 126937) ((-694 . -1070) 126921) ((-630 . -102) T) ((-858 . -23) T) ((-852 . -23) T) ((-1187 . -298) 126873) ((-1145 . -321) 126811) ((-496 . -1083) 126712) ((-1129 . -242) 126696) ((-61 . -411) T) ((-61 . -410) T) ((-1185 . -102) T) ((-110 . -102) T) ((-496 . -662) 126618) ((-40 . -390) 126595) ((-96 . -102) T) ((-677 . -877) 126579) ((-1203 . -236) 126566) ((-1167 . -1115) T) ((-1094 . -21) T) ((-1094 . -25) T) ((-1086 . -1083) 126550) ((-839 . -274) 126519) ((-839 . -234) 126488) ((-976 . -25) T) ((-976 . -21) T) ((-1152 . -381) T) ((-1086 . -662) 126430) ((-638 . -1089) T) ((-1059 . -321) 126368) ((-914 . -632) 126350) ((-692 . -668) 126309) ((-495 . -25) T) ((-495 . -21) T) ((-394 . -1083) 126293) ((-911 . -632) 126275) ((-894 . -1249) T) ((-537 . -528) 126208) ((-260 . -872) 126159) ((-259 . -872) 126110) ((-394 . -662) 126080) ((-896 . -660) 126057) ((-490 . -321) 125995) ((-562 . -1249) T) ((-477 . -321) 125933) ((-365 . -302) T) ((-1187 . -1288) 125917) ((-1174 . -632) 125879) ((-1174 . -633) 125840) ((-1172 . -102) T) ((-1028 . -1088) 125736) ((-40 . -928) 125688) ((-1187 . -618) 125665) ((-1329 . -670) 125652) ((-1095 . -153) 125598) ((-501 . -922) NIL) ((-891 . -504) 125575) ((-1028 . -111) 125457) ((-897 . -1254) T) ((-221 . -922) NIL) ((-352 . -739) 125441) ((-891 . -632) 125403) ((-177 . -739) 125335) ((-897 . -571) T) ((-421 . -298) 125293) ((-246 . -239) 125190) ((-108 . -414) 125172) ((-85 . -398) T) ((-85 . -410) T) ((-723 . -175) T) ((-636 . -632) 125154) ((-99 . -748) T) ((-496 . -102) 124886) ((-99 . -487) T) ((-118 . -175) T) ((-1321 . -668) 124845) ((-1320 . -668) 124804) ((-171 . -660) 124752) ((-1111 . -930) 124623) ((-1086 . -102) T) ((-1028 . -635) 124513) ((-896 . -25) T) ((-839 . -245) 124492) ((-896 . -21) T) ((-842 . -102) T) ((-1036 . -239) T) ((-44 . -668) 124435) ((-429 . -102) T) ((-394 . -102) T) ((-110 . -321) NIL) ((-231 . -102) 124385) ((-218 . -1249) T) ((-129 . -1249) T) ((-123 . -1249) T) ((-108 . -930) NIL) ((-841 . -1083) 124336) ((-58 . -875) 124315) ((-841 . -662) 124257) ((-530 . -875) 124236) ((-510 . -875) 124215) ((-1066 . -133) T) ((-692 . -380) 124199) ((-154 . -668) 124158) ((-1329 . -748) T) ((-652 . -298) 124116) ((-620 . -298) 124074) ((-1289 . -147) 124053) ((-1268 . -660) 124001) ((-1028 . -1081) T) ((-1135 . -632) 123983) ((-1035 . -632) 123965) ((-594 . -1249) T) ((-560 . -1249) T) ((-509 . -1249) T) ((-529 . -23) T) ((-525 . -23) T) ((-357 . -319) T) ((-522 . -23) T) ((-334 . -133) T) ((-3 . -1133) T) ((-1035 . -633) 123949) ((-1028 . -250) 123928) ((-1028 . -240) 123907) ((-1289 . -149) 123886) ((-1285 . -1254) 123865) ((-856 . -1133) T) ((-1280 . -149) 123844) ((-1280 . -147) 123823) ((-1264 . -1254) 123802) ((-1259 . -147) 123709) ((-1259 . -149) 123616) ((-391 . -133) T) ((-229 . -236) 123603) ((-177 . -175) T) ((-560 . -912) 123585) ((0 . -1133) T) ((-171 . -21) T) ((-171 . -25) T) ((-55 . -1249) T) ((-49 . -1133) T) ((-1286 . -670) 123490) ((-1285 . -571) 123441) ((-1264 . -571) 123392) ((-736 . -1144) T) ((-659 . -23) T) ((-560 . -1070) 123374) ((-609 . -149) 123353) ((-609 . -147) 123332) ((-509 . -1070) 123275) ((-1167 . -1169) T) ((-88 . -398) T) ((-88 . -410) T) ((-897 . -376) T) ((-858 . -133) T) ((-852 . -133) T) ((-994 . -668) 123219) ((-736 . -23) T) ((-520 . -632) 123169) ((-516 . -632) 123151) ((-839 . -668) 122930) ((-1324 . -1089) T) ((-391 . -1092) T) ((-1058 . -1133) 122908) ((-55 . -1070) 122890) ((-931 . -34) T) ((-496 . -321) 122828) ((-606 . -102) T) ((-1187 . -633) 122789) ((-1187 . -632) 122721) ((-1211 . -1083) 122604) ((-45 . -102) T) ((-841 . -102) T) ((-1211 . -662) 122501) ((-1302 . -1249) T) ((-1268 . -25) T) ((-1268 . -21) T) ((-1094 . -236) 122488) ((-880 . -25) T) ((-526 . -875) T) ((-256 . -1249) T) ((-44 . -380) 122472) ((-880 . -21) T) ((-753 . -466) 122423) ((-1323 . -632) 122405) ((-732 . -1249) T) ((-721 . -1249) T) ((-1312 . -1083) 122375) ((-1086 . -321) 122313) ((-693 . -1115) T) ((-619 . -1115) T) ((-404 . -1133) T) ((-585 . -25) T) ((-585 . -21) T) ((-183 . -1115) T) ((-164 . -1115) T) ((-158 . -1115) T) ((-156 . -1115) T) ((-1312 . -662) 122283) ((-638 . -1133) T) ((-721 . -912) 122265) ((-1299 . -1249) T) ((-231 . -321) 122203) ((-146 . -381) T) ((-1223 . -1249) T) ((-1078 . -633) 122145) ((-1078 . -632) 122088) ((-325 . -940) NIL) ((-1258 . -868) T) ((-1145 . -930) 121957) ((-721 . -1070) 121902) ((-733 . -951) T) ((-488 . -1254) 121881) ((-1206 . -466) 121860) ((-1200 . -466) 121839) ((-342 . -102) T) ((-897 . -1144) T) ((-331 . -668) 121721) ((-326 . -670) 121450) ((-325 . -670) 121379) ((-488 . -571) 121330) ((-352 . -528) 121296) ((-565 . -153) 121246) ((-40 . -319) T) ((-866 . -632) 121228) ((-723 . -302) T) ((-897 . -23) T) ((-391 . -507) T) ((-1111 . -274) 121198) ((-1111 . -234) 121168) ((-524 . -102) T) ((-421 . -633) 120975) ((-421 . -632) 120957) ((-270 . -632) 120939) ((-118 . -302) T) ((-1286 . -748) T) ((-642 . -1249) T) ((-1325 . -1133) T) ((-1285 . -376) 120918) ((-1264 . -376) 120897) ((-1313 . -34) T) ((-1258 . -1133) T) ((-119 . -1249) T) ((-108 . -274) 120879) ((-108 . -234) 120861) ((-1211 . -102) T) ((-491 . -1133) T) ((-537 . -503) 120845) ((-758 . -34) T) ((-677 . -1083) 120829) ((-677 . -662) 120799) ((-896 . -236) NIL) ((-143 . -34) T) ((-119 . -910) 120776) ((-119 . -912) NIL) ((-1312 . -102) T) ((-1289 . -239) 120735) ((-642 . -1070) 120618) ((-625 . -102) T) ((-624 . -102) T) ((-622 . -102) T) ((-663 . -872) 120597) ((-1280 . -239) 120549) ((-1259 . -239) 120372) ((-307 . -102) T) ((-734 . -381) 120351) 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. -319) T) ((-560 . -319) T) ((-509 . -319) T) ((-1324 . -739) 116675) ((-716 . -390) 116657) ((-716 . -351) 116639) ((-491 . -175) T) ((-395 . -739) 116609) ((-891 . -635) 116544) ((-896 . -872) NIL) ((-560 . -1052) T) ((-509 . -1052) T) ((-1165 . -632) 116526) ((-1145 . -245) 116505) ((-217 . -102) T) ((-1183 . -102) T) ((-71 . -632) 116487) ((-1056 . -1249) T) ((-1174 . -1081) T) ((-1211 . -38) 116384) ((-883 . -632) 116366) ((-560 . -559) T) ((-692 . -1089) T) ((-753 . -980) 116319) ((-1174 . -240) 116298) ((-353 . -1249) T) ((-1114 . -1133) T) ((-1066 . -25) T) ((-1066 . -21) T) ((-1035 . -1088) 116243) ((-339 . -875) 116222) ((-932 . -102) T) ((-891 . -1081) T) ((-716 . -928) NIL) ((-368 . -341) 116206) ((-368 . -376) T) ((-366 . -341) 116190) ((-366 . -376) T) ((-358 . -341) 116174) ((-358 . -376) T) ((-501 . -102) T) ((-1312 . -38) 116144) ((-561 . -872) T) ((-537 . -708) 116094) ((-221 . -102) T) ((-1056 . -1070) 115974) ((-1035 . -111) 115903) ((-657 . -632) 115885) ((-1207 . 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. |RecordCategory|) T) ((-1145 . -1089) 105375) ((-856 . -632) 105357) ((-1094 . -239) T) ((-594 . -951) T) ((-560 . -844) T) ((-560 . -951) T) ((-509 . -951) T) ((-137 . -1070) 105341) ((-229 . -95) T) ((-171 . -149) 105320) ((-76 . -455) T) ((0 . -632) 105302) ((-76 . -410) T) ((-171 . -147) 105253) ((-229 . -35) T) ((-49 . -632) 105235) ((-491 . -1089) T) ((-501 . -274) 105217) ((-501 . -234) 105199) ((-498 . -1000) 105183) ((-221 . -274) 105165) ((-221 . -234) 105147) ((-81 . -455) T) ((-81 . -410) T) ((-1178 . -34) T) ((-753 . -102) T) ((-677 . -668) 105106) ((-1058 . -632) 105073) ((-514 . -298) 105023) ((-326 . -390) 104992) ((-325 . -390) 104953) ((-325 . -351) 104914) ((-1117 . -632) 104896) ((-840 . -980) 104843) ((-674 . -133) T) ((-1268 . -147) 104822) ((-1268 . -149) 104801) ((-1207 . -102) T) ((-1206 . -102) T) ((-1200 . -102) T) ((-1192 . -1133) T) ((-1158 . -102) T) ((-1108 . -1249) T) ((-226 . -34) T) ((-301 . -739) 104788) ((-1289 . -1292) 104772) ((-1192 . -629) 104748) ((-607 . -321) NIL) ((-1289 . -1278) 104725) ((-1183 . -233) 104675) ((-498 . -1133) 104653) ((-452 . -1249) T) ((-404 . -632) 104635) ((-525 . -872) T) ((-1152 . -1249) T) ((-1280 . -1284) 104596) ((-1280 . -1278) 104566) ((-1280 . -1282) 104550) ((-1259 . -1263) 104511) ((-1259 . -1278) 104488) ((-1259 . -1261) 104472) ((-1207 . -296) 104438) ((-638 . -632) 104420) ((-1206 . -296) 104386) ((-721 . -951) T) ((-1200 . -296) 104352) ((-1158 . -296) 104318) ((-1152 . -912) 104300) ((-1111 . -1133) T) ((-1093 . -1133) T) ((-48 . -310) T) ((-326 . -928) 104266) ((-325 . -928) NIL) ((-1093 . -1100) 104245) ((-822 . -38) 104229) ((-275 . -660) 104177) ((-114 . -875) T) ((-255 . -660) 104125) ((-723 . -1088) 104112) ((-609 . -1278) 104089) ((-1152 . -1070) 104071) ((-331 . -175) 104002) ((-372 . -1133) T) ((-367 . -1133) T) ((-359 . -1133) T) ((-514 . -19) 103984) ((-1129 . -153) 103968) ((-896 . -239) NIL) ((-108 . -1133) T) ((-118 . -1088) 103955) ((-733 . -376) T) ((-514 . -618) 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100142) ((-73 . -1249) T) ((-105 . -632) 100124) ((-919 . -1249) T) ((-1324 . -632) 100106) ((-395 . -632) 100088) ((-352 . -635) 100040) ((-177 . -635) 99957) ((-1250 . -504) 99938) ((-753 . -38) 99787) ((-585 . -1238) T) ((-585 . -1235) T) ((-545 . -632) 99769) ((-534 . -321) 99707) ((-514 . -632) 99689) ((-514 . -633) 99671) ((-1250 . -632) 99637) ((-1200 . -1184) NIL) ((-216 . -1249) T) ((-1059 . -1103) 99606) ((-1059 . -1133) T) ((-1036 . -102) T) ((-1003 . -102) T) ((-944 . -102) T) ((-919 . -1070) 99583) ((-1174 . -748) T) ((-1035 . -670) 99490) ((-490 . -1133) T) ((-477 . -1133) T) ((-597 . -23) T) ((-585 . -35) T) ((-585 . -95) T) ((-443 . -102) T) ((-1095 . -233) 99436) ((-1207 . -38) 99333) ((-1206 . -38) 99174) ((-949 . -875) T) ((-891 . -748) T) ((-793 . -875) T) ((-716 . -951) T) ((-694 . -875) T) ((-526 . -25) T) ((-521 . -21) T) ((-521 . -25) T) ((-1200 . -38) 98970) ((-352 . -1081) T) ((-146 . -1249) T) ((-1111 . -175) T) ((-177 . -1081) T) ((-1158 . -38) 98867) ((-734 . -47) 98844) ((-372 . -175) T) ((-367 . -175) T) ((-533 . -57) 98818) ((-511 . -57) 98768) ((-365 . -1318) 98745) ((-229 . -466) T) ((-331 . -302) 98696) ((-359 . -175) T) ((-177 . -250) T) ((-1264 . -872) 98595) ((-108 . -175) T) ((-897 . -1023) 98579) ((-676 . -1144) T) ((-595 . -376) T) ((-595 . -341) 98566) ((-532 . -341) 98543) ((-532 . -376) T) ((-326 . -319) 98522) ((-325 . -319) T) ((-616 . -872) 98501) ((-1145 . -739) 98443) ((-623 . -1249) T) ((-534 . -294) 98427) ((-676 . -23) T) ((-419 . -234) 98411) ((-419 . -274) 98395) ((-325 . -1052) NIL) ((-346 . -23) T) ((-103 . -1042) 98379) ((-657 . -381) T) ((-45 . -36) 98358) ((-630 . -1133) T) ((-365 . -381) T) ((-538 . -102) T) ((-509 . -27) T) ((-246 . -321) 98296) ((-1119 . -1144) T) ((-1323 . -670) 98270) ((-803 . -1144) T) ((-802 . -1144) T) ((-1211 . -426) 98254) ((-468 . -1144) T) ((-1094 . -466) T) ((-1185 . -1133) T) ((-976 . -466) 98205) ((-1148 . -1115) T) ((-110 . -1133) T) ((-1119 . -23) T) ((-1192 . -528) 97988) 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-298) 94594) ((-130 . -632) 94576) ((-51 . -632) 94558) ((-218 . -875) T) ((-677 . -426) 94542) ((-1259 . -102) T) ((-1191 . -528) NIL) ((-674 . -25) T) ((-638 . -1088) 94526) ((-674 . -21) T) ((-986 . -668) 94436) ((-757 . -668) 94381) ((-737 . -668) 94353) ((-404 . -111) 94332) ((-226 . -263) 94316) ((-1086 . -1085) 94256) ((-1086 . -1133) T) ((-1036 . -1184) T) ((-842 . -1133) T) ((-467 . -668) 94171) ((-652 . -670) 94155) ((-638 . -111) 94134) ((-620 . -670) 94118) ((-357 . -1254) T) ((-610 . -102) T) ((-324 . -504) 94099) ((-597 . -133) T) ((-609 . -102) T) ((-429 . -1133) T) ((-394 . -1133) T) ((-324 . -632) 94065) ((-231 . -1133) 94043) ((-669 . -528) 93976) ((-651 . -528) 93820) ((-856 . -1081) 93799) ((-663 . -153) 93783) ((-357 . -571) T) ((-734 . -928) 93726) ((-565 . -233) 93676) ((-1289 . -296) 93642) ((-1280 . -296) 93608) ((-1111 . -302) 93559) ((-560 . -875) T) ((-501 . -871) T) ((-227 . -1144) T) ((-1259 . -296) 93525) ((-1242 . -507) 93491) ((-1036 . -38) 93441) 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-1133) T) ((-394 . -739) 92211) ((-841 . -1133) T) ((-490 . -528) 92144) ((-477 . -528) 92077) ((-1325 . -635) 92058) ((-467 . -380) 92028) ((-45 . -629) 92007) ((-413 . -1249) T) ((-326 . -310) T) ((-1299 . -875) 91986) ((-852 . -239) 91965) ((-491 . -635) 91915) ((-1259 . -321) 91800) ((-692 . -632) 91762) ((-58 . -872) 91741) ((-1036 . -414) 91723) ((-563 . -632) 91705) ((-822 . -668) 91664) ((-839 . -618) 91641) ((-530 . -872) 91620) ((-510 . -872) 91599) ((-1028 . -1070) 91495) ((-40 . -1254) T) ((-246 . -930) 91364) ((-50 . -133) T) ((-595 . -133) T) ((-532 . -133) T) ((-305 . -670) 91224) ((-357 . -341) 91201) ((-357 . -376) T) ((-334 . -335) 91178) ((-331 . -298) 91136) ((-40 . -571) T) ((-391 . -1235) T) ((-391 . -1238) T) ((-1067 . -1226) 91111) ((-1221 . -242) 91061) ((-1200 . -234) 91013) ((-1200 . -274) 90965) ((-342 . -1133) T) ((-391 . -95) T) ((-391 . -35) T) ((-1067 . -107) 90911) ((-491 . -1081) T) ((-1324 . -1088) 90895) ((-493 . -242) 90845) ((-1192 . -503) 90779) 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-590) T) ((-1320 . -397) 88234) ((-716 . -875) T) ((-1086 . -528) 88167) ((-1192 . -298) 88143) ((-246 . -274) 88112) ((-246 . -234) 88081) ((-260 . -1083) 87982) ((-259 . -1083) 87883) ((-1312 . -739) 87853) ((-1199 . -93) T) ((-1026 . -93) T) ((-841 . -175) 87832) ((-260 . -662) 87754) ((-259 . -662) 87676) ((-1247 . -504) 87653) ((-592 . -1249) T) ((-231 . -528) 87586) ((-638 . -821) 87565) ((-638 . -816) 87544) ((-1247 . -632) 87456) ((-226 . -1249) T) ((-697 . -632) 87388) ((-1207 . -668) 87298) ((-1187 . -1042) 87282) ((-973 . -102) 87212) ((-365 . -748) T) ((-887 . -632) 87194) ((-1206 . -668) 87076) ((-1200 . -668) 86913) ((-1158 . -668) 86823) ((-1259 . -414) 86775) ((-1145 . -503) 86759) ((-60 . -321) 86697) ((-343 . -102) T) ((-1242 . -21) T) ((-1242 . -25) T) ((-40 . -1144) T) ((-733 . -21) T) ((-646 . -632) 86679) ((-529 . -335) 86658) ((-733 . -25) T) ((-453 . -102) T) ((-108 . -298) NIL) ((-949 . -1144) T) ((-40 . -23) T) ((-793 . -1144) T) ((-560 . -1254) T) ((-509 . -1254) T) ((-1036 . -274) 86640) ((-331 . -632) 86622) ((-1036 . -234) 86604) ((-171 . -168) 86588) ((-594 . -571) T) ((-560 . -571) T) ((-509 . -571) T) ((-793 . -23) T) ((-1285 . -149) 86567) ((-1285 . -147) 86546) ((-1192 . -618) 86522) ((-1264 . -147) 86447) ((-1059 . -503) 86431) ((-1257 . -1249) T) ((-1264 . -149) 86356) ((-1315 . -1322) 86335) ((-896 . -922) NIL) ((-490 . -503) 86319) ((-477 . -503) 86303) ((-537 . -34) T) ((-677 . -739) 86273) ((-1289 . -930) 86186) ((-1280 . -930) 86092) ((-1259 . -930) 85853) ((-114 . -999) T) ((-1211 . -175) 85804) ((-674 . -872) 85783) ((-377 . -102) T) ((-609 . -930) 85696) ((-246 . -245) 85675) ((-260 . -102) T) ((-259 . -102) T) ((-1268 . -980) 85644) ((-252 . -872) 85623) ((-1056 . -875) T) ((-840 . -38) 85472) ((-45 . -528) 85264) ((-1191 . -298) 85214) ((-217 . -1133) T) ((-1183 . -1133) T) ((-897 . -239) 85165) ((-1183 . -629) 85144) ((-597 . -25) T) ((-597 . -21) T) ((-1129 . -321) 85082) ((-986 . -426) 85066) ((-721 . -1254) T) 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83947) ((-1203 . -1083) 83770) ((-1174 . -1249) T) ((-1157 . -1083) 83613) ((-879 . -1083) 83597) ((-651 . -618) 83572) ((-1285 . -95) 83538) ((-1285 . -239) 83490) ((-1266 . -102) 83468) ((-1203 . -662) 83297) ((-1157 . -662) 83146) ((-879 . -662) 83116) ((-1264 . -1235) 83082) ((-1119 . -25) T) ((-564 . -1133) T) ((-1119 . -21) T) ((-986 . -1089) T) ((-545 . -816) T) ((-545 . -821) T) ((-119 . -1254) T) ((-891 . -1249) T) ((-642 . -571) T) ((-803 . -25) T) ((-803 . -21) T) ((-802 . -21) T) ((-802 . -25) T) ((-757 . -1089) T) ((-737 . -1089) T) ((-692 . -1088) 83066) ((-531 . -1115) T) ((-475 . -25) T) ((-119 . -571) T) ((-475 . -21) T) ((-468 . -25) T) ((-468 . -21) T) ((-1264 . -1238) 83032) ((-1185 . -93) T) ((-1174 . -1070) 82928) ((-841 . -302) 82907) ((-1264 . -239) 82766) ((-848 . -1133) T) ((-996 . -999) T) ((-692 . -111) 82745) ((-636 . -1249) T) ((-307 . -528) 82537) ((-1259 . -234) 82489) ((-1259 . -274) 82441) ((-1258 . -381) T) ((-260 . -321) 82379) ((-259 . -321) 82317) 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. -1249) T) ((-114 . -684) T) ((-365 . -1249) T) ((-372 . -635) 69568) ((-367 . -635) 69505) ((-359 . -635) 69442) ((-77 . -1249) T) ((-108 . -635) 69392) ((-114 . -113) T) ((-1094 . -38) 69379) ((-686 . -387) 69358) ((-976 . -38) 69207) ((-753 . -1133) T) ((-495 . -38) 69056) ((-82 . -1249) T) ((-606 . -504) 69037) ((-1259 . -871) NIL) ((-1207 . -1133) T) ((-585 . -296) T) ((-1206 . -1133) T) ((-606 . -632) 69003) ((-1200 . -1133) T) ((-1152 . -875) T) ((-1111 . -1081) T) ((-365 . -1070) 68980) ((-841 . -504) 68964) ((-1036 . -1089) T) ((-45 . -632) 68946) ((-45 . -633) NIL) ((-944 . -1089) T) ((-841 . -632) 68915) ((-1180 . -102) 68865) ((-1111 . -250) 68816) ((-443 . -1089) T) ((-372 . -1081) T) ((-367 . -1081) T) ((-377 . -378) 68793) ((-359 . -1081) T) ((-357 . -236) 68780) ((-260 . -245) 68759) ((-259 . -245) 68738) ((-1111 . -240) 68663) ((-1158 . -1133) T) ((-305 . -928) 68622) ((-108 . -1081) T) ((-716 . -133) T) ((-419 . -528) 68464) ((-372 . -240) 68443) ((-372 . -250) T) 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. -503) 37533) ((-697 . -1249) T) ((-492 . -102) T) ((-252 . -102) 37463) ((-561 . -868) T) ((-140 . -102) T) ((-139 . -102) T) ((-135 . -102) T) ((-1119 . -922) 37358) ((-896 . -1133) T) ((-1203 . -528) 37305) ((-1094 . -739) 37292) ((-803 . -922) 37195) ((-753 . -1088) 37038) ((-802 . -922) 37020) ((-976 . -739) 36869) ((-1157 . -528) 36821) ((-1311 . -1133) T) ((-1310 . -1133) T) ((-468 . -922) 36796) ((-495 . -739) 36645) ((-67 . -632) 36627) ((-646 . -1249) T) ((-753 . -111) 36456) ((-973 . -503) 36440) ((-1312 . -670) 36400) ((-1207 . -1088) 36283) ((-841 . -748) T) ((-1206 . -1088) 36118) ((-1200 . -1088) 35908) ((-331 . -1249) T) ((-1158 . -1088) 35791) ((-1035 . -1254) T) ((-1121 . -102) 35769) ((-839 . -390) 35738) ((-593 . -632) 35720) ((-561 . -1133) T) ((-1035 . -571) T) ((-1207 . -111) 35589) ((-1206 . -111) 35410) ((-1200 . -111) 35179) ((-1158 . -111) 35048) ((-1137 . -1136) 35012) ((-391 . -871) T) ((-1289 . -632) 34994) ((-1280 . -632) 34976) ((-897 . -668) 34913) 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. -668) 25814) ((-255 . -668) 25724) ((-1315 . -397) 25696) ((-531 . -1133) T) ((-119 . -466) T) ((-1229 . -102) T) ((-1124 . -1133) 25666) ((-1066 . -1133) T) ((-1148 . -93) T) ((-919 . -872) T) ((-1289 . -111) 25535) ((-365 . -1254) T) ((-1289 . -1088) 25418) ((-1145 . -390) 25387) ((-1280 . -1088) 25222) ((-1259 . -1088) 25012) ((-1280 . -111) 24833) ((-1259 . -111) 24602) ((-1242 . -321) 24589) ((-1035 . -133) T) ((-936 . -668) 24539) ((-377 . -632) 24521) ((-365 . -571) T) ((-301 . -319) T) ((-610 . -1088) 24481) ((-609 . -1088) 24364) ((-595 . -1083) 24329) ((-532 . -1083) 24274) ((-374 . -1133) T) ((-334 . -1133) T) ((-260 . -632) 24235) ((-259 . -632) 24196) ((-595 . -662) 24161) ((-532 . -662) 24106) ((-716 . -424) 24073) ((-652 . -23) T) ((-620 . -23) T) ((-40 . -922) 23980) ((-676 . -102) T) ((-610 . -111) 23933) ((-609 . -111) 23802) ((-391 . -1133) T) ((-346 . -102) T) ((-171 . -302) 23713) ((-1264 . -871) 23666) ((-736 . -1089) T) ((-630 . -1249) T) ((-1180 . -528) 23599) 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-668) 203778) ((-1315 . -133) T) ((-1315 . -25) T) ((-1315 . -102) T) ((-1315 . -1249) T) ((-1315 . -632) 203760) ((-1315 . -1133) T) ((-1315 . -23) T) ((-1315 . -21) T) ((-1315 . -1088) 203744) ((-1315 . -1083) 203728) ((-1315 . -111) 203707) ((-1315 . -1322) 203686) ((-1315 . -1081) T) ((-1315 . -1089) T) ((-1315 . -1144) T) ((-1315 . -748) T) ((-1315 . -1314) 203670) ((-1315 . -38) 203640) ((-1315 . -1319) 203619) ((-1313 . -1244) 203588) ((-1313 . -632) 203550) ((-1313 . -153) 203534) ((-1313 . -34) T) ((-1313 . -1249) T) ((-1313 . -102) T) ((-1313 . -321) 203472) ((-1313 . -528) 203405) ((-1313 . -1133) T) ((-1313 . -503) 203389) ((-1313 . -633) 203350) ((-1313 . -1008) 203319) ((-1312 . -1081) T) ((-1312 . -1089) T) ((-1312 . -1144) T) ((-1312 . -748) T) ((-1312 . -21) T) ((-1312 . -668) 203264) ((-1312 . -23) T) ((-1312 . -1133) T) ((-1312 . -632) 203233) ((-1312 . -1249) T) ((-1312 . -102) T) ((-1312 . -25) T) ((-1312 . -133) T) ((-1312 . -670) 203193) ((-1312 . -635) 203135) ((-1312 . -504) 203119) ((-1312 . -38) 203089) ((-1312 . -111) 203054) ((-1312 . -1083) 203024) ((-1312 . -1088) 202994) ((-1312 . -662) 202964) ((-1312 . -739) 202934) ((-1311 . -1115) T) ((-1311 . -504) 202915) ((-1311 . -632) 202881) ((-1311 . -635) 202862) ((-1311 . -1133) T) ((-1311 . -1249) T) ((-1311 . -102) T) ((-1311 . -93) T) ((-1310 . -1115) T) ((-1310 . -504) 202843) ((-1310 . -632) 202809) ((-1310 . -635) 202790) ((-1310 . -1133) T) ((-1310 . -1249) T) ((-1310 . -102) T) ((-1310 . -93) T) ((-1305 . -632) 202772) ((-1303 . -1133) T) ((-1303 . -632) 202754) ((-1303 . -1249) T) ((-1303 . -102) T) ((-1302 . -1133) T) ((-1302 . -632) 202736) ((-1302 . -1249) T) ((-1302 . -102) T) ((-1299 . -1298) 202720) ((-1299 . -385) 202704) ((-1299 . -875) 202683) ((-1299 . -872) 202662) ((-1299 . -153) 202646) ((-1299 . -34) T) ((-1299 . -1249) T) ((-1299 . -102) 202576) ((-1299 . -632) 202488) ((-1299 . -321) 202426) ((-1299 . -528) 202359) ((-1299 . -1133) 202309) ((-1299 . -503) 202293) ((-1299 . -633) 202254) ((-1299 . -298) 202206) ((-1299 . -618) 202183) ((-1299 . -300) 202160) ((-1299 . -673) 202144) ((-1299 . -19) 202128) ((-1296 . -1133) T) ((-1296 . -632) 202094) ((-1296 . -1249) T) ((-1296 . -102) T) ((-1289 . -1292) 202078) ((-1289 . -240) 202037) ((-1289 . -635) 201919) ((-1289 . -670) 201844) ((-1289 . -668) 201754) ((-1289 . -133) T) ((-1289 . -25) T) ((-1289 . -102) T) ((-1289 . -632) 201736) ((-1289 . -1133) T) ((-1289 . -23) T) ((-1289 . -21) T) ((-1289 . -748) T) ((-1289 . -1144) T) ((-1289 . -1089) T) ((-1289 . -1081) T) ((-1289 . -236) 201689) ((-1289 . -1249) T) ((-1289 . -239) 201648) ((-1289 . -298) 201613) ((-1289 . -928) 201526) ((-1289 . -922) 201414) ((-1289 . -930) 201327) ((-1289 . -1005) 201296) ((-1289 . -38) 201193) ((-1289 . -111) 201062) ((-1289 . -1083) 200945) ((-1289 . -1088) 200828) ((-1289 . -662) 200725) ((-1289 . -739) 200622) ((-1289 . -147) 200601) ((-1289 . -149) 200580) ((-1289 . -175) 200531) ((-1289 . -571) 200510) ((-1289 . -302) 200489) ((-1289 . -47) 200466) ((-1289 . -1278) 200443) ((-1289 . -35) 200409) ((-1289 . -95) 200375) ((-1289 . -296) 200341) ((-1289 . -507) 200307) ((-1289 . -1238) 200273) ((-1289 . -1235) 200239) ((-1289 . -1034) 200205) ((-1286 . -338) 200149) ((-1286 . -1070) 200115) ((-1286 . -426) 200081) ((-1286 . -38) 199973) ((-1286 . -635) 199847) ((-1286 . -670) 199752) ((-1286 . -668) 199642) ((-1286 . -748) T) ((-1286 . -1144) T) ((-1286 . -1089) T) ((-1286 . -1081) T) ((-1286 . -111) 199534) ((-1286 . -1083) 199439) ((-1286 . -1088) 199344) ((-1286 . -21) T) ((-1286 . -23) T) ((-1286 . -1133) T) ((-1286 . -632) 199326) ((-1286 . -1249) T) ((-1286 . -102) T) ((-1286 . -25) T) ((-1286 . -133) T) ((-1286 . -662) 199218) ((-1286 . -739) 199110) ((-1286 . -147) 199071) ((-1286 . -149) 199032) ((-1286 . -175) T) ((-1286 . -571) T) ((-1286 . -302) T) ((-1286 . -47) 198976) ((-1285 . -1284) 198955) ((-1285 . -376) 198934) ((-1285 . -1254) 198913) ((-1285 . -951) 198892) ((-1285 . -571) 198843) ((-1285 . -175) 198774) ((-1285 . -635) 198587) ((-1285 . -739) 198428) ((-1285 . -662) 198269) ((-1285 . -38) 198110) ((-1285 . -466) 198089) ((-1285 . -319) 198068) ((-1285 . -670) 197965) ((-1285 . -668) 197847) ((-1285 . -748) T) ((-1285 . -1144) T) ((-1285 . -1089) T) ((-1285 . -1081) T) ((-1285 . -111) 197668) ((-1285 . -1083) 197503) ((-1285 . -1088) 197338) ((-1285 . -21) T) ((-1285 . -23) T) ((-1285 . -1133) T) ((-1285 . -632) 197320) ((-1285 . -1249) T) ((-1285 . -102) T) ((-1285 . -25) T) ((-1285 . -133) T) ((-1285 . -302) 197271) ((-1285 . -250) 197250) ((-1285 . -1034) 197216) ((-1285 . -1235) 197182) ((-1285 . -1238) 197148) ((-1285 . -507) 197114) ((-1285 . -296) 197080) ((-1285 . -95) 197046) ((-1285 . -35) 197012) ((-1285 . -1278) 196982) ((-1285 . -47) 196952) ((-1285 . -149) 196931) ((-1285 . -147) 196910) ((-1285 . -1005) 196872) ((-1285 . -930) 196778) ((-1285 . -922) 196682) ((-1285 . -928) 196588) ((-1285 . -298) 196546) ((-1285 . -239) 196498) ((-1285 . -236) 196444) ((-1285 . -240) 196396) ((-1285 . -1282) 196380) ((-1285 . -1070) 196364) ((-1280 . -1284) 196325) ((-1280 . -376) 196304) ((-1280 . -1254) 196283) ((-1280 . -951) 196262) ((-1280 . -571) 196213) ((-1280 . -175) 196144) ((-1280 . -635) 195887) ((-1280 . -739) 195728) ((-1280 . -662) 195569) ((-1280 . -38) 195410) ((-1280 . -466) 195389) ((-1280 . -319) 195368) ((-1280 . -670) 195265) ((-1280 . -668) 195147) ((-1280 . -748) T) ((-1280 . -1144) T) ((-1280 . -1089) T) ((-1280 . -1081) T) ((-1280 . -111) 194968) ((-1280 . -1083) 194803) ((-1280 . -1088) 194638) ((-1280 . -21) T) ((-1280 . -23) T) ((-1280 . -1133) T) ((-1280 . -632) 194620) ((-1280 . -1249) T) ((-1280 . -102) T) ((-1280 . -25) T) ((-1280 . -133) T) ((-1280 . -302) 194571) ((-1280 . -250) 194550) ((-1280 . -1034) 194516) ((-1280 . -1235) 194482) ((-1280 . -1238) 194448) ((-1280 . -507) 194414) ((-1280 . -296) 194380) ((-1280 . -95) 194346) ((-1280 . -35) 194312) ((-1280 . -1278) 194282) ((-1280 . -47) 194252) ((-1280 . -149) 194231) ((-1280 . -147) 194210) ((-1280 . -1005) 194172) ((-1280 . -930) 194078) ((-1280 . -922) 193959) ((-1280 . -928) 193865) ((-1280 . -298) 193823) ((-1280 . -239) 193775) ((-1280 . -236) 193721) ((-1280 . -240) 193673) ((-1280 . -1282) 193657) ((-1280 . -1070) 193592) ((-1268 . -1275) 193576) ((-1268 . -1184) 193554) ((-1268 . -633) NIL) ((-1268 . -321) 193541) ((-1268 . -528) 193488) ((-1268 . -338) 193465) ((-1268 . -1070) 193345) ((-1268 . -426) 193329) ((-1268 . -38) 193158) ((-1268 . -111) 192967) ((-1268 . -1083) 192790) ((-1268 . -1088) 192613) ((-1268 . -668) 192523) ((-1268 . -670) 192412) ((-1268 . -662) 192241) ((-1268 . -739) 192070) ((-1268 . -635) 191818) ((-1268 . -147) 191797) ((-1268 . -149) 191776) ((-1268 . -47) 191753) ((-1268 . -390) 191737) ((-1268 . -660) 191685) ((-1268 . -928) 191628) ((-1268 . -922) 191531) ((-1268 . -930) 191438) ((-1268 . -912) NIL) ((-1268 . -940) 191417) ((-1268 . -1254) 191396) ((-1268 . -980) 191365) ((-1268 . -951) 191344) ((-1268 . -571) 191255) ((-1268 . -302) 191166) ((-1268 . -175) 191057) ((-1268 . -466) 190988) ((-1268 . -319) 190967) ((-1268 . -298) 190894) ((-1268 . -240) T) ((-1268 . -133) T) ((-1268 . -25) T) ((-1268 . -102) T) ((-1268 . -632) 190876) ((-1268 . -1133) T) ((-1268 . -23) T) ((-1268 . -21) T) ((-1268 . -748) T) ((-1268 . -1144) T) ((-1268 . -1089) T) ((-1268 . -1081) T) ((-1268 . -236) 190863) ((-1268 . -1249) T) ((-1268 . -239) T) ((-1268 . -274) 190847) ((-1268 . -234) 190831) ((-1266 . -1126) 190815) ((-1266 . -637) 190799) ((-1266 . -1133) 190777) ((-1266 . -632) 190744) ((-1266 . -1249) 190722) ((-1266 . -102) 190700) ((-1266 . -1127) 190657) ((-1264 . -1263) 190636) ((-1264 . -1034) 190602) ((-1264 . -1235) 190568) ((-1264 . -1238) 190534) ((-1264 . -507) 190500) ((-1264 . -296) 190466) ((-1264 . -95) 190432) ((-1264 . -35) 190398) ((-1264 . -1278) 190375) ((-1264 . -47) 190352) ((-1264 . -635) 190100) ((-1264 . -739) 189914) ((-1264 . -662) 189728) ((-1264 . -670) 189536) ((-1264 . -668) 189391) ((-1264 . -1088) 189199) ((-1264 . -1083) 189007) ((-1264 . -111) 188796) ((-1264 . -38) 188610) ((-1264 . -1005) 188579) ((-1264 . -298) 188479) ((-1264 . -1261) 188463) ((-1264 . -748) T) ((-1264 . -1144) T) ((-1264 . -1089) T) ((-1264 . -1081) T) ((-1264 . -21) T) ((-1264 . -23) T) ((-1264 . -1133) T) ((-1264 . -632) 188445) ((-1264 . -1249) T) ((-1264 . -102) T) ((-1264 . -25) T) ((-1264 . -133) T) ((-1264 . -147) 188370) ((-1264 . -149) 188295) ((-1264 . -633) 187966) ((-1264 . -234) 187936) ((-1264 . -928) 187787) ((-1264 . -930) 187584) ((-1264 . -922) 187379) ((-1264 . -274) 187349) ((-1264 . -239) 187208) ((-1264 . -236) 187061) ((-1264 . -240) 186966) ((-1264 . -376) 186945) ((-1264 . -1254) 186924) ((-1264 . -951) 186903) ((-1264 . -571) 186854) ((-1264 . -175) 186785) ((-1264 . -466) 186764) ((-1264 . -319) 186743) ((-1264 . -302) 186694) ((-1264 . -250) 186673) ((-1264 . -351) 186643) ((-1264 . -528) 186503) ((-1264 . -321) 186442) ((-1264 . -390) 186412) ((-1264 . -660) 186320) ((-1264 . -414) 186290) ((-1264 . -912) 186163) ((-1264 . -844) 186116) ((-1264 . -814) 186069) ((-1264 . -816) 186022) ((-1264 . -872) 185921) ((-1264 . -875) 185820) ((-1264 . -818) 185773) ((-1264 . -821) 185726) ((-1264 . -871) 185679) ((-1264 . -910) 185649) ((-1264 . -940) 185602) ((-1264 . -1052) 185554) ((-1264 . -1070) 185340) ((-1264 . -1184) 185292) ((-1264 . -1023) 185262) ((-1259 . -1263) 185223) ((-1259 . -1034) 185189) ((-1259 . -1235) 185155) ((-1259 . -1238) 185121) ((-1259 . -507) 185087) ((-1259 . -296) 185053) ((-1259 . -95) 185019) ((-1259 . -35) 184985) ((-1259 . -1278) 184962) ((-1259 . -47) 184939) ((-1259 . -635) 184734) ((-1259 . -739) 184530) ((-1259 . -662) 184326) ((-1259 . -670) 184178) ((-1259 . -668) 184015) ((-1259 . -1088) 183805) ((-1259 . -1083) 183595) ((-1259 . -111) 183364) ((-1259 . -38) 183160) ((-1259 . -1005) 183129) ((-1259 . -298) 182957) ((-1259 . -1261) 182941) ((-1259 . -748) T) ((-1259 . -1144) T) ((-1259 . -1089) T) ((-1259 . -1081) T) ((-1259 . -21) T) ((-1259 . -23) T) ((-1259 . -1133) T) ((-1259 . -632) 182923) ((-1259 . -1249) T) ((-1259 . -102) T) ((-1259 . -25) T) ((-1259 . -133) T) ((-1259 . -147) 182830) ((-1259 . -149) 182737) ((-1259 . -633) NIL) ((-1259 . -234) 182689) ((-1259 . -928) 182522) ((-1259 . -930) 182283) ((-1259 . -922) 182019) ((-1259 . -274) 181971) ((-1259 . -239) 181794) ((-1259 . -236) 181611) ((-1259 . -240) 181498) ((-1259 . -376) 181477) ((-1259 . -1254) 181456) ((-1259 . -951) 181435) ((-1259 . -571) 181386) ((-1259 . -175) 181317) ((-1259 . -466) 181296) ((-1259 . -319) 181275) ((-1259 . -302) 181226) ((-1259 . -250) 181205) ((-1259 . -351) 181157) ((-1259 . -528) 180926) ((-1259 . -321) 180811) ((-1259 . -390) 180763) ((-1259 . -660) 180715) ((-1259 . -414) 180667) ((-1259 . -912) NIL) ((-1259 . -844) NIL) ((-1259 . -814) NIL) ((-1259 . -816) NIL) ((-1259 . -872) NIL) ((-1259 . -875) NIL) ((-1259 . -818) NIL) ((-1259 . -821) NIL) ((-1259 . -871) NIL) ((-1259 . -910) 180619) ((-1259 . -940) NIL) ((-1259 . -1052) NIL) ((-1259 . -1070) 180585) ((-1259 . -1184) NIL) ((-1259 . -1023) 180537) ((-1258 . -868) T) ((-1258 . -875) T) ((-1258 . -872) T) ((-1258 . -1133) T) ((-1258 . -632) 180519) ((-1258 . -1249) T) ((-1258 . -102) T) ((-1258 . -381) T) ((-1258 . -684) T) ((-1257 . -868) T) ((-1257 . -875) T) ((-1257 . -872) T) ((-1257 . -1133) T) ((-1257 . -632) 180501) ((-1257 . -1249) T) ((-1257 . -102) T) ((-1257 . -381) T) ((-1257 . -684) T) ((-1256 . -868) T) ((-1256 . -875) T) ((-1256 . -872) T) ((-1256 . -1133) T) ((-1256 . -632) 180483) ((-1256 . -1249) T) ((-1256 . -102) T) ((-1256 . -381) T) ((-1256 . -684) T) ((-1255 . -868) T) ((-1255 . -875) T) ((-1255 . -872) T) ((-1255 . -1133) T) ((-1255 . -632) 180465) ((-1255 . -1249) T) ((-1255 . -102) T) ((-1255 . -381) T) ((-1255 . -684) T) ((-1250 . -1115) T) ((-1250 . -504) 180446) ((-1250 . -632) 180412) ((-1250 . -635) 180393) ((-1250 . -1133) T) ((-1250 . -1249) T) ((-1250 . -102) T) ((-1250 . -93) T) ((-1247 . -504) 180370) ((-1247 . -632) 180282) ((-1247 . -635) 180259) ((-1247 . -1133) 180237) ((-1247 . -1249) 180215) ((-1247 . -102) 180193) ((-1242 . -762) 180169) ((-1242 . -35) 180135) ((-1242 . -95) 180101) ((-1242 . -296) 180067) ((-1242 . -507) 180033) ((-1242 . -1238) 179999) ((-1242 . -1235) 179965) ((-1242 . -1034) 179931) ((-1242 . -47) 179900) ((-1242 . -38) 179797) ((-1242 . -662) 179694) ((-1242 . -739) 179591) ((-1242 . -635) 179473) ((-1242 . -302) 179452) ((-1242 . -571) 179431) ((-1242 . -111) 179300) ((-1242 . -1083) 179183) ((-1242 . -1088) 179066) ((-1242 . -175) 179017) ((-1242 . -149) 178996) ((-1242 . -147) 178975) ((-1242 . -670) 178900) ((-1242 . -668) 178810) ((-1242 . -1005) 178772) ((-1242 . -930) 178753) ((-1242 . -1249) T) ((-1242 . -922) 178732) ((-1242 . -1081) T) ((-1242 . -1089) T) ((-1242 . -1144) T) ((-1242 . -748) T) ((-1242 . -21) T) ((-1242 . -23) T) ((-1242 . -1133) T) ((-1242 . -632) 178714) ((-1242 . -102) T) ((-1242 . -25) T) ((-1242 . -133) T) ((-1242 . -928) 178695) ((-1242 . -528) 178662) ((-1242 . -321) 178649) ((-1236 . -1042) 178633) ((-1236 . -34) T) ((-1236 . -1249) T) ((-1236 . -102) 178583) ((-1236 . -632) 178515) ((-1236 . -321) 178453) ((-1236 . -528) 178386) ((-1236 . -1133) 178364) ((-1236 . -503) 178348) ((-1231 . -378) 178322) ((-1231 . -102) T) ((-1231 . -1249) T) ((-1231 . -632) 178304) ((-1231 . -1133) T) ((-1229 . -1133) T) ((-1229 . -632) 178286) ((-1229 . -1249) T) ((-1229 . -102) T) ((-1229 . -635) 178268) ((-1223 . -860) 178252) ((-1223 . -102) T) ((-1223 . -1249) T) ((-1223 . -632) 178234) ((-1223 . -1133) T) ((-1221 . -1226) 178213) ((-1221 . -233) 178163) ((-1221 . -107) 178113) ((-1221 . -321) 177917) ((-1221 . -528) 177709) ((-1221 . -503) 177646) ((-1221 . -153) 177596) ((-1221 . -633) NIL) ((-1221 . -242) 177546) ((-1221 . -629) 177525) ((-1221 . -300) 177504) ((-1221 . -1249) T) ((-1221 . -298) 177483) ((-1221 . -1133) T) ((-1221 . -632) 177465) ((-1221 . -102) T) ((-1221 . -34) T) ((-1221 . -618) 177444) ((-1219 . -1249) T) ((-1217 . -1133) T) ((-1217 . -632) 177426) ((-1217 . -1249) T) ((-1217 . -102) T) ((-1216 . -868) T) ((-1216 . -875) T) ((-1216 . -872) T) ((-1216 . -1133) T) ((-1216 . -632) 177408) ((-1216 . -1249) T) ((-1216 . -102) T) ((-1216 . -381) T) ((-1216 . -684) T) ((-1215 . -868) T) ((-1215 . -875) T) ((-1215 . -872) T) ((-1215 . -1133) T) ((-1215 . -632) 177390) ((-1215 . -1249) T) ((-1215 . -102) T) ((-1215 . -381) T) ((-1214 . -1295) T) ((-1214 . -1133) T) ((-1214 . -632) 177357) ((-1214 . -1249) T) ((-1214 . -102) T) ((-1214 . -1070) 177293) ((-1214 . -635) 177229) ((-1213 . -632) 177211) ((-1212 . -632) 177193) ((-1211 . -338) 177169) ((-1211 . -1070) 177065) ((-1211 . -426) 177049) ((-1211 . -38) 176946) ((-1211 . -635) 176799) ((-1211 . -670) 176724) ((-1211 . -668) 176634) ((-1211 . -748) T) ((-1211 . -1144) T) ((-1211 . -1089) T) ((-1211 . -1081) T) ((-1211 . -111) 176503) ((-1211 . -1083) 176386) ((-1211 . -1088) 176269) ((-1211 . -21) T) ((-1211 . -23) T) ((-1211 . -1133) T) ((-1211 . -632) 176251) ((-1211 . -1249) T) ((-1211 . -102) T) ((-1211 . -25) T) ((-1211 . -133) T) ((-1211 . -662) 176148) ((-1211 . -739) 176045) ((-1211 . -147) 176024) ((-1211 . -149) 176003) ((-1211 . -175) 175954) ((-1211 . -571) 175933) ((-1211 . -302) 175912) ((-1211 . -47) 175888) ((-1209 . -872) T) ((-1209 . -632) 175870) ((-1209 . -1133) T) ((-1209 . -102) T) ((-1209 . -1249) T) ((-1209 . -875) T) ((-1209 . -633) 175792) ((-1209 . -845) T) ((-1209 . -635) 175773) ((-1209 . -912) 175740) ((-1208 . -632) 175722) ((-1207 . -1292) 175706) ((-1207 . -240) 175665) ((-1207 . -635) 175547) ((-1207 . -670) 175472) ((-1207 . -668) 175382) ((-1207 . -133) T) ((-1207 . -25) T) ((-1207 . -102) T) ((-1207 . -632) 175364) ((-1207 . -1133) T) ((-1207 . -23) T) ((-1207 . -21) T) ((-1207 . -748) T) ((-1207 . -1144) T) ((-1207 . -1089) T) ((-1207 . -1081) T) ((-1207 . -236) 175317) ((-1207 . -1249) T) ((-1207 . -239) 175276) ((-1207 . -298) 175241) ((-1207 . -928) 175154) ((-1207 . -922) 175042) ((-1207 . -930) 174955) ((-1207 . -1005) 174924) ((-1207 . -38) 174821) ((-1207 . -111) 174690) ((-1207 . -1083) 174573) ((-1207 . -1088) 174456) ((-1207 . -662) 174353) ((-1207 . -739) 174250) ((-1207 . -147) 174229) ((-1207 . -149) 174208) ((-1207 . -175) 174159) ((-1207 . -571) 174138) ((-1207 . -302) 174117) ((-1207 . -47) 174094) ((-1207 . -1278) 174071) ((-1207 . -35) 174037) ((-1207 . -95) 174003) ((-1207 . -296) 173969) ((-1207 . -507) 173935) ((-1207 . -1238) 173901) ((-1207 . -1235) 173867) ((-1207 . -1034) 173833) ((-1206 . -1284) 173794) ((-1206 . -376) 173773) ((-1206 . -1254) 173752) ((-1206 . -951) 173731) ((-1206 . -571) 173682) ((-1206 . -175) 173613) ((-1206 . -635) 173356) ((-1206 . -739) 173197) ((-1206 . -662) 173038) ((-1206 . -38) 172879) ((-1206 . -466) 172858) ((-1206 . -319) 172837) ((-1206 . -670) 172734) ((-1206 . -668) 172616) ((-1206 . -748) T) ((-1206 . -1144) T) ((-1206 . -1089) T) ((-1206 . -1081) T) ((-1206 . -111) 172437) ((-1206 . -1083) 172272) ((-1206 . -1088) 172107) ((-1206 . -21) T) ((-1206 . -23) T) ((-1206 . -1133) T) ((-1206 . -632) 172089) ((-1206 . -1249) T) ((-1206 . -102) T) ((-1206 . -25) T) ((-1206 . -133) T) ((-1206 . -302) 172040) ((-1206 . -250) 172019) ((-1206 . -1034) 171985) ((-1206 . -1235) 171951) ((-1206 . -1238) 171917) ((-1206 . -507) 171883) ((-1206 . -296) 171849) ((-1206 . -95) 171815) ((-1206 . -35) 171781) ((-1206 . -1278) 171751) ((-1206 . -47) 171721) ((-1206 . -149) 171700) ((-1206 . -147) 171679) ((-1206 . -1005) 171641) ((-1206 . -930) 171547) ((-1206 . -922) 171428) ((-1206 . -928) 171334) ((-1206 . -298) 171292) ((-1206 . -239) 171244) ((-1206 . -236) 171190) ((-1206 . -240) 171142) ((-1206 . -1282) 171126) ((-1206 . -1070) 171061) ((-1203 . -1275) 171045) ((-1203 . -1184) 171023) ((-1203 . -633) NIL) ((-1203 . -321) 171010) ((-1203 . -528) 170957) ((-1203 . -338) 170934) ((-1203 . -1070) 170814) ((-1203 . -426) 170798) ((-1203 . -38) 170627) ((-1203 . -111) 170436) ((-1203 . -1083) 170259) ((-1203 . -1088) 170082) ((-1203 . -668) 169992) ((-1203 . -670) 169881) ((-1203 . -662) 169710) ((-1203 . -739) 169539) ((-1203 . -635) 169308) ((-1203 . -147) 169287) ((-1203 . -149) 169266) ((-1203 . -47) 169243) ((-1203 . -390) 169227) ((-1203 . -660) 169175) ((-1203 . -928) 169118) ((-1203 . -922) 169021) ((-1203 . -930) 168928) ((-1203 . -912) NIL) ((-1203 . -940) 168907) ((-1203 . -1254) 168886) ((-1203 . -980) 168855) ((-1203 . -951) 168834) ((-1203 . -571) 168745) ((-1203 . -302) 168656) ((-1203 . -175) 168547) ((-1203 . -466) 168478) ((-1203 . -319) 168457) ((-1203 . -298) 168384) ((-1203 . -240) T) ((-1203 . -133) T) ((-1203 . -25) T) ((-1203 . -102) T) ((-1203 . -632) 168366) ((-1203 . -1133) T) ((-1203 . -23) T) ((-1203 . -21) T) ((-1203 . -748) T) ((-1203 . -1144) T) ((-1203 . -1089) T) ((-1203 . -1081) T) ((-1203 . -236) 168353) ((-1203 . -1249) T) ((-1203 . -239) T) ((-1203 . -274) 168337) ((-1203 . -234) 168321) ((-1200 . -1263) 168282) ((-1200 . -1034) 168248) ((-1200 . -1235) 168214) ((-1200 . -1238) 168180) ((-1200 . -507) 168146) ((-1200 . -296) 168112) ((-1200 . -95) 168078) ((-1200 . -35) 168044) ((-1200 . -1278) 168021) ((-1200 . -47) 167998) ((-1200 . -635) 167793) ((-1200 . -739) 167589) ((-1200 . -662) 167385) ((-1200 . -670) 167237) ((-1200 . -668) 167074) ((-1200 . -1088) 166864) ((-1200 . -1083) 166654) ((-1200 . -111) 166423) ((-1200 . -38) 166219) ((-1200 . -1005) 166188) ((-1200 . -298) 166016) ((-1200 . -1261) 166000) ((-1200 . -748) T) ((-1200 . -1144) T) ((-1200 . -1089) T) ((-1200 . -1081) T) ((-1200 . -21) T) ((-1200 . -23) T) ((-1200 . -1133) T) ((-1200 . -632) 165982) ((-1200 . -1249) T) ((-1200 . -102) T) ((-1200 . -25) T) ((-1200 . -133) T) ((-1200 . -147) 165889) ((-1200 . -149) 165796) ((-1200 . -633) NIL) ((-1200 . -234) 165748) ((-1200 . -928) 165581) ((-1200 . -930) 165342) ((-1200 . -922) 165078) ((-1200 . -274) 165030) ((-1200 . -239) 164853) ((-1200 . -236) 164670) ((-1200 . -240) 164557) ((-1200 . -376) 164536) ((-1200 . -1254) 164515) ((-1200 . -951) 164494) ((-1200 . -571) 164445) ((-1200 . -175) 164376) ((-1200 . -466) 164355) ((-1200 . -319) 164334) ((-1200 . -302) 164285) ((-1200 . -250) 164264) ((-1200 . -351) 164216) ((-1200 . -528) 163985) ((-1200 . -321) 163870) ((-1200 . -390) 163822) ((-1200 . -660) 163774) ((-1200 . -414) 163726) ((-1200 . -912) NIL) ((-1200 . -844) NIL) ((-1200 . -814) NIL) ((-1200 . -816) NIL) ((-1200 . -872) NIL) ((-1200 . -875) NIL) ((-1200 . -818) NIL) ((-1200 . -821) NIL) ((-1200 . -871) NIL) ((-1200 . -910) 163678) ((-1200 . -940) NIL) ((-1200 . -1052) NIL) ((-1200 . -1070) 163644) ((-1200 . -1184) NIL) ((-1200 . -1023) 163596) ((-1199 . -1115) T) ((-1199 . -504) 163577) ((-1199 . -632) 163543) ((-1199 . -635) 163524) ((-1199 . -1133) T) ((-1199 . -1249) T) ((-1199 . -102) T) ((-1199 . -93) T) ((-1198 . -1133) T) ((-1198 . -632) 163506) ((-1198 . -1249) T) ((-1198 . -102) T) ((-1197 . -1133) T) ((-1197 . -632) 163488) ((-1197 . -1249) T) ((-1197 . -102) T) ((-1192 . -1226) 163464) ((-1192 . -233) 163411) ((-1192 . -107) 163358) ((-1192 . -321) 163153) ((-1192 . -528) 162936) ((-1192 . -503) 162870) ((-1192 . -153) 162817) ((-1192 . -633) NIL) ((-1192 . -242) 162764) ((-1192 . -629) 162740) ((-1192 . -300) 162716) ((-1192 . -1249) T) ((-1192 . -298) 162692) ((-1192 . -1133) T) ((-1192 . -632) 162674) ((-1192 . -102) T) ((-1192 . -34) T) ((-1192 . -618) 162650) ((-1191 . -1176) T) ((-1191 . -385) 162632) ((-1191 . -875) T) ((-1191 . -872) T) ((-1191 . -153) 162614) ((-1191 . -34) T) ((-1191 . -1249) T) ((-1191 . -102) T) ((-1191 . -632) 162596) ((-1191 . -321) NIL) ((-1191 . -528) NIL) ((-1191 . -1133) T) ((-1191 . -503) 162578) ((-1191 . -633) NIL) ((-1191 . -298) 162528) ((-1191 . -618) 162503) ((-1191 . -300) 162478) ((-1191 . -673) 162460) ((-1191 . -19) 162442) ((-1191 . -845) T) ((-1187 . -696) 162426) ((-1187 . -673) 162410) ((-1187 . -300) 162387) ((-1187 . -298) 162339) ((-1187 . -618) 162316) ((-1187 . -633) 162277) ((-1187 . -503) 162261) ((-1187 . -1133) 162239) ((-1187 . -528) 162172) ((-1187 . -321) 162110) ((-1187 . -632) 162042) ((-1187 . -102) 161992) ((-1187 . -1249) T) ((-1187 . -34) T) ((-1187 . -153) 161976) ((-1187 . -1288) 161960) ((-1187 . -1042) 161944) ((-1187 . -1182) 161928) ((-1187 . -635) 161905) ((-1185 . -1115) T) ((-1185 . -504) 161886) ((-1185 . -632) 161852) ((-1185 . -635) 161833) ((-1185 . -1133) T) ((-1185 . -1249) T) ((-1185 . -102) T) ((-1185 . -93) T) ((-1183 . -1226) 161812) ((-1183 . -233) 161762) ((-1183 . -107) 161712) ((-1183 . -321) 161516) ((-1183 . -528) 161308) ((-1183 . -503) 161245) ((-1183 . -153) 161195) ((-1183 . -633) NIL) ((-1183 . -242) 161145) ((-1183 . -629) 161124) ((-1183 . -300) 161103) ((-1183 . -1249) T) ((-1183 . -298) 161082) ((-1183 . -1133) T) ((-1183 . -632) 161064) ((-1183 . -102) T) ((-1183 . -34) T) ((-1183 . -618) 161043) ((-1180 . -1153) 161027) ((-1180 . -503) 161011) ((-1180 . -1133) 160989) ((-1180 . -528) 160922) ((-1180 . -321) 160860) ((-1180 . -632) 160792) ((-1180 . -102) 160742) ((-1180 . -1249) T) ((-1180 . -34) T) ((-1180 . -107) 160726) ((-1178 . -1141) 160695) ((-1178 . -1244) 160664) ((-1178 . -632) 160626) ((-1178 . -153) 160610) ((-1178 . -34) T) ((-1178 . -1249) T) ((-1178 . -102) T) ((-1178 . -321) 160548) ((-1178 . -528) 160481) ((-1178 . -1133) T) ((-1178 . -503) 160465) ((-1178 . -633) 160426) ((-1178 . -1008) 160395) ((-1178 . -1103) 160364) ((-1174 . -1155) 160309) ((-1174 . -503) 160293) ((-1174 . -528) 160226) ((-1174 . -321) 160164) ((-1174 . -34) T) ((-1174 . -1085) 160104) ((-1174 . -1070) 160000) ((-1174 . -635) 159918) ((-1174 . -426) 159902) ((-1174 . -660) 159850) ((-1174 . -670) 159788) ((-1174 . -390) 159772) ((-1174 . -240) 159751) ((-1174 . -236) 159696) ((-1174 . -239) 159647) ((-1174 . -274) 159631) ((-1174 . -922) 159552) ((-1174 . -930) 159475) ((-1174 . -928) 159434) ((-1174 . -234) 159418) ((-1174 . -739) 159350) ((-1174 . -662) 159282) ((-1174 . -668) 159241) ((-1174 . -133) T) ((-1174 . -25) T) ((-1174 . -102) T) ((-1174 . -1249) T) ((-1174 . -632) 159203) ((-1174 . -1133) T) ((-1174 . -23) T) ((-1174 . -21) T) ((-1174 . -1088) 159187) ((-1174 . -1083) 159171) ((-1174 . -111) 159150) ((-1174 . -1081) T) ((-1174 . -1089) T) ((-1174 . -1144) T) ((-1174 . -748) T) ((-1174 . -38) 159110) ((-1174 . -633) 159071) ((-1173 . -1042) 159042) ((-1173 . -34) T) ((-1173 . -1249) T) ((-1173 . -102) T) ((-1173 . -632) 159024) ((-1173 . -321) 158950) ((-1173 . -528) 158869) ((-1173 . -1133) T) ((-1173 . -503) 158840) ((-1172 . -1133) T) ((-1172 . -632) 158822) ((-1172 . -1249) T) ((-1172 . -102) T) ((-1167 . -1169) T) ((-1167 . -1295) T) ((-1167 . -93) T) ((-1167 . -102) T) ((-1167 . -1249) T) ((-1167 . -632) 158788) ((-1167 . -1133) T) ((-1167 . -635) 158769) ((-1167 . -504) 158750) ((-1167 . -1115) T) ((-1165 . -1166) 158734) ((-1165 . -102) T) ((-1165 . -1249) T) ((-1165 . -632) 158716) ((-1165 . -1133) T) ((-1158 . -762) 158695) ((-1158 . -35) 158661) ((-1158 . -95) 158627) ((-1158 . -296) 158593) ((-1158 . -507) 158559) ((-1158 . -1238) 158525) ((-1158 . -1235) 158491) ((-1158 . -1034) 158457) ((-1158 . -47) 158429) ((-1158 . -38) 158326) ((-1158 . -662) 158223) ((-1158 . -739) 158120) ((-1158 . -635) 158002) ((-1158 . -302) 157981) ((-1158 . -571) 157960) ((-1158 . -111) 157829) ((-1158 . -1083) 157712) ((-1158 . -1088) 157595) ((-1158 . -175) 157546) ((-1158 . -149) 157525) ((-1158 . -147) 157504) ((-1158 . -670) 157429) ((-1158 . -668) 157339) ((-1158 . -1005) 157306) ((-1158 . -930) 157290) ((-1158 . -1249) T) ((-1158 . -922) 157272) ((-1158 . -1081) T) ((-1158 . -1089) T) ((-1158 . -1144) T) ((-1158 . -748) T) ((-1158 . -21) T) ((-1158 . -23) T) ((-1158 . -1133) T) ((-1158 . -632) 157254) ((-1158 . -102) T) ((-1158 . -25) T) ((-1158 . -133) T) ((-1158 . -928) 157238) ((-1158 . -528) 157208) ((-1158 . -321) 157195) ((-1157 . -980) 157162) ((-1157 . -635) 156954) ((-1157 . -1070) 156837) ((-1157 . -1254) 156816) ((-1157 . -940) 156795) ((-1157 . -912) 156654) ((-1157 . -930) 156638) ((-1157 . -922) 156620) ((-1157 . -928) 156604) ((-1157 . -528) 156556) ((-1157 . -466) 156507) ((-1157 . -660) 156455) ((-1157 . -670) 156344) ((-1157 . -390) 156328) ((-1157 . -47) 156300) ((-1157 . -38) 156149) ((-1157 . -662) 155998) ((-1157 . -739) 155847) ((-1157 . -302) 155778) ((-1157 . -571) 155709) ((-1157 . -111) 155538) ((-1157 . -1083) 155381) ((-1157 . -1088) 155224) ((-1157 . -175) 155135) ((-1157 . -149) 155114) ((-1157 . -147) 155093) ((-1157 . -668) 155003) ((-1157 . -133) T) ((-1157 . -25) T) ((-1157 . -102) T) ((-1157 . -1249) T) ((-1157 . -632) 154985) ((-1157 . -1133) T) ((-1157 . -23) T) ((-1157 . -21) T) ((-1157 . -1081) T) ((-1157 . -1089) T) ((-1157 . -1144) T) ((-1157 . -748) T) ((-1157 . -426) 154969) ((-1157 . -338) 154941) ((-1157 . -321) 154928) ((-1157 . -633) 154676) ((-1152 . -559) T) ((-1152 . -1254) T) ((-1152 . -1184) T) ((-1152 . -1070) 154658) ((-1152 . -633) 154573) ((-1152 . -1052) T) ((-1152 . -912) 154555) ((-1152 . -871) T) ((-1152 . -821) T) ((-1152 . -818) T) ((-1152 . -875) T) ((-1152 . -872) T) ((-1152 . -816) T) ((-1152 . -814) T) ((-1152 . -844) T) ((-1152 . -670) 154527) ((-1152 . -660) 154509) ((-1152 . -951) T) ((-1152 . -571) T) ((-1152 . -302) T) ((-1152 . -175) T) ((-1152 . -635) 154481) ((-1152 . -739) 154468) ((-1152 . -662) 154455) ((-1152 . -1088) 154442) ((-1152 . -1083) 154429) ((-1152 . -111) 154414) ((-1152 . -38) 154401) ((-1152 . -466) T) ((-1152 . -319) T) ((-1152 . -239) T) ((-1152 . -236) 154388) ((-1152 . -240) T) ((-1152 . -145) T) ((-1152 . -1081) T) ((-1152 . -1089) T) ((-1152 . -1144) T) ((-1152 . -748) T) ((-1152 . -21) T) ((-1152 . -668) 154360) ((-1152 . -23) T) ((-1152 . -1133) T) ((-1152 . -632) 154342) ((-1152 . -1249) T) ((-1152 . -102) T) ((-1152 . -25) T) ((-1152 . -133) T) ((-1152 . -149) T) ((-1152 . -868) T) ((-1152 . -381) T) ((-1152 . -113) T) ((-1152 . -684) T) ((-1152 . -845) T) ((-1148 . -1115) T) ((-1148 . -504) 154323) ((-1148 . -632) 154289) ((-1148 . -635) 154270) ((-1148 . -1133) T) ((-1148 . -1249) T) ((-1148 . -102) T) ((-1148 . -93) T) ((-1147 . -1133) T) ((-1147 . -632) 154252) ((-1147 . -1249) T) ((-1147 . -102) T) ((-1145 . -245) 154231) ((-1145 . -1307) 154201) ((-1145 . -821) 154180) ((-1145 . -818) 154159) ((-1145 . -875) 154110) ((-1145 . -872) 154061) ((-1145 . -816) 154040) ((-1145 . -817) 154019) ((-1145 . -739) 153961) ((-1145 . -662) 153883) ((-1145 . -300) 153860) ((-1145 . -298) 153837) ((-1145 . -503) 153821) ((-1145 . -528) 153754) ((-1145 . -321) 153692) ((-1145 . -34) T) ((-1145 . -618) 153669) ((-1145 . -1070) 153496) ((-1145 . -635) 153294) ((-1145 . -426) 153263) ((-1145 . -660) 153169) ((-1145 . -670) 153002) ((-1145 . -390) 152971) ((-1145 . -381) 152950) ((-1145 . -240) 152902) ((-1145 . -668) 152681) ((-1145 . -748) 152659) ((-1145 . -1144) 152637) ((-1145 . -1089) 152615) ((-1145 . -1081) 152593) ((-1145 . -236) 152484) ((-1145 . -239) 152381) ((-1145 . -274) 152350) ((-1145 . -922) 152217) ((-1145 . -930) 152086) ((-1145 . -928) 152018) ((-1145 . -234) 151987) ((-1145 . -632) 151680) ((-1145 . -1088) 151601) ((-1145 . -1083) 151502) ((-1145 . -111) 151418) ((-1145 . -133) 151289) ((-1145 . -25) 151122) ((-1145 . -102) 150854) ((-1145 . -1249) T) ((-1145 . -1133) 150606) ((-1145 . -23) 150458) ((-1145 . -21) 150369) ((-1138 . -410) T) ((-1138 . -1249) T) ((-1138 . -632) 150351) ((-1137 . -1136) 150315) ((-1137 . -102) T) ((-1137 . -632) 150297) ((-1137 . -1133) T) ((-1137 . -298) 150253) ((-1137 . -1249) T) ((-1137 . -637) 150168) ((-1135 . -1136) 150120) ((-1135 . -102) T) ((-1135 . -632) 150102) ((-1135 . -1133) T) ((-1135 . -298) 150058) ((-1135 . -1249) T) ((-1135 . -637) 149961) ((-1134 . -381) T) ((-1134 . -102) T) ((-1134 . -1249) T) ((-1134 . -632) 149943) ((-1134 . -1133) T) ((-1129 . -440) 149927) ((-1129 . -1131) 149911) ((-1129 . -381) 149890) ((-1129 . -242) 149874) ((-1129 . -633) 149835) ((-1129 . -153) 149819) ((-1129 . -503) 149803) ((-1129 . -1133) T) ((-1129 . -528) 149736) ((-1129 . -321) 149674) ((-1129 . -632) 149656) ((-1129 . -102) T) ((-1129 . -1249) T) ((-1129 . -34) T) ((-1129 . -107) 149640) ((-1129 . -233) 149624) ((-1128 . -1115) T) ((-1128 . -504) 149605) ((-1128 . -632) 149571) ((-1128 . -635) 149552) ((-1128 . -1133) T) ((-1128 . -1249) T) ((-1128 . -102) T) ((-1128 . -93) T) ((-1124 . -1249) T) ((-1124 . -1133) 149522) ((-1124 . -632) 149481) ((-1124 . -102) 149451) ((-1123 . -1115) T) ((-1123 . -504) 149432) ((-1123 . -632) 149398) ((-1123 . -635) 149379) ((-1123 . -1133) T) ((-1123 . -1249) T) ((-1123 . -102) T) ((-1123 . -93) T) ((-1121 . -1126) 149363) ((-1121 . -637) 149347) ((-1121 . -1133) 149325) ((-1121 . -632) 149292) ((-1121 . -1249) 149270) ((-1121 . -102) 149248) ((-1121 . -1127) 149206) ((-1120 . -277) 149190) ((-1120 . -635) 149174) ((-1120 . -1070) 149158) ((-1120 . -875) T) ((-1120 . -102) T) ((-1120 . -1133) T) ((-1120 . -632) 149140) ((-1120 . -872) T) ((-1120 . -236) 149127) ((-1120 . -1249) T) ((-1120 . -239) T) ((-1119 . -262) 149064) ((-1119 . -635) 148800) ((-1119 . -1070) 148627) ((-1119 . -633) NIL) ((-1119 . -338) 148588) ((-1119 . -426) 148572) ((-1119 . -38) 148421) ((-1119 . -111) 148250) ((-1119 . -1083) 148093) ((-1119 . -1088) 147936) ((-1119 . -668) 147846) ((-1119 . -670) 147735) ((-1119 . -662) 147584) ((-1119 . -739) 147433) ((-1119 . -147) 147412) ((-1119 . -149) 147391) ((-1119 . -175) 147302) ((-1119 . -571) 147233) ((-1119 . -302) 147164) ((-1119 . -47) 147125) ((-1119 . -390) 147109) ((-1119 . -660) 147057) ((-1119 . -466) 147008) ((-1119 . -528) 146875) ((-1119 . -928) 146810) ((-1119 . -922) 146705) ((-1119 . -930) 146604) ((-1119 . -912) NIL) ((-1119 . -940) 146583) ((-1119 . -1254) 146562) ((-1119 . -980) 146507) ((-1119 . -321) 146494) ((-1119 . -240) 146473) ((-1119 . -133) T) ((-1119 . -25) T) ((-1119 . -102) T) ((-1119 . -632) 146455) ((-1119 . -1133) T) ((-1119 . -23) T) ((-1119 . -21) T) ((-1119 . -748) T) ((-1119 . -1144) T) ((-1119 . -1089) T) ((-1119 . -1081) T) ((-1119 . -236) 146400) ((-1119 . -1249) T) ((-1119 . -239) 146351) ((-1119 . -274) 146335) ((-1119 . -234) 146319) ((-1117 . -632) 146301) ((-1114 . -872) T) ((-1114 . -632) 146283) ((-1114 . -1133) T) ((-1114 . -102) T) ((-1114 . -1249) T) ((-1114 . -875) T) ((-1114 . -633) 146264) ((-1111 . -746) 146243) ((-1111 . -1070) 146139) ((-1111 . -426) 146123) ((-1111 . -660) 146071) ((-1111 . -670) 145945) ((-1111 . -390) 145929) ((-1111 . -383) 145908) ((-1111 . -149) 145887) ((-1111 . -635) 145705) ((-1111 . -739) 145573) ((-1111 . -662) 145441) ((-1111 . -668) 145336) ((-1111 . -1088) 145246) ((-1111 . -1083) 145156) ((-1111 . -111) 145052) ((-1111 . -38) 144920) ((-1111 . -424) 144899) ((-1111 . -416) 144878) ((-1111 . -147) 144829) ((-1111 . -1184) 144808) ((-1111 . -363) 144787) ((-1111 . -381) 144738) ((-1111 . -250) 144689) ((-1111 . -302) 144640) ((-1111 . -319) 144591) ((-1111 . -466) 144542) ((-1111 . -571) 144493) ((-1111 . -951) 144444) ((-1111 . -1254) 144395) ((-1111 . -376) 144346) ((-1111 . -240) 144271) ((-1111 . -236) 144144) ((-1111 . -239) 144023) ((-1111 . -274) 143993) ((-1111 . -922) 143862) ((-1111 . -930) 143733) ((-1111 . -928) 143666) ((-1111 . -234) 143636) ((-1111 . -633) 143620) ((-1111 . -21) T) ((-1111 . -23) T) ((-1111 . -1133) T) ((-1111 . -632) 143602) ((-1111 . -1249) T) ((-1111 . -102) T) ((-1111 . -25) T) ((-1111 . -133) T) ((-1111 . -1081) T) ((-1111 . -1089) T) ((-1111 . -1144) T) ((-1111 . -748) T) ((-1111 . -175) T) ((-1109 . -1133) T) ((-1109 . -632) 143584) ((-1109 . -1249) T) ((-1109 . -102) T) ((-1109 . -298) 143563) ((-1108 . -1133) T) ((-1108 . -632) 143545) ((-1108 . -1249) T) ((-1108 . -102) T) ((-1107 . -1133) T) ((-1107 . -632) 143527) ((-1107 . -1249) T) ((-1107 . -102) T) ((-1107 . -298) 143506) ((-1107 . -1070) 143483) ((-1107 . -635) 143460) ((-1106 . -1249) T) ((-1105 . -1115) T) ((-1105 . -504) 143441) ((-1105 . -632) 143407) ((-1105 . -635) 143388) ((-1105 . -1133) T) ((-1105 . -1249) T) ((-1105 . -102) T) ((-1105 . -93) T) ((-1098 . -1115) T) ((-1098 . -504) 143369) ((-1098 . -632) 143335) ((-1098 . -635) 143316) ((-1098 . -1133) T) ((-1098 . -1249) T) ((-1098 . -102) T) ((-1098 . -93) T) ((-1095 . -1226) 143291) ((-1095 . -233) 143237) ((-1095 . -107) 143183) ((-1095 . -321) 143034) ((-1095 . -528) 142878) ((-1095 . -503) 142809) ((-1095 . -153) 142755) ((-1095 . -633) NIL) ((-1095 . -242) 142701) ((-1095 . -629) 142676) ((-1095 . -300) 142651) ((-1095 . -1249) T) ((-1095 . -298) 142626) ((-1095 . -1133) T) ((-1095 . -632) 142608) ((-1095 . -102) T) ((-1095 . -34) T) ((-1095 . -618) 142583) ((-1094 . -559) T) ((-1094 . -1254) T) ((-1094 . -1184) T) ((-1094 . -1070) 142565) ((-1094 . -633) 142480) ((-1094 . -1052) T) ((-1094 . -912) 142462) ((-1094 . -871) T) ((-1094 . -821) T) ((-1094 . -818) T) ((-1094 . -875) T) ((-1094 . -872) T) ((-1094 . -816) T) ((-1094 . -814) T) ((-1094 . -844) T) ((-1094 . -670) 142434) ((-1094 . -660) 142416) ((-1094 . -951) T) ((-1094 . -571) T) ((-1094 . -302) T) ((-1094 . -175) T) ((-1094 . -635) 142388) ((-1094 . -739) 142375) ((-1094 . -662) 142362) ((-1094 . -1088) 142349) ((-1094 . -1083) 142336) ((-1094 . -111) 142321) ((-1094 . -38) 142308) ((-1094 . -466) T) ((-1094 . -319) T) ((-1094 . -239) T) ((-1094 . -236) 142295) ((-1094 . -240) T) ((-1094 . -145) T) ((-1094 . -1081) T) ((-1094 . -1089) T) ((-1094 . -1144) T) ((-1094 . -748) T) ((-1094 . -21) T) ((-1094 . -668) 142267) ((-1094 . -23) T) ((-1094 . -1133) T) ((-1094 . -632) 142249) ((-1094 . -1249) T) ((-1094 . -102) T) ((-1094 . -25) T) ((-1094 . -133) T) ((-1094 . -149) T) ((-1094 . -637) 142230) ((-1093 . -1100) 142209) ((-1093 . -102) T) ((-1093 . -1249) T) ((-1093 . -632) 142191) ((-1093 . -1133) T) ((-1090 . -1249) T) ((-1090 . -1133) 142169) ((-1090 . -632) 142136) ((-1090 . -102) 142114) ((-1086 . -1085) 142054) ((-1086 . -662) 141996) ((-1086 . -739) 141938) ((-1086 . -34) T) ((-1086 . -321) 141876) ((-1086 . -528) 141809) ((-1086 . -503) 141793) ((-1086 . -670) 141777) ((-1086 . -668) 141746) ((-1086 . -133) T) ((-1086 . -25) T) ((-1086 . -102) T) ((-1086 . -1249) T) ((-1086 . -632) 141708) ((-1086 . -1133) T) ((-1086 . -23) T) ((-1086 . -21) T) ((-1086 . -1088) 141692) ((-1086 . -1083) 141676) ((-1086 . -111) 141655) ((-1086 . -1307) 141625) ((-1086 . -633) 141586) ((-1078 . -1103) 141515) ((-1078 . -1008) 141444) ((-1078 . -633) 141386) ((-1078 . -503) 141351) ((-1078 . -1133) T) ((-1078 . -528) 141252) ((-1078 . -321) 141160) ((-1078 . -632) 141103) ((-1078 . -102) T) ((-1078 . -1249) T) ((-1078 . -34) T) ((-1078 . -153) 141068) ((-1078 . -1244) 140997) ((-1068 . -1115) T) ((-1068 . -504) 140978) ((-1068 . -632) 140944) ((-1068 . -635) 140925) ((-1068 . -1133) T) ((-1068 . -1249) T) ((-1068 . -102) T) ((-1068 . -93) T) ((-1067 . -1226) 140900) ((-1067 . -233) 140846) ((-1067 . -107) 140792) ((-1067 . -321) 140643) ((-1067 . -528) 140487) ((-1067 . -503) 140418) ((-1067 . -153) 140364) ((-1067 . -633) NIL) ((-1067 . -242) 140310) ((-1067 . -629) 140285) ((-1067 . -300) 140260) ((-1067 . -1249) T) ((-1067 . -298) 140235) ((-1067 . -1133) T) ((-1067 . -632) 140217) ((-1067 . -102) T) ((-1067 . -34) T) ((-1067 . -618) 140192) ((-1066 . -175) T) ((-1066 . -635) 140161) ((-1066 . -748) T) ((-1066 . -1144) T) ((-1066 . -1089) T) ((-1066 . -1081) T) ((-1066 . -670) 140135) ((-1066 . -668) 140094) ((-1066 . -133) T) ((-1066 . -25) T) ((-1066 . -102) T) ((-1066 . -1249) T) ((-1066 . -632) 140076) ((-1066 . -1133) T) ((-1066 . -23) T) ((-1066 . -21) T) ((-1066 . -1088) 140050) ((-1066 . -1083) 140024) ((-1066 . -111) 139991) ((-1066 . -38) 139975) ((-1066 . -662) 139959) ((-1066 . -739) 139943) ((-1059 . -1103) 139912) ((-1059 . -1008) 139881) ((-1059 . -633) 139842) ((-1059 . -503) 139826) ((-1059 . -1133) T) ((-1059 . -528) 139759) ((-1059 . -321) 139697) ((-1059 . -632) 139659) ((-1059 . -102) T) ((-1059 . -1249) T) ((-1059 . -34) T) ((-1059 . -153) 139643) ((-1059 . -1244) 139612) ((-1058 . -1249) T) ((-1058 . -1133) 139590) ((-1058 . -632) 139557) ((-1058 . -102) 139535) ((-1056 . -1044) T) ((-1056 . -1034) T) ((-1056 . -814) T) ((-1056 . -816) T) ((-1056 . -872) T) ((-1056 . -875) T) ((-1056 . -818) T) ((-1056 . -821) T) ((-1056 . -871) T) ((-1056 . -1070) 139415) ((-1056 . -426) 139377) ((-1056 . -250) T) ((-1056 . -302) T) ((-1056 . -319) T) ((-1056 . -466) T) ((-1056 . -38) 139314) ((-1056 . -662) 139251) ((-1056 . -739) 139188) ((-1056 . -635) 139125) ((-1056 . -571) T) ((-1056 . -951) T) ((-1056 . -1254) T) ((-1056 . -376) T) ((-1056 . -111) 139041) ((-1056 . -1083) 138978) ((-1056 . -1088) 138915) ((-1056 . -175) T) ((-1056 . -149) T) ((-1056 . -670) 138852) ((-1056 . -668) 138789) ((-1056 . -133) T) ((-1056 . -25) T) ((-1056 . -102) T) ((-1056 . -1249) T) ((-1056 . -632) 138771) ((-1056 . -1133) T) ((-1056 . -23) T) ((-1056 . -21) T) ((-1056 . -1081) T) ((-1056 . -1089) T) ((-1056 . -1144) T) ((-1056 . -748) T) ((-1051 . -1115) T) ((-1051 . -504) 138752) ((-1051 . -632) 138718) ((-1051 . -635) 138699) ((-1051 . -1133) T) ((-1051 . -1249) T) ((-1051 . -102) T) ((-1051 . -93) T) ((-1036 . -1023) 138681) ((-1036 . -1184) T) ((-1036 . -635) 138631) ((-1036 . -1070) 138591) ((-1036 . -633) 138521) ((-1036 . -1052) T) ((-1036 . -940) NIL) ((-1036 . -910) 138503) ((-1036 . -871) T) ((-1036 . -821) T) ((-1036 . -818) T) ((-1036 . -875) T) ((-1036 . -872) T) ((-1036 . -816) T) ((-1036 . -814) T) ((-1036 . -844) T) ((-1036 . -912) 138485) ((-1036 . -414) 138467) ((-1036 . -660) 138449) ((-1036 . -390) 138431) ((-1036 . -298) NIL) ((-1036 . -321) NIL) ((-1036 . -528) NIL) ((-1036 . -351) 138413) ((-1036 . -250) T) ((-1036 . -111) 138347) ((-1036 . -1083) 138297) ((-1036 . -1088) 138247) ((-1036 . -302) T) ((-1036 . -739) 138197) ((-1036 . -662) 138147) ((-1036 . -670) 138097) ((-1036 . -668) 138047) ((-1036 . -38) 137997) ((-1036 . -319) T) ((-1036 . -466) T) ((-1036 . -175) T) ((-1036 . -571) T) ((-1036 . -951) T) ((-1036 . -1254) T) ((-1036 . -376) T) ((-1036 . -240) T) ((-1036 . -236) 137984) ((-1036 . -239) T) ((-1036 . -274) 137966) ((-1036 . -922) NIL) ((-1036 . -930) NIL) ((-1036 . -928) NIL) ((-1036 . -234) 137948) ((-1036 . -149) T) ((-1036 . -147) NIL) ((-1036 . -133) T) ((-1036 . -25) T) ((-1036 . -102) T) ((-1036 . -1249) T) ((-1036 . -632) 137908) ((-1036 . -1133) T) ((-1036 . -23) T) ((-1036 . -21) T) ((-1036 . -1081) T) ((-1036 . -1089) T) ((-1036 . -1144) T) ((-1036 . -748) T) ((-1035 . -355) 137882) ((-1035 . -175) T) ((-1035 . -635) 137812) ((-1035 . -748) T) ((-1035 . -1144) T) ((-1035 . -1089) T) ((-1035 . -1081) T) ((-1035 . -670) 137719) ((-1035 . -668) 137649) ((-1035 . -133) T) ((-1035 . -25) T) ((-1035 . -102) T) ((-1035 . -1249) T) ((-1035 . -632) 137631) ((-1035 . -1133) T) ((-1035 . -23) T) ((-1035 . -21) T) ((-1035 . -1088) 137576) ((-1035 . -1083) 137521) ((-1035 . -111) 137450) ((-1035 . -633) 137434) ((-1035 . -234) 137411) ((-1035 . -928) 137363) ((-1035 . -930) 137272) ((-1035 . -922) 137179) ((-1035 . -274) 137156) ((-1035 . -239) 137093) ((-1035 . -236) 137024) ((-1035 . -240) 136996) ((-1035 . -376) T) ((-1035 . -1254) T) ((-1035 . -951) T) ((-1035 . -571) T) ((-1035 . -739) 136941) ((-1035 . -662) 136886) ((-1035 . -38) 136831) ((-1035 . -466) T) ((-1035 . -319) T) ((-1035 . -302) T) ((-1035 . -250) T) ((-1035 . -381) NIL) ((-1035 . -363) NIL) ((-1035 . -1184) NIL) ((-1035 . -147) 136803) ((-1035 . -416) NIL) ((-1035 . -424) 136775) ((-1035 . -149) 136747) ((-1035 . -383) 136719) ((-1035 . -390) 136696) ((-1035 . -660) 136635) ((-1035 . -426) 136612) ((-1035 . -1070) 136500) ((-1035 . -746) 136472) ((-1032 . -1027) 136456) ((-1032 . -503) 136440) ((-1032 . -1133) 136418) ((-1032 . -528) 136351) ((-1032 . -321) 136289) ((-1032 . -632) 136221) ((-1032 . -102) 136171) ((-1032 . -1249) T) ((-1032 . -34) T) ((-1032 . -107) 136155) ((-1028 . -1030) 136139) ((-1028 . -875) 136118) ((-1028 . -872) 136097) ((-1028 . -1070) 135993) ((-1028 . -426) 135977) ((-1028 . -660) 135925) ((-1028 . -670) 135827) ((-1028 . -390) 135811) ((-1028 . -298) 135769) ((-1028 . -321) 135734) ((-1028 . -528) 135646) ((-1028 . -351) 135630) ((-1028 . -38) 135578) ((-1028 . -111) 135460) ((-1028 . -1083) 135356) ((-1028 . -1088) 135252) ((-1028 . -668) 135175) ((-1028 . -662) 135123) ((-1028 . -739) 135071) ((-1028 . -635) 134961) ((-1028 . -302) 134912) ((-1028 . -250) 134891) ((-1028 . -240) 134870) ((-1028 . -236) 134815) ((-1028 . -239) 134766) ((-1028 . -274) 134750) ((-1028 . -922) 134671) ((-1028 . -930) 134594) ((-1028 . -928) 134553) ((-1028 . -234) 134537) ((-1028 . -633) 134498) ((-1028 . -149) 134477) ((-1028 . -147) 134456) ((-1028 . -133) T) ((-1028 . -25) T) ((-1028 . -102) T) ((-1028 . -1249) T) ((-1028 . -632) 134438) ((-1028 . -1133) T) ((-1028 . -23) T) ((-1028 . -21) T) ((-1028 . -1081) T) ((-1028 . -1089) T) ((-1028 . -1144) T) ((-1028 . -748) T) ((-1026 . -1115) T) ((-1026 . -504) 134419) ((-1026 . -632) 134385) ((-1026 . -635) 134366) ((-1026 . -1133) T) ((-1026 . -1249) T) ((-1026 . -102) T) ((-1026 . -93) T) ((-1025 . -21) T) ((-1025 . -668) 134348) ((-1025 . -23) T) ((-1025 . -1133) T) ((-1025 . -632) 134330) ((-1025 . -1249) T) ((-1025 . -102) T) ((-1025 . -25) T) ((-1025 . -133) T) ((-1025 . -298) 134297) ((-1021 . -632) 134279) ((-1018 . -1133) T) ((-1018 . -632) 134261) ((-1018 . -1249) T) ((-1018 . -102) T) ((-1003 . -821) T) ((-1003 . -818) T) ((-1003 . -875) T) ((-1003 . -872) T) ((-1003 . -816) T) ((-1003 . -23) T) ((-1003 . -1133) T) ((-1003 . -632) 134221) ((-1003 . -1249) T) ((-1003 . -102) T) ((-1003 . -25) T) ((-1003 . -133) T) ((-1002 . -1115) T) ((-1002 . -504) 134202) ((-1002 . -632) 134168) ((-1002 . -635) 134149) ((-1002 . -1133) T) ((-1002 . -1249) T) ((-1002 . -102) T) ((-1002 . -93) T) ((-998 . -1249) T) ((-997 . -1249) T) ((-996 . -999) T) ((-996 . -102) T) ((-996 . -632) 134131) ((-996 . -1133) T) ((-996 . -684) T) ((-996 . -1249) T) ((-996 . -113) T) ((-996 . -635) 134115) ((-995 . -632) 134097) ((-994 . -1133) T) ((-994 . -632) 134079) ((-994 . -1249) T) ((-994 . -102) T) ((-994 . -381) 134032) ((-994 . -748) 133931) ((-994 . -1144) 133830) ((-994 . -23) 133641) ((-994 . -25) 133452) ((-994 . -133) 133307) ((-994 . -487) 133260) ((-994 . -21) 133215) ((-994 . -668) 133159) ((-994 . -817) 133112) ((-994 . -816) 133065) ((-994 . -872) 132964) ((-994 . -875) 132863) ((-994 . -818) 132816) ((-994 . -821) 132769) ((-988 . -19) 132753) ((-988 . -673) 132737) ((-988 . -300) 132714) ((-988 . -298) 132666) ((-988 . -618) 132643) ((-988 . -633) 132604) ((-988 . -503) 132588) ((-988 . -1133) 132538) ((-988 . -528) 132471) ((-988 . -321) 132409) ((-988 . -632) 132321) ((-988 . -102) 132251) ((-988 . -1249) T) ((-988 . -34) T) ((-988 . -153) 132235) ((-988 . -872) 132214) ((-988 . -875) 132193) ((-988 . -385) 132177) ((-986 . -338) 132156) ((-986 . -1070) 132052) ((-986 . -426) 132036) ((-986 . -38) 131933) ((-986 . -635) 131786) 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. -739) 129533) ((-976 . -302) 129464) ((-976 . -571) 129395) ((-976 . -111) 129224) ((-976 . -1083) 129067) ((-976 . -1088) 128910) ((-976 . -175) 128821) ((-976 . -149) 128800) ((-976 . -147) 128779) ((-976 . -668) 128689) ((-976 . -133) T) ((-976 . -25) T) ((-976 . -102) T) ((-976 . -1249) T) ((-976 . -632) 128671) ((-976 . -1133) T) ((-976 . -23) T) ((-976 . -21) T) ((-976 . -1081) T) ((-976 . -1089) T) ((-976 . -1144) T) ((-976 . -748) T) ((-976 . -426) 128655) ((-976 . -338) 128624) ((-976 . -321) 128611) ((-976 . -633) 128472) ((-973 . -1012) 128456) ((-973 . -19) 128440) ((-973 . -673) 128424) ((-973 . -300) 128401) ((-973 . -298) 128353) ((-973 . -618) 128330) ((-973 . -633) 128291) ((-973 . -503) 128275) ((-973 . -1133) 128225) ((-973 . -528) 128158) ((-973 . -321) 128096) ((-973 . -632) 128008) ((-973 . -102) 127938) ((-973 . -1249) T) ((-973 . -34) T) ((-973 . -153) 127922) ((-973 . -872) 127901) ((-973 . -875) 127880) ((-973 . -385) 127864) ((-973 . -1298) 127848) ((-973 . 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122793) ((-894 . -1083) 122780) ((-894 . -111) 122765) ((-894 . -38) 122752) ((-894 . -466) T) ((-894 . -319) T) ((-894 . -1081) T) ((-894 . -1089) T) ((-894 . -1144) T) ((-894 . -748) T) ((-894 . -21) T) ((-894 . -668) 122724) ((-894 . -23) T) ((-894 . -1133) T) ((-894 . -632) 122706) ((-894 . -1249) T) ((-894 . -102) T) ((-894 . -25) T) ((-894 . -133) T) ((-894 . -670) 122693) ((-894 . -149) T) ((-891 . -1081) T) ((-891 . -1089) T) ((-891 . -1144) T) ((-891 . -748) T) ((-891 . -21) T) ((-891 . -668) 122638) ((-891 . -23) T) ((-891 . -1133) T) ((-891 . -632) 122600) ((-891 . -1249) T) ((-891 . -102) T) ((-891 . -25) T) ((-891 . -133) T) ((-891 . -670) 122560) ((-891 . -635) 122495) ((-891 . -504) 122472) ((-891 . -38) 122442) ((-891 . -111) 122407) ((-891 . -1083) 122377) ((-891 . -1088) 122347) ((-891 . -662) 122317) ((-891 . -739) 122287) ((-890 . -1133) T) ((-890 . -632) 122269) ((-890 . -1249) T) ((-890 . -102) T) ((-889 . -868) T) ((-889 . -875) T) ((-889 . -872) T) ((-889 . 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121374) ((-879 . -670) 121348) ((-879 . -668) 121307) ((-879 . -133) T) ((-879 . -25) T) ((-879 . -102) T) ((-879 . -1249) T) ((-879 . -632) 121289) ((-879 . -1133) T) ((-879 . -23) T) ((-879 . -21) T) ((-879 . -1088) 121273) ((-879 . -1083) 121257) ((-879 . -111) 121236) ((-879 . -1081) T) ((-879 . -1089) T) ((-879 . -1144) T) ((-879 . -748) T) ((-879 . -38) 121206) ((-873 . -875) T) ((-873 . -1249) T) ((-873 . -102) T) ((-873 . -504) 121190) ((-873 . -632) 121138) ((-873 . -635) 121122) ((-866 . -1133) T) ((-866 . -632) 121104) ((-866 . -1249) T) ((-866 . -102) T) ((-866 . -426) 121088) ((-866 . -635) 120956) ((-866 . -1070) 120852) ((-866 . -21) 120804) ((-866 . -668) 120721) ((-866 . -23) 120673) ((-866 . -25) 120625) ((-866 . -133) 120577) ((-866 . -871) 120556) ((-866 . -670) 120529) ((-866 . -1089) 120508) ((-866 . -1081) 120487) ((-866 . -821) 120466) ((-866 . -818) 120445) ((-866 . -875) 120424) ((-866 . -872) 120403) ((-866 . -816) 120382) ((-866 . -814) 120361) ((-866 . 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119282) ((-856 . -871) 119261) ((-856 . -670) 119234) ((-856 . -1089) 119213) ((-856 . -1081) 119192) ((-856 . -821) 119171) ((-856 . -818) 119150) ((-856 . -875) 119129) ((-856 . -872) 119108) ((-856 . -816) 119087) ((-856 . -814) 119066) ((-856 . -1144) 119045) ((-856 . -748) 119024) ((-852 . -730) 119008) ((-852 . -635) 118963) ((-852 . -739) 118933) ((-852 . -662) 118903) ((-852 . -670) 118877) ((-852 . -668) 118836) ((-852 . -133) T) ((-852 . -25) T) ((-852 . -102) T) ((-852 . -1249) T) ((-852 . -632) 118818) ((-852 . -1133) T) ((-852 . -23) T) ((-852 . -21) T) ((-852 . -1088) 118802) ((-852 . -1083) 118786) ((-852 . -111) 118765) ((-852 . -1081) T) ((-852 . -1089) T) ((-852 . -1144) T) ((-852 . -748) T) ((-852 . -38) 118735) ((-852 . -240) 118714) ((-852 . -236) 118687) ((-852 . -239) 118666) ((-850 . -1133) T) ((-850 . -632) 118648) ((-850 . -1249) T) ((-850 . -102) T) ((-849 . -1133) T) ((-849 . -632) 118630) ((-849 . -1249) T) ((-849 . -102) T) ((-848 . -1133) T) ((-848 . -632) 118612) ((-848 . -1249) T) ((-848 . -102) T) ((-843 . -399) 118596) ((-843 . -635) 118580) ((-843 . -1070) 118564) ((-843 . -875) T) ((-843 . -872) T) ((-843 . -1144) T) ((-843 . -102) T) ((-843 . -1249) T) ((-843 . -632) 118546) ((-843 . -1133) T) ((-843 . -748) T) ((-843 . -870) T) ((-843 . -882) T) ((-842 . -277) 118530) ((-842 . -635) 118514) ((-842 . -1070) 118498) ((-842 . -875) T) ((-842 . -102) T) ((-842 . -1133) T) ((-842 . -632) 118480) ((-842 . -872) T) ((-842 . -236) 118467) ((-842 . -1249) T) ((-842 . -239) T) ((-841 . -111) 118409) ((-841 . -1083) 118360) ((-841 . -1088) 118311) ((-841 . -21) T) ((-841 . -668) 118247) ((-841 . -23) T) ((-841 . -1133) T) ((-841 . -632) 118216) ((-841 . -1249) T) ((-841 . -102) T) ((-841 . -25) T) ((-841 . -133) T) ((-841 . -670) 118167) ((-841 . -240) T) ((-841 . -635) 118081) ((-841 . -748) T) ((-841 . -1144) T) ((-841 . -1089) T) ((-841 . -1081) T) ((-841 . -236) 118068) ((-841 . -239) T) ((-841 . -504) 118052) ((-841 . -376) 118031) ((-841 . -1254) 118010) ((-841 . -951) 117989) ((-841 . -571) 117968) ((-841 . -175) 117947) ((-841 . -739) 117889) ((-841 . -662) 117831) ((-841 . -38) 117773) ((-841 . -466) 117752) ((-841 . -319) 117731) ((-841 . -302) 117710) ((-841 . -250) 117689) ((-840 . -262) 117628) ((-840 . -635) 117365) ((-840 . -1070) 117193) ((-840 . -633) NIL) ((-840 . -338) 117155) ((-840 . -426) 117139) ((-840 . -38) 116988) ((-840 . -111) 116817) ((-840 . -1083) 116660) ((-840 . -1088) 116503) ((-840 . -668) 116413) ((-840 . -670) 116302) ((-840 . -662) 116151) ((-840 . -739) 116000) ((-840 . -147) 115979) ((-840 . -149) 115958) ((-840 . -175) 115869) ((-840 . -571) 115800) ((-840 . -302) 115731) ((-840 . -47) 115693) ((-840 . -390) 115677) ((-840 . -660) 115625) ((-840 . -466) 115576) ((-840 . -528) 115444) ((-840 . -928) 115380) ((-840 . -922) 115276) ((-840 . -930) 115176) ((-840 . -912) NIL) ((-840 . -940) 115155) ((-840 . -1254) 115134) ((-840 . -980) 115081) ((-840 . -321) 115068) ((-840 . -240) 115047) ((-840 . -133) T) ((-840 . -25) T) ((-840 . -102) T) ((-840 . -632) 115029) ((-840 . -1133) T) ((-840 . -23) T) ((-840 . -21) T) ((-840 . -748) T) ((-840 . -1144) T) ((-840 . -1089) T) ((-840 . -1081) T) ((-840 . -236) 114974) ((-840 . -1249) T) ((-840 . -239) 114925) ((-840 . -274) 114909) ((-840 . -234) 114893) ((-839 . -245) 114872) ((-839 . -1307) 114842) ((-839 . -821) 114821) ((-839 . -818) 114800) ((-839 . -875) 114751) ((-839 . -872) 114702) ((-839 . -816) 114681) ((-839 . -817) 114660) ((-839 . -739) 114602) ((-839 . -662) 114524) ((-839 . -300) 114501) ((-839 . -298) 114478) ((-839 . -503) 114462) ((-839 . -528) 114395) ((-839 . -321) 114333) ((-839 . -34) T) ((-839 . -618) 114310) ((-839 . -1070) 114137) ((-839 . -635) 113935) ((-839 . -426) 113904) ((-839 . -660) 113810) ((-839 . -670) 113643) ((-839 . -390) 113612) ((-839 . -381) 113591) ((-839 . -240) 113543) ((-839 . -668) 113322) ((-839 . -748) 113300) ((-839 . -1144) 113278) ((-839 . -1089) 113256) ((-839 . -1081) 113234) ((-839 . -236) 113125) ((-839 . -239) 113022) ((-839 . -274) 112991) ((-839 . -922) 112858) ((-839 . -930) 112727) ((-839 . -928) 112659) ((-839 . -234) 112628) ((-839 . -632) 112321) ((-839 . -1088) 112242) ((-839 . -1083) 112143) ((-839 . -111) 112059) ((-839 . -133) 111930) ((-839 . -25) 111763) ((-839 . -102) 111495) ((-839 . -1249) T) ((-839 . -1133) 111247) ((-839 . -23) 111099) ((-839 . -21) 111010) ((-832 . -1133) T) ((-832 . -632) 110992) ((-832 . -1249) T) ((-832 . -102) T) ((-822 . -820) 110976) ((-822 . -875) 110955) ((-822 . -872) 110934) ((-822 . -1070) 110714) ((-822 . -635) 110560) ((-822 . -426) 110523) ((-822 . -298) 110481) ((-822 . -321) 110446) ((-822 . -528) 110358) ((-822 . -351) 110342) ((-822 . -381) 110321) ((-822 . -633) 110282) ((-822 . -149) 110261) ((-822 . -147) 110240) ((-822 . -739) 110224) ((-822 . -662) 110208) ((-822 . -670) 110182) ((-822 . -668) 110141) ((-822 . -133) T) ((-822 . -25) T) ((-822 . -102) T) ((-822 . -1249) T) ((-822 . -632) 110123) ((-822 . -1133) T) ((-822 . -23) T) ((-822 . -21) T) ((-822 . -1088) 110107) ((-822 . -1083) 110091) ((-822 . -111) 110070) ((-822 . -1081) T) ((-822 . -1089) T) ((-822 . -1144) T) ((-822 . -748) T) ((-822 . -38) 110054) ((-803 . -1275) 110038) ((-803 . -1184) 110016) ((-803 . -633) NIL) ((-803 . -321) 110003) ((-803 . -528) 109950) ((-803 . -338) 109927) ((-803 . -1070) 109786) ((-803 . -426) 109770) ((-803 . -38) 109599) ((-803 . -111) 109408) ((-803 . -1083) 109231) ((-803 . -1088) 109054) ((-803 . -668) 108964) ((-803 . -670) 108853) ((-803 . -662) 108682) ((-803 . -739) 108511) ((-803 . -635) 108259) ((-803 . -147) 108238) ((-803 . -149) 108217) ((-803 . -47) 108194) ((-803 . -390) 108178) ((-803 . -660) 108126) ((-803 . -928) 108069) ((-803 . -922) 107972) ((-803 . -930) 107879) ((-803 . -912) NIL) ((-803 . -940) 107858) ((-803 . -1254) 107837) ((-803 . -980) 107806) ((-803 . -951) 107785) ((-803 . -571) 107696) ((-803 . -302) 107607) ((-803 . -175) 107498) ((-803 . -466) 107429) ((-803 . -319) 107408) ((-803 . -298) 107335) ((-803 . -240) T) ((-803 . -133) T) ((-803 . -25) T) ((-803 . -102) T) ((-803 . -632) 107296) ((-803 . -1133) T) ((-803 . -23) T) ((-803 . -21) T) ((-803 . -748) T) ((-803 . -1144) T) ((-803 . -1089) T) ((-803 . -1081) T) ((-803 . -236) 107283) ((-803 . -1249) T) ((-803 . -239) T) ((-803 . -274) 107267) ((-803 . -234) 107251) ((-802 . -1097) 107218) ((-802 . -633) 106852) ((-802 . -321) 106839) ((-802 . -528) 106791) ((-802 . -338) 106763) ((-802 . -1070) 106620) ((-802 . -426) 106604) ((-802 . -38) 106453) ((-802 . -635) 106219) ((-802 . -670) 106108) ((-802 . -668) 106018) ((-802 . -748) T) ((-802 . -1144) T) ((-802 . -1089) T) ((-802 . -1081) T) ((-802 . -111) 105847) ((-802 . -1083) 105690) ((-802 . -1088) 105533) ((-802 . -21) T) ((-802 . -23) T) ((-802 . -1133) T) ((-802 . -632) 105447) ((-802 . -1249) T) ((-802 . -102) T) ((-802 . -25) T) ((-802 . -133) T) ((-802 . -662) 105296) ((-802 . -739) 105145) ((-802 . -147) 105124) ((-802 . -149) 105103) ((-802 . -175) 105014) ((-802 . -571) 104945) ((-802 . -302) 104876) ((-802 . -47) 104848) ((-802 . -390) 104832) ((-802 . -660) 104780) ((-802 . -466) 104731) ((-802 . -928) 104715) ((-802 . -922) 104697) ((-802 . -930) 104681) ((-802 . -912) 104540) ((-802 . -940) 104519) ((-802 . -1254) 104498) ((-802 . -980) 104465) ((-795 . -1133) T) ((-795 . -632) 104447) ((-795 . -1249) T) ((-795 . -102) T) ((-793 . -817) T) ((-793 . -133) T) ((-793 . -25) T) ((-793 . -102) T) ((-793 . -1249) T) ((-793 . -632) 104429) ((-793 . -1133) T) ((-793 . -23) T) ((-793 . -816) T) ((-793 . -872) T) ((-793 . -875) T) ((-793 . -818) T) ((-793 . -821) T) ((-793 . -748) T) ((-793 . -1144) T) ((-791 . -1133) T) ((-791 . -632) 104411) ((-791 . -1249) T) ((-791 . -102) T) ((-758 . -759) 104395) ((-758 . -1131) 104379) ((-758 . -242) 104363) ((-758 . -633) 104324) ((-758 . -153) 104308) ((-758 . -503) 104292) ((-758 . -1133) T) ((-758 . -528) 104225) ((-758 . -321) 104163) ((-758 . -632) 104145) ((-758 . -102) T) ((-758 . -1249) T) ((-758 . -34) T) ((-758 . -107) 104129) ((-758 . -717) 104113) ((-757 . -1081) T) ((-757 . -1089) T) ((-757 . -1144) T) ((-757 . -748) T) ((-757 . -21) T) ((-757 . -668) 104058) ((-757 . -23) T) ((-757 . -1133) T) ((-757 . -632) 104040) ((-757 . -1249) T) ((-757 . -102) T) ((-757 . -25) T) ((-757 . -133) T) ((-757 . -670) 104000) ((-757 . -635) 103956) ((-757 . -1070) 103927) ((-757 . -149) 103906) ((-757 . -147) 103885) ((-757 . -38) 103855) ((-757 . -111) 103820) ((-757 . -1083) 103790) ((-757 . -1088) 103760) ((-757 . -662) 103730) ((-757 . -739) 103700) ((-757 . -381) 103653) ((-753 . -980) 103606) ((-753 . -635) 103391) ((-753 . -1070) 103267) ((-753 . -1254) 103246) ((-753 . -940) 103225) ((-753 . -912) NIL) ((-753 . -930) 103202) ((-753 . -922) 103177) ((-753 . -928) 103154) ((-753 . -528) 103097) ((-753 . -466) 103048) ((-753 . -660) 102996) ((-753 . -670) 102885) ((-753 . -390) 102869) ((-753 . -47) 102834) ((-753 . -38) 102683) ((-753 . -662) 102532) ((-753 . -739) 102381) ((-753 . -302) 102312) ((-753 . -571) 102243) ((-753 . -111) 102072) ((-753 . -1083) 101915) ((-753 . -1088) 101758) ((-753 . -175) 101669) ((-753 . -149) 101648) ((-753 . -147) 101627) ((-753 . -668) 101537) ((-753 . -133) T) ((-753 . -25) T) ((-753 . -102) T) ((-753 . -1249) T) ((-753 . -632) 101519) ((-753 . -1133) T) ((-753 . -23) T) ((-753 . -21) T) ((-753 . -1081) T) ((-753 . -1089) T) ((-753 . -1144) T) ((-753 . -748) T) ((-753 . -426) 101503) ((-753 . -338) 101468) ((-753 . -321) 101455) ((-753 . -633) 101316) ((-740 . -487) T) ((-740 . -1144) T) ((-740 . -102) T) ((-740 . -1249) T) ((-740 . -632) 101298) ((-740 . -1133) T) ((-740 . -748) T) ((-737 . -1081) T) ((-737 . -1089) T) ((-737 . -1144) T) ((-737 . -748) T) ((-737 . -21) T) ((-737 . -668) 101270) ((-737 . -23) T) ((-737 . -1133) T) ((-737 . -632) 101252) ((-737 . -1249) T) ((-737 . -102) T) ((-737 . -25) T) ((-737 . -133) T) ((-737 . -670) 101239) ((-737 . -635) 101221) ((-736 . -1081) T) ((-736 . -1089) T) ((-736 . -1144) T) ((-736 . -748) T) ((-736 . -21) T) ((-736 . -668) 101166) ((-736 . -23) T) ((-736 . -1133) T) ((-736 . -632) 101148) ((-736 . -1249) T) ((-736 . -102) T) ((-736 . -25) T) ((-736 . -133) T) ((-736 . -670) 101108) ((-736 . -635) 101062) ((-736 . -1070) 101031) ((-736 . -298) 101010) ((-736 . -149) 100989) ((-736 . -147) 100968) ((-736 . -38) 100938) ((-736 . -111) 100903) ((-736 . -1083) 100873) ((-736 . -1088) 100843) ((-736 . -662) 100813) ((-736 . -739) 100783) ((-735 . -872) T) ((-735 . -632) 100718) ((-735 . -1133) T) ((-735 . -102) T) ((-735 . -1249) T) ((-735 . -875) T) ((-735 . -504) 100668) ((-735 . -635) 100618) ((-734 . -1275) 100602) ((-734 . -1184) 100580) ((-734 . -633) NIL) ((-734 . -321) 100567) ((-734 . -528) 100514) ((-734 . -338) 100491) ((-734 . -1070) 100371) ((-734 . -426) 100355) ((-734 . -38) 100184) ((-734 . -111) 99993) ((-734 . -1083) 99816) ((-734 . -1088) 99639) ((-734 . -668) 99549) ((-734 . -670) 99438) ((-734 . -662) 99267) ((-734 . -739) 99096) ((-734 . -635) 98852) ((-734 . -147) 98831) ((-734 . -149) 98810) ((-734 . -47) 98787) ((-734 . -390) 98771) ((-734 . -660) 98719) ((-734 . -928) 98662) ((-734 . -922) 98565) ((-734 . -930) 98472) ((-734 . -912) NIL) ((-734 . -940) 98451) ((-734 . -1254) 98430) ((-734 . -980) 98399) ((-734 . -951) 98378) ((-734 . -571) 98289) ((-734 . -302) 98200) ((-734 . -175) 98091) ((-734 . -466) 98022) ((-734 . -319) 98001) ((-734 . -298) 97928) ((-734 . -240) T) ((-734 . -133) T) ((-734 . -25) T) ((-734 . -102) T) ((-734 . -632) 97910) ((-734 . -1133) T) ((-734 . -23) T) ((-734 . -21) T) ((-734 . -748) T) ((-734 . -1144) T) ((-734 . -1089) T) ((-734 . -1081) T) ((-734 . -236) 97897) ((-734 . -1249) T) ((-734 . -239) T) ((-734 . -274) 97881) ((-734 . -234) 97865) ((-734 . -381) 97844) ((-733 . -376) T) ((-733 . -1254) T) ((-733 . -951) T) ((-733 . -571) T) ((-733 . -175) T) ((-733 . -635) 97794) ((-733 . -739) 97759) ((-733 . -662) 97724) 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97254) ((-723 . -175) T) ((-723 . -302) T) ((-723 . -571) T) ((-723 . -559) T) ((-723 . -1254) T) ((-723 . -1184) T) ((-723 . -633) 97169) ((-723 . -1052) T) ((-723 . -912) 97151) ((-723 . -871) T) ((-723 . -821) T) ((-723 . -818) T) ((-723 . -816) T) ((-723 . -814) T) ((-723 . -844) T) ((-723 . -660) 97133) ((-723 . -951) T) ((-723 . -466) T) ((-723 . -319) T) ((-723 . -239) T) ((-723 . -236) 97120) ((-723 . -240) T) ((-723 . -145) T) ((-723 . -149) T) ((-721 . -418) T) ((-721 . -149) T) ((-721 . -635) 97055) ((-721 . -670) 97020) ((-721 . -668) 96970) ((-721 . -133) T) ((-721 . -25) T) ((-721 . -102) T) ((-721 . -1249) T) ((-721 . -632) 96952) ((-721 . -1133) T) ((-721 . -23) T) ((-721 . -21) T) ((-721 . -748) T) ((-721 . -1144) T) ((-721 . -1089) T) ((-721 . -1081) T) ((-721 . -633) 96897) ((-721 . -376) T) ((-721 . -1254) T) ((-721 . -951) T) ((-721 . -571) T) ((-721 . -175) T) ((-721 . -739) 96862) ((-721 . -662) 96827) ((-721 . -38) 96792) ((-721 . -466) T) ((-721 . -319) T) ((-721 . -111) 96748) ((-721 . -1083) 96713) ((-721 . -1088) 96678) ((-721 . -302) T) ((-721 . -250) T) ((-721 . -871) T) ((-721 . -821) T) ((-721 . -818) T) ((-721 . -875) T) ((-721 . -872) T) ((-721 . -816) T) ((-721 . -814) T) ((-721 . -912) 96660) ((-721 . -1034) T) ((-721 . -1052) T) ((-721 . -1070) 96605) ((-721 . -1092) T) ((-721 . -401) T) ((-716 . -401) T) ((-716 . -1070) 96550) ((-716 . -875) T) ((-716 . -872) T) ((-716 . -38) 96500) ((-716 . -635) 96435) ((-716 . -748) T) ((-716 . -1144) T) ((-716 . -1089) T) ((-716 . -1081) T) ((-716 . -111) 96369) ((-716 . -1083) 96319) ((-716 . -1088) 96269) ((-716 . -21) T) ((-716 . -668) 96204) ((-716 . -23) T) ((-716 . -1133) T) ((-716 . -632) 96186) ((-716 . -1249) T) ((-716 . -102) T) ((-716 . -25) T) ((-716 . -133) T) ((-716 . -670) 96136) ((-716 . -662) 96086) ((-716 . -739) 96036) ((-716 . -175) T) ((-716 . -302) T) ((-716 . -571) T) ((-716 . -168) 96018) ((-716 . -35) NIL) ((-716 . -95) NIL) ((-716 . -296) NIL) ((-716 . -507) NIL) ((-716 . -1238) NIL) ((-716 . -1235) NIL) ((-716 . -1034) NIL) ((-716 . -940) NIL) ((-716 . -633) 95926) ((-716 . -910) 95908) ((-716 . -381) NIL) ((-716 . -363) NIL) ((-716 . -1184) NIL) ((-716 . -416) NIL) ((-716 . -424) 95875) ((-716 . -383) 95842) ((-716 . -746) 95809) ((-716 . -426) 95791) ((-716 . -912) 95773) ((-716 . -414) 95755) ((-716 . -660) 95737) ((-716 . -390) 95719) ((-716 . -298) NIL) ((-716 . -321) NIL) ((-716 . -528) NIL) ((-716 . -351) 95701) ((-716 . -250) T) ((-716 . -1254) T) ((-716 . -376) T) ((-716 . -951) T) ((-716 . -466) T) ((-716 . -319) T) ((-716 . -240) NIL) ((-716 . -236) NIL) ((-716 . -239) NIL) ((-716 . -274) 95683) ((-716 . -922) NIL) ((-716 . -930) NIL) ((-716 . -928) NIL) ((-716 . -234) 95665) ((-716 . -149) T) ((-716 . -147) NIL) ((-713 . -1295) T) ((-713 . -1070) 95649) ((-713 . -635) 95633) ((-713 . -632) 95615) ((-711 . -708) 95573) ((-711 . -503) 95557) ((-711 . -1133) 95535) ((-711 . -528) 95468) ((-711 . -321) 95406) ((-711 . -632) 95338) ((-711 . -102) 95288) ((-711 . -1249) T) ((-711 . -34) T) ((-711 . -57) 95246) ((-711 . -633) 95207) ((-703 . -1115) T) ((-703 . -504) 95188) ((-703 . -632) 95138) ((-703 . -635) 95119) ((-703 . -1133) T) ((-703 . -1249) T) ((-703 . -102) T) ((-703 . -93) T) ((-699 . -872) T) ((-699 . -632) 95101) ((-699 . -1133) T) ((-699 . -102) T) ((-699 . -1249) T) ((-699 . -875) T) ((-699 . -1070) 95085) ((-699 . -635) 95069) ((-698 . -1115) T) ((-698 . -504) 95050) ((-698 . -632) 95016) ((-698 . -635) 94997) ((-698 . -1133) T) ((-698 . -1249) T) ((-698 . -102) T) ((-698 . -93) T) ((-697 . -503) 94981) ((-697 . -1133) 94959) ((-697 . -528) 94892) ((-697 . -321) 94830) ((-697 . -632) 94762) ((-697 . -102) 94712) ((-697 . -1249) T) ((-697 . -34) T) ((-694 . -872) T) ((-694 . -632) 94694) ((-694 . -1133) T) ((-694 . -102) T) ((-694 . -1249) T) ((-694 . -875) T) ((-694 . -1070) 94678) ((-694 . -635) 94662) ((-693 . -1115) T) ((-693 . -504) 94643) ((-693 . -632) 94609) ((-693 . -635) 94590) ((-693 . -1133) T) ((-693 . -1249) T) ((-693 . -102) T) ((-693 . -93) T) ((-692 . -1155) 94535) ((-692 . -503) 94519) ((-692 . -528) 94452) ((-692 . -321) 94390) ((-692 . -34) T) ((-692 . -1085) 94330) ((-692 . -1070) 94226) ((-692 . -635) 94144) ((-692 . -426) 94128) ((-692 . -660) 94076) ((-692 . -670) 94014) ((-692 . -390) 93998) ((-692 . -240) 93977) ((-692 . -236) 93922) ((-692 . -239) 93873) ((-692 . -274) 93857) ((-692 . -922) 93778) ((-692 . -930) 93701) ((-692 . -928) 93660) ((-692 . -234) 93644) ((-692 . -739) 93628) ((-692 . -662) 93612) ((-692 . -668) 93571) ((-692 . -133) T) ((-692 . -25) T) ((-692 . -102) T) ((-692 . -1249) T) ((-692 . -632) 93533) ((-692 . -1133) T) ((-692 . -23) T) ((-692 . -21) T) ((-692 . -1088) 93517) ((-692 . -1083) 93501) ((-692 . -111) 93480) ((-692 . -1081) T) ((-692 . -1089) T) ((-692 . -1144) T) ((-692 . -748) T) ((-692 . -38) 93440) ((-692 . -432) 93424) ((-692 . -766) 93408) ((-692 . -742) T) ((-692 . -783) T) ((-692 . -380) 93392) ((-692 . -298) 93369) ((-686 . -387) 93348) ((-686 . -739) 93332) ((-686 . -662) 93316) ((-686 . -670) 93300) ((-686 . -668) 93269) ((-686 . -133) T) ((-686 . -25) T) ((-686 . -102) T) ((-686 . -1249) T) ((-686 . -632) 93251) ((-686 . -1133) T) ((-686 . -23) T) ((-686 . -21) T) ((-686 . -1088) 93235) ((-686 . -1083) 93219) ((-686 . -111) 93198) ((-686 . -654) 93182) ((-686 . -397) 93154) ((-686 . -635) 93131) ((-686 . -1070) 93108) ((-678 . -680) 93092) ((-678 . -38) 93062) ((-678 . -635) 92980) ((-678 . -670) 92954) ((-678 . -668) 92913) ((-678 . -748) T) ((-678 . -1144) T) ((-678 . -1089) T) ((-678 . -1081) T) ((-678 . -111) 92892) ((-678 . -1083) 92876) ((-678 . -1088) 92860) ((-678 . -21) T) ((-678 . -23) T) ((-678 . -1133) T) ((-678 . -632) 92842) ((-678 . -102) T) ((-678 . -25) T) ((-678 . -133) T) ((-678 . -662) 92812) ((-678 . -739) 92782) ((-678 . -426) 92766) ((-678 . -1070) 92662) ((-678 . -877) 92646) ((-678 . -1249) T) ((-678 . -298) 92607) ((-677 . -680) 92591) ((-677 . -38) 92561) 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. -1133) T) ((-489 . -632) 64731) ((-489 . -102) T) ((-489 . -34) T) ((-489 . -618) 64710) ((-488 . -1282) 64694) ((-488 . -240) 64646) ((-488 . -236) 64592) ((-488 . -239) 64544) ((-488 . -298) 64502) ((-488 . -928) 64408) ((-488 . -922) 64289) ((-488 . -930) 64195) ((-488 . -1005) 64157) ((-488 . -38) 63998) ((-488 . -111) 63819) ((-488 . -1083) 63654) ((-488 . -1088) 63489) ((-488 . -668) 63371) ((-488 . -670) 63268) ((-488 . -662) 63109) ((-488 . -739) 62950) ((-488 . -635) 62776) ((-488 . -147) 62755) ((-488 . -149) 62734) ((-488 . -47) 62704) ((-488 . -1278) 62674) ((-488 . -35) 62640) ((-488 . -95) 62606) ((-488 . -296) 62572) ((-488 . -507) 62538) ((-488 . -1238) 62504) ((-488 . -1235) 62470) ((-488 . -1034) 62436) ((-488 . -250) 62415) ((-488 . -302) 62366) ((-488 . -133) T) ((-488 . -25) T) ((-488 . -102) T) ((-488 . -1249) T) ((-488 . -632) 62348) ((-488 . -1133) T) ((-488 . -23) T) ((-488 . -21) T) ((-488 . -1081) T) ((-488 . -1089) T) ((-488 . -1144) T) ((-488 . -748) T) 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. -102) T) ((-229 . -1249) T) ((-229 . -632) 17713) ((-229 . -1133) T) ((-229 . -23) T) ((-229 . -21) T) ((-229 . -748) T) ((-229 . -1144) T) ((-229 . -1089) T) ((-229 . -1081) T) ((-229 . -633) 17643) ((-229 . -376) T) ((-229 . -1254) T) ((-229 . -951) T) ((-229 . -571) T) ((-229 . -175) T) ((-229 . -739) 17608) ((-229 . -662) 17573) ((-229 . -38) 17538) ((-229 . -466) T) ((-229 . -319) T) ((-229 . -111) 17494) ((-229 . -1083) 17459) ((-229 . -1088) 17424) ((-229 . -302) T) ((-229 . -250) T) ((-229 . -871) T) ((-229 . -821) T) ((-229 . -818) T) ((-229 . -875) T) ((-229 . -872) T) ((-229 . -816) T) ((-229 . -814) T) ((-229 . -912) 17406) ((-229 . -1034) T) ((-229 . -1052) T) ((-229 . -1070) 17366) ((-229 . -1092) T) ((-229 . -240) T) ((-229 . -236) 17353) ((-229 . -239) T) ((-229 . -845) T) ((-229 . -1235) T) ((-229 . -1238) T) ((-229 . -507) T) ((-229 . -296) T) ((-229 . -95) T) ((-229 . -35) T) ((-227 . -640) 17330) ((-227 . -635) 17292) ((-227 . -670) 17259) ((-227 . -668) 17211) 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. -1249) T) ((-187 . -102) T) ((-186 . -189) T) ((-186 . -1133) T) ((-186 . -632) 15502) ((-186 . -1249) T) ((-186 . -102) T) ((-186 . -860) 15484) ((-183 . -1115) T) ((-183 . -504) 15465) ((-183 . -632) 15431) ((-183 . -635) 15412) ((-183 . -1133) T) ((-183 . -1249) T) ((-183 . -102) T) ((-183 . -93) T) ((-178 . -632) 15394) ((-177 . -38) 15326) ((-177 . -635) 15243) ((-177 . -670) 15175) ((-177 . -668) 15092) ((-177 . -748) T) ((-177 . -1144) T) ((-177 . -1089) T) ((-177 . -1081) T) ((-177 . -111) 15003) ((-177 . -1083) 14935) ((-177 . -1088) 14867) ((-177 . -21) T) ((-177 . -23) T) ((-177 . -1133) T) ((-177 . -632) 14849) ((-177 . -1249) T) ((-177 . -102) T) ((-177 . -25) T) ((-177 . -133) T) ((-177 . -662) 14781) ((-177 . -739) 14713) ((-177 . -376) T) ((-177 . -1254) T) ((-177 . -951) T) ((-177 . -571) T) ((-177 . -175) T) ((-177 . -466) T) ((-177 . -319) T) ((-177 . -302) T) ((-177 . -250) T) ((-174 . -1133) T) ((-174 . -632) 14695) ((-174 . -1249) T) ((-174 . -102) T) ((-171 . 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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 c9c457fc..01f9493e 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,316 +1,277 @@ -(30 . 3515605023) -(4513 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3518066230) +(4514 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| - |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| - |AbelianMonoid&| |AbelianMonoid| |AbelianSemiGroup&| - |AbelianSemiGroup| |AlgebraicallyClosedField&| - |AlgebraicallyClosedField| |AlgebraicallyClosedFunctionSpace&| - |AlgebraicallyClosedFunctionSpace| |PlaneAlgebraicCurvePlot| |AddAst| - |AlgebraicFunction| |Aggregate&| |Aggregate| - |ArcHyperbolicFunctionCategory| |AssociationListAggregate| |Algebra&| - |Algebra| |AlgFactor| |AlgebraicFunctionField| + |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| + |AbelianMonoid| |AbelianSemiGroup&| |AbelianSemiGroup| + |AlgebraicallyClosedField&| |AlgebraicallyClosedField| + |AlgebraicallyClosedFunctionSpace&| |AlgebraicallyClosedFunctionSpace| + |PlaneAlgebraicCurvePlot| |AddAst| |AlgebraicFunction| |Aggregate&| + |Aggregate| |ArcHyperbolicFunctionCategory| |AssociationListAggregate| + |Algebra&| |Algebra| |AlgFactor| |AlgebraicFunctionField| |AlgebraicManipulations| |AlgebraicMultFact| |AlgebraPackage| - |AlgebraGivenByStructuralConstants| |AssociationList| - |AbelianMonoidRing&| |AbelianMonoidRing| |AlgebraicNumber| - |AnonymousFunction| |AntiSymm| |Any| |AnyFunctions1| - |ApplyUnivariateSkewPolynomial| |ApplyRules| |Arity| + |AlgebraGivenByStructuralConstants| |AssociationList| |AbelianMonoidRing&| + |AbelianMonoidRing| |AlgebraicNumber| |AnonymousFunction| |AntiSymm| |Any| + |AnyFunctions1| |ApplyUnivariateSkewPolynomial| |ApplyRules| |Arity| |TwoDimensionalArrayCategory&| |TwoDimensionalArrayCategory| - |OneDimensionalArray| |OneDimensionalArrayFunctions2| - |TwoDimensionalArray| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| - |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| - |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| - |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |AssociatedEquations| - |ArrayStack| |AbstractSyntaxCategory&| |AbstractSyntaxCategory| - |ArcTrigonometricFunctionCategory&| |ArcTrigonometricFunctionCategory| - |AttributeAst| |AttributeButtons| |AttributeRegistry| |Automorphism| - |BalancedFactorisation| |BasicType&| |BasicType| |BalancedBinaryTree| - |BezoutMatrix| |BasicFunctions| |BagAggregate&| |BagAggregate| - |BinaryExpansion| |Binding| |Bits| |BiModule| |BooleanLogic&| - |BooleanLogic| |Boolean| |BasicOperator| |BasicOperatorFunctions1| - |BoundIntegerRoots| |BalancedPAdicInteger| |BalancedPAdicRational| - |BinaryRecursiveAggregate&| |BinaryRecursiveAggregate| + |OneDimensionalArray| |OneDimensionalArrayFunctions2| |TwoDimensionalArray| + |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| + |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| + |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| + |AssociatedEquations| |ArrayStack| |AbstractSyntaxCategory&| + |AbstractSyntaxCategory| |ArcTrigonometricFunctionCategory&| + |ArcTrigonometricFunctionCategory| |AttributeAst| |AttributeButtons| + |AttributeRegistry| |Automorphism| |BalancedFactorisation| |BasicType&| + |BasicType| |BalancedBinaryTree| |BezoutMatrix| |BasicFunctions| + |BagAggregate&| |BagAggregate| |BinaryExpansion| |Binding| |Bits| |BiModule| + |BooleanLogic&| |BooleanLogic| |Boolean| |BasicOperator| + |BasicOperatorFunctions1| |BoundIntegerRoots| |BalancedPAdicInteger| + |BalancedPAdicRational| |BinaryRecursiveAggregate&| |BinaryRecursiveAggregate| |BrillhartTests| |BinarySearchTree| |BitAggregate&| |BitAggregate| - |BinaryTreeCategory&| |BinaryTreeCategory| |BinaryTournament| - |BinaryTree| |Byte| |ByteBuffer| |ByteOrder| - |CancellationAbelianMonoid| |CachableSet| |CapsuleAst| - |CardinalNumber| |CartesianTensor| |CartesianTensorFunctions2| - |CaseAst| |CategoryAst| |CategoryConstructor| |Category| - |CharacterClass| |CommonDenominator| |CombinatorialFunctionCategory| - |Character| |CharacteristicNonZero| |CharacteristicPolynomialPackage| - |CharacteristicZero| |ChangeOfVariable| - |ComplexIntegerSolveLinearPolynomialEquation| |Collection&| - |Collection| |CliffordAlgebra| |TwoDimensionalPlotClipping| - |CollectAst| |ComplexRootPackage| |ColonAst| |Color| - |CombinatorialFunction| |IntegerCombinatoricFunctions| - |CombinatorialOpsCategory| |Commutator| |CommaAst| |CommonOperators| - |CommuteUnivariatePolynomialCategory| |ComplexCategory&| - |ComplexCategory| |ComplexFactorization| |CompilerPackage| |Complex| - |ComplexFunctions2| |ComplexPattern| |SubSpaceComponentProperty| - |CommutativeRing| |Conduit| |ContinuedFraction| |Contour| - |CoordinateSystems| |CharacteristicPolynomialInMonogenicalAlgebra| - |ComplexPatternMatch| |CRApackage| |CoerceAst| - |ComplexRootFindingPackage| |CyclicStreamTools| |Constructor| - |ConstructorCall| |ConstructorCategory&| |ConstructorCategory| + |BinaryTreeCategory&| |BinaryTreeCategory| |BinaryTournament| |BinaryTree| + |Byte| |ByteBuffer| |ByteOrder| |CancellationAbelianMonoid| |CachableSet| + |CapsuleAst| |CardinalNumber| |CartesianTensor| |CartesianTensorFunctions2| + |CaseAst| |CategoryAst| |CategoryConstructor| |Category| |CharacterClass| + |CommonDenominator| |CombinatorialFunctionCategory| |Character| + |CharacteristicNonZero| |CharacteristicPolynomialPackage| |CharacteristicZero| + |ChangeOfVariable| |ComplexIntegerSolveLinearPolynomialEquation| |Collection&| + |Collection| |CliffordAlgebra| |TwoDimensionalPlotClipping| |CollectAst| + |ComplexRootPackage| |ColonAst| |Color| |CombinatorialFunction| + |IntegerCombinatoricFunctions| |CombinatorialOpsCategory| |Commutator| + |CommaAst| |CommonOperators| |CommuteUnivariatePolynomialCategory| + |ComplexCategory&| |ComplexCategory| |ComplexFactorization| |CompilerPackage| + |Complex| |ComplexFunctions2| |ComplexPattern| |SubSpaceComponentProperty| + |CommutativeRing| |Conduit| |ContinuedFraction| |Contour| |CoordinateSystems| + |CharacteristicPolynomialInMonogenicalAlgebra| |ComplexPatternMatch| + |CRApackage| |CoerceAst| |ComplexRootFindingPackage| |CyclicStreamTools| + |Constructor| |ConstructorCall| |ConstructorCategory&| |ConstructorCategory| |ConstructorKind| |ComplexTrigonometricManipulations| - |CoerceVectorMatrixPackage| |CycleIndicators| - |CyclotomicPolynomialPackage| |d01AgentsPackage| |d01ajfAnnaType| - |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| - |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| - |d01gbfAnnaType| |d01TransformFunctionType| |d01WeightsPackage| - |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| - |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| |d03fafAnnaType| - |DataArray| |Database| |DualBasis| |DoubleResultantPackage| + |CoerceVectorMatrixPackage| |CycleIndicators| |CyclotomicPolynomialPackage| + |d01AgentsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| + |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| + |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d01TransformFunctionType| + |d01WeightsPackage| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| + |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| + |d03fafAnnaType| |DataArray| |Database| |DualBasis| |DoubleResultantPackage| |DistinctDegreeFactorize| |DecimalExpansion| |DefinitionAst| - |ElementaryFunctionDefiniteIntegration| - |RationalFunctionDefiniteIntegration| |DegreeReductionPackage| - |Dequeue| |DeRhamComplex| |DefiniteIntegrationTools| |DoubleFloat| - |DoubleFloatSpecialFunctions| |DenavitHartenbergMatrix| |Dictionary&| - |Dictionary| |DifferentialExtension| |DifferentialDomain&| + |ElementaryFunctionDefiniteIntegration| |RationalFunctionDefiniteIntegration| + |DegreeReductionPackage| |Dequeue| |DeRhamComplex| |DefiniteIntegrationTools| + |DoubleFloat| |DoubleFloatSpecialFunctions| |DenavitHartenbergMatrix| + |Dictionary&| |Dictionary| |DifferentialExtension| |DifferentialDomain&| |DifferentialDomain| |DifferentialModule| |DifferentialSpace&| |DifferentialSpace| |DifferentialRing| |DictionaryOperations&| - |DictionaryOperations| |DiophantineSolutionPackage| - |DirectProductCategory&| |DirectProductCategory| |DirectProduct| - |DirectProductFunctions2| |DisplayPackage| |DivisionRing&| - |DivisionRing| |DoublyLinkedAggregate| |DataList| - |DiscreteLogarithmPackage| |DifferentialModuleExtension| + |DictionaryOperations| |DiophantineSolutionPackage| |DirectProductCategory&| + |DirectProductCategory| |DirectProduct| |DirectProductFunctions2| + |DisplayPackage| |DivisionRing&| |DivisionRing| |DoublyLinkedAggregate| + |DataList| |DiscreteLogarithmPackage| |DifferentialModuleExtension| |DistributedMultivariatePolynomial| |Domain| |DomainConstructor| |DomainTemplate| |DirectProductMatrixModule| |DirectProductModule| |DifferentialPolynomialCategory&| |DifferentialPolynomialCategory| |DequeueAggregate| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForCompiledFunctions| - |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex| - |DrawNumericHack| |TopLevelDrawFunctionsForPoints| |DrawOption| - |DrawOptionFunctions0| |DrawOptionFunctions1| - |DifferentialSpaceExtension&| |DifferentialSpaceExtension| - |DifferentialSparseMultivariatePolynomial| + |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex| |DrawNumericHack| + |TopLevelDrawFunctionsForPoints| |DrawOption| |DrawOptionFunctions0| + |DrawOptionFunctions1| |DifferentialSpaceExtension&| + |DifferentialSpaceExtension| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DifferentialVariableCategory| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType| - |ExtAlgBasis| |ElementaryFunction| - |ElementaryFunctionStructurePackage| + |ExtAlgBasis| |ElementaryFunction| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElaboratedExpression| |Elaboration| |ExtensibleLinearAggregate&| |ExtensibleLinearAggregate| |ElementaryFunctionCategory&| |ElementaryFunctionCategory| - |EllipticFunctionsUnivariateTaylorSeries| |Eltable| - |EltableAggregate&| |EltableAggregate| |EuclideanModularRing| - |EntireRing| |Environment| |EigenPackage| |Equation| - |EquationFunctions2| |EqTable| |ErrorFunctions| |ExpressionSpace&| - |ExpressionSpace| |ExpressionSpaceFunctions1| + |EllipticFunctionsUnivariateTaylorSeries| |Eltable| |EltableAggregate&| + |EltableAggregate| |EuclideanModularRing| |EntireRing| |Environment| + |EigenPackage| |Equation| |EquationFunctions2| |EqTable| |ErrorFunctions| + |ExpressionSpace&| |ExpressionSpace| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |ExpertSystemContinuityPackage| |ExpertSystemContinuityPackage1| |ExpertSystemToolsPackage| - |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| - |EuclideanDomain&| |EuclideanDomain| |Evalable&| |Evalable| - |EvaluateCycleIndicators| |Exit| |ExitAst| |ExponentialExpansion| - |Expression| |ExpressionFunctions2| + |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| |EuclideanDomain&| + |EuclideanDomain| |Evalable&| |Evalable| |EvaluateCycleIndicators| |Exit| + |ExitAst| |ExponentialExpansion| |Expression| |ExpressionFunctions2| |ExpressionToUnivariatePowerSeries| |ExpressionSpaceODESolver| |ExpressionTubePlot| |ExponentialOfUnivariatePuiseuxSeries| |FactoredFunctions| |FactoringUtilities| |FreeAbelianGroup| - |FreeAbelianMonoidCategory| |FreeAbelianMonoid| - |FiniteAbelianMonoidRing&| |FiniteAbelianMonoidRing| |FlexibleArray| - |FiniteAlgebraicExtensionField&| |FiniteAlgebraicExtensionField| - |FortranCode| |FourierComponent| |FortranCodePackage1| |FunctorData| - |FiniteDivisor| |FiniteDivisorFunctions2| |FiniteDivisorCategory&| - |FiniteDivisorCategory| |FullyEvalableOver&| |FullyEvalableOver| - |FortranExpression| |FiniteField| |FunctionFieldCategory&| + |FreeAbelianMonoidCategory| |FreeAbelianMonoid| |FiniteAbelianMonoidRing&| + |FiniteAbelianMonoidRing| |FlexibleArray| |FiniteAlgebraicExtensionField&| + |FiniteAlgebraicExtensionField| |FortranCode| |FourierComponent| + |FortranCodePackage1| |FunctorData| |FiniteDivisor| |FiniteDivisorFunctions2| + |FiniteDivisorCategory&| |FiniteDivisorCategory| |FullyEvalableOver&| + |FullyEvalableOver| |FortranExpression| |FiniteField| |FunctionFieldCategory&| |FunctionFieldCategory| |FunctionFieldCategoryFunctions2| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldCyclicGroupExtension| |FiniteFieldFunctions| - |FiniteFieldHomomorphisms| |FiniteFieldCategory&| - |FiniteFieldCategory| |FunctionFieldIntegralBasis| - |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtensionByPolynomial| + |FiniteFieldHomomorphisms| |FiniteFieldCategory&| |FiniteFieldCategory| + |FunctionFieldIntegralBasis| |FiniteFieldNormalBasis| + |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldNormalBasisExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldExtension| |FGLMIfCanPackage| |FreeGroup| |Field&| |Field| |File| |FileCategory| - |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| - |Finite| |FiniteRankAlgebra&| |FiniteRankAlgebra| - |FiniteLinearAggregate&| |FiniteLinearAggregate| - |FiniteLinearAggregateFunctions2| |FreeLieAlgebra| + |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| |Finite| + |FiniteRankAlgebra&| |FiniteRankAlgebra| |FiniteLinearAggregate&| + |FiniteLinearAggregate| |FiniteLinearAggregateFunctions2| |FreeLieAlgebra| |FiniteLinearAggregateSort| |FullyLinearlyExplicitRingOver&| |FullyLinearlyExplicitRingOver| |Float| |FloatingComplexPackage| - |FloatingRealPackage| |FreeModule| |FreeModule1| - |FortranMatrixCategory| |FreeModuleCat| - |FortranMatrixFunctionCategory| |FreeMonoidCategory| |FreeMonoid| - |FortranMachineTypeCategory| |FileName| |FileNameCategory| + |FloatingRealPackage| |FreeModule| |FreeModule1| |FortranMatrixCategory| + |FreeModuleCat| |FortranMatrixFunctionCategory| |FreeMonoidCategory| + |FreeMonoid| |FortranMachineTypeCategory| |FileName| |FileNameCategory| |FreeNilpotentLie| |FortranOutputStackPackage| |FindOrderFinite| |ScriptFormulaFormat| |ScriptFormulaFormat1| |FortranPackage| |FortranProgramCategory| |FortranFunctionCategory| |FortranProgram| |FullPartialFractionExpansion| |FullyPatternMatchable| |FieldOfPrimeCharacteristic&| |FieldOfPrimeCharacteristic| - |FloatingPointSystem&| |FloatingPointSystem| |Factored| - |FactoredFunctions2| |Fraction| |FractionFunctions2| |FramedAlgebra&| - |FramedAlgebra| |FullyRetractableTo&| |FullyRetractableTo| - |FractionalIdeal| |FractionalIdealFunctions2| |FramedModule| + |FloatingPointSystem&| |FloatingPointSystem| |Factored| |FactoredFunctions2| + |Fraction| |FractionFunctions2| |FramedAlgebra&| |FramedAlgebra| + |FullyRetractableTo&| |FullyRetractableTo| |FractionalIdeal| + |FractionalIdealFunctions2| |FramedModule| |FramedNonAssociativeAlgebraFunctions2| |FramedNonAssociativeAlgebra&| - |FramedNonAssociativeAlgebra| |FactoredFunctionUtilities| - |FunctionSpace&| |FunctionSpace| |FunctionSpaceFunctions2| - |FunctionSpaceToExponentialExpansion| - |FunctionSpaceToUnivariatePowerSeries| |FiniteSetAggregate&| - |FiniteSetAggregate| |FiniteSetAggregateFunctions2| - |FunctionSpaceComplexIntegration| |FourierSeries| - |FunctionSpaceIntegration| |FunctionalSpecialFunction| - |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| - |FortranScalarType| |FunctionSpaceUnivariatePolynomialFactor| - |FortranType| |FortranTemplate| |FunctionCalled| |FunctionDescriptor| - |FortranVectorCategory| |FortranVectorFunctionCategory| - |GaloisGroupFactorizer| |GaloisGroupFactorizationUtilities| - |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| - |GaussianFactorizationPackage| |GroebnerPackage| + |FramedNonAssociativeAlgebra| |FactoredFunctionUtilities| |FunctionSpace&| + |FunctionSpace| |FunctionSpaceFunctions2| + |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| + |FiniteSetAggregate&| |FiniteSetAggregate| |FiniteSetAggregateFunctions2| + |FunctionSpaceComplexIntegration| |FourierSeries| |FunctionSpaceIntegration| + |FunctionalSpecialFunction| |FunctionSpacePrimitiveElement| + |FunctionSpaceReduce| |FortranScalarType| + |FunctionSpaceUnivariatePolynomialFactor| |FortranType| |FortranTemplate| + |FunctionCalled| |FunctionDescriptor| |FortranVectorCategory| + |FortranVectorFunctionCategory| |GaloisGroupFactorizer| + |GaloisGroupFactorizationUtilities| |GaloisGroupPolynomialUtilities| + |GaloisGroupUtilities| |GaussianFactorizationPackage| |GroebnerPackage| |EuclideanGroebnerBasisPackage| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GcdDomain&| |GcdDomain| - |GenericNonAssociativeAlgebra| - |GeneralDistributedMultivariatePolynomial| |GenExEuclid| - |GeneralizedMultivariateFactorize| |GeneralPolynomialGcdPackage| + |GenericNonAssociativeAlgebra| |GeneralDistributedMultivariatePolynomial| + |GenExEuclid| |GeneralizedMultivariateFactorize| |GeneralPolynomialGcdPackage| |GenUFactorize| |GenerateUnivariatePowerSeries| |GeneralHenselPackage| - |GeneralModulePolynomial| |GosperSummationMethod| - |GeneralPolynomialSet| |GradedAlgebra&| |GradedAlgebra| |GrayCode| - |GraphicsDefaults| |GraphImage| |GradedModule&| |GradedModule| - |GroebnerSolve| |Group&| |Group| |GeneralUnivariatePowerSeries| - |GeneralSparseTable| |GeneralTriangularSet| |Pi| |HasAst| |HashTable| - |HallBasis| |HomogeneousDistributedMultivariatePolynomial| - |HomogeneousDirectProduct| |HeadAst| |Heap| - |HyperellipticFiniteDivisor| |HeuGcd| |HexadecimalExpansion| - |HomogeneousAggregate&| |HomogeneousAggregate| |HomotopicTo| - |Hostname| |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| - |InnerAlgFactor| |InnerAlgebraicNumber| |IndexedOneDimensionalArray| + |GeneralModulePolynomial| |GosperSummationMethod| |GeneralPolynomialSet| + |GradedAlgebra&| |GradedAlgebra| |GrayCode| |GraphicsDefaults| |GraphImage| + |GradedModule&| |GradedModule| |GroebnerSolve| |Group&| |Group| + |GeneralUnivariatePowerSeries| |GeneralSparseTable| |GeneralTriangularSet| + |Pi| |HasAst| |HashTable| |HallBasis| + |HomogeneousDistributedMultivariatePolynomial| |HomogeneousDirectProduct| + |HeadAst| |Heap| |HyperellipticFiniteDivisor| |HeuGcd| |HexadecimalExpansion| + |HomogeneousAggregate&| |HomogeneousAggregate| |HomotopicTo| |Hostname| + |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| |InnerAlgFactor| + |InnerAlgebraicNumber| |IndexedOneDimensionalArray| |IndexedTwoDimensionalArray| |ChineseRemainderToolsForIntegralBases| - |IntegralBasisTools| |IndexedBits| |IntegralBasisPolynomialTools| - |IndexCard| |InnerCommonDenominator| |PolynomialIdeals| - |IdealDecompositionPackage| |Identifier| - |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| - |IndexedDirectProductCategory| |IndexedDirectProductObject| - |IndexedDirectProductOrderedAbelianMonoid| - |IndexedDirectProductOrderedAbelianMonoidSup| |InnerEvalable&| - |InnerEvalable| |InnerFreeAbelianMonoid| |IndexedFlexibleArray| - |IfAst| |InnerFiniteField| |InnerIndexedTwoDimensionalArray| - |IndexedList| |InnerMatrixLinearAlgebraFunctions| - |InnerMatrixQuotientFieldFunctions| |IndexedMatrix| |ImportAst| - |InAst| |InputByteConduit&| |InputByteConduit| + |IntegralBasisTools| |IndexedBits| |IntegralBasisPolynomialTools| |IndexCard| + |InnerCommonDenominator| |PolynomialIdeals| |IdealDecompositionPackage| + |Identifier| |IndexedDirectProductAbelianGroup| + |IndexedDirectProductAbelianMonoid| |IndexedDirectProductCategory| + |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| + |IndexedDirectProductOrderedAbelianMonoidSup| |InnerEvalable&| |InnerEvalable| + |InnerFreeAbelianMonoid| |IndexedFlexibleArray| |IfAst| |InnerFiniteField| + |InnerIndexedTwoDimensionalArray| |IndexedList| + |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| + |IndexedMatrix| |ImportAst| |InAst| |InputByteConduit&| |InputByteConduit| |InnerNormalBasisFieldFunctions| |InputBinaryFile| |IncrementingMaps| |IndexedExponents| |InnerNumericEigenPackage| |InetClientStreamSocket| |Infinity| |InputForm| |InputFormFunctions1| |InfiniteProductCharacteristicZero| |InnerNumericFloatSolvePackage| |InnerModularGcd| |InnerMultFact| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InnerPolySign| |IntegerNumberSystem&| - |IntegerNumberSystem| |Integer| |Int16| |Int32| |Int64| |Int8| - |InnerTable| |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits| - |IntervalCategory| |IntegralDomain&| |IntegralDomain| - |ElementaryIntegration| |IntegerFactorizationPackage| - |IntegrationFunctionsTable| |GenusZeroIntegration| - |IntegerNumberTheoryFunctions| |AlgebraicHermiteIntegration| - |TranscendentalHermiteIntegration| |AnnaNumericalIntegrationPackage| - |PureAlgebraicIntegration| |PatternMatchIntegration| - |RationalIntegration| |IntegerRetractions| + |IntegerNumberSystem| |Integer| |Int16| |Int32| |Int64| |Int8| |InnerTable| + |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits| |IntervalCategory| + |IntegralDomain&| |IntegralDomain| |ElementaryIntegration| + |IntegerFactorizationPackage| |IntegrationFunctionsTable| + |GenusZeroIntegration| |IntegerNumberTheoryFunctions| + |AlgebraicHermiteIntegration| |TranscendentalHermiteIntegration| + |AnnaNumericalIntegrationPackage| |PureAlgebraicIntegration| + |PatternMatchIntegration| |RationalIntegration| |IntegerRetractions| |RationalFunctionIntegration| |Interval| |IntegerSolveLinearPolynomialEquation| |IntegrationTools| - |TranscendentalIntegration| |InverseLaplaceTransform| - |InputOutputByteConduit| |InputOutputBinaryFile| |IOMode| |IP4Address| - |InnerPAdicInteger| |InnerPrimeField| |InternalPrintPackage| - |IntegrationResult| |IntegrationResultFunctions2| - |IntegrationResultToFunction| |InternalRepresentationForm| - |IntegerRoots| |IrredPolyOverFiniteField| + |TranscendentalIntegration| |InverseLaplaceTransform| |InputOutputByteConduit| + |InputOutputBinaryFile| |IOMode| |IP4Address| |InnerPAdicInteger| + |InnerPrimeField| |InternalPrintPackage| |IntegrationResult| + |IntegrationResultFunctions2| |IntegrationResultToFunction| + |InternalRepresentationForm| |IntegerRoots| |IrredPolyOverFiniteField| |IntegrationResultRFToFunction| |IrrRepSymNatPackage| - |InternalRationalUnivariateRepresentationPackage| |IsAst| - |IndexedString| |InnerPolySum| |InnerSparseUnivariatePowerSeries| - |InnerTaylorSeries| |InternalTypeForm| |InfiniteTupleFunctions2| - |InfiniteTupleFunctions3| |InnerTrigonometricManipulations| - |InfiniteTuple| |IndexedVector| |IndexedAggregate&| |IndexedAggregate| - |JoinAst| |AssociatedJordanAlgebra| |JVMBytecode| |JVMClassFileAccess| - |JVMConstantTag| |JVMFieldAccess| |JVMMethodAccess| |JVMOpcode| - |KeyedAccessFile| |KeyedDictionary&| |KeyedDictionary| |Kernel| - |KernelFunctions2| |CoercibleTo| |ConvertibleTo| |Kovacic| - |CoercibleFrom| |KleeneTrivalentLogic| |ConvertibleFrom| + |InternalRationalUnivariateRepresentationPackage| |IsAst| |IndexedString| + |InnerPolySum| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| + |InternalTypeForm| |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| + |InnerTrigonometricManipulations| |InfiniteTuple| |IndexedVector| + |IndexedAggregate&| |IndexedAggregate| |JoinAst| |AssociatedJordanAlgebra| + |JVMBytecode| |JVMClassFileAccess| |JVMConstantTag| |JVMFieldAccess| + |JVMMethodAccess| |JVMOpcode| |KeyedAccessFile| |KeyedDictionary&| + |KeyedDictionary| |Kernel| |KernelFunctions2| |CoercibleTo| |ConvertibleTo| + |Kovacic| |CoercibleFrom| |KleeneTrivalentLogic| |ConvertibleFrom| |LocalAlgebra| |LeftAlgebra&| |LeftAlgebra| |LaplaceTransform| - |LaurentPolynomial| |LazardSetSolvingPackage| - |LeadingCoefDetermination| |LetAst| |LieExponentials| - |LexTriangularPackage| |LiouvillianFunction| + |LaurentPolynomial| |LazardSetSolvingPackage| |LeadingCoefDetermination| + |LetAst| |LieExponentials| |LexTriangularPackage| |LiouvillianFunction| |LiouvillianFunctionCategory| |LinGroebnerPackage| |Library| - |AssociatedLieAlgebra| |LieAlgebra&| |LieAlgebra| - |PowerSeriesLimitPackage| |RationalFunctionLimitPackage| |LinearBasis| - |LinearDependence| |LinearElement| |LinearlyExplicitRingOver| - |LinearForm| |LinearSet| |List| |ListFunctions2| |ListToMap| - |ListFunctions3| |Literal| |LeftLinearSet| |ListMultiDictionary| - |LeftModule| |ListMonoidOps| |LinearAggregate&| |LinearAggregate| - |Localize| |ElementaryFunctionLODESolver| - |LinearOrdinaryDifferentialOperator| - |LinearOrdinaryDifferentialOperator1| + |AssociatedLieAlgebra| |LieAlgebra&| |LieAlgebra| |PowerSeriesLimitPackage| + |RationalFunctionLimitPackage| |LinearBasis| |LinearDependence| + |LinearElement| |LinearlyExplicitRingOver| |LinearForm| |LinearSet| |List| + |ListFunctions2| |ListToMap| |ListFunctions3| |Literal| |LeftLinearSet| + |ListMultiDictionary| |LeftModule| |ListMonoidOps| |LinearAggregate&| + |LinearAggregate| |Localize| |ElementaryFunctionLODESolver| + |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| |LinearOrdinaryDifferentialOperatorCategory| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearOrdinaryDifferentialOperatorsOps| |Logic&| |Logic| |LinearPolynomialEquationByFractions| |LiePolynomial| |ListAggregate&| - |ListAggregate| |LinearSystemMatrixPackage| - |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| - |LieSquareMatrix| |ConstructAst| |LyndonWord| |LazyStreamAggregate&| - |LazyStreamAggregate| |ThreeDimensionalMatrix| |MacroAst| |Magma| - |MappingPackageInternalHacks1| |MappingPackageInternalHacks2| - |MappingPackageInternalHacks3| |MappingAst| |MappingPackage1| - |MappingPackage2| |MappingPackage3| |MatrixCategory&| |MatrixCategory| - |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| |Matrix| - |StorageEfficientMatrixOperations| |Maybe| - |MultiVariableCalculusFunctions| |MatrixCommonDenominator| - |MachineComplex| |MultiDictionary| |ModularDistinctDegreeFactorizer| - |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| - |MachineFloat| |ModularHermitianRowReduction| |MachineInteger| - |MakeBinaryCompiledFunction| |MakeFloatCompiledFunction| - |MakeFunction| |MakeRecord| |MakeUnaryCompiledFunction| - |MultivariateLifting| |MonogenicLinearOperator| |MultipleMap| - |MathMLFormat| |ModularField| |ModMonic| |ModuleMonomial| - |ModuleOperator| |ModularRing| |Module&| |Module| |MoebiusTransform| - |Monad&| |Monad| |MonadWithUnit&| |MonadWithUnit| |MonogenicAlgebra&| + |ListAggregate| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| + |LinearSystemPolynomialPackage| |LieSquareMatrix| |ConstructAst| |LyndonWord| + |LazyStreamAggregate&| |LazyStreamAggregate| |ThreeDimensionalMatrix| + |MacroAst| |Magma| |MappingPackageInternalHacks1| + |MappingPackageInternalHacks2| |MappingPackageInternalHacks3| |MappingAst| + |MappingPackage1| |MappingPackage2| |MappingPackage3| |MatrixCategory&| + |MatrixCategory| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| + |Matrix| |StorageEfficientMatrixOperations| |Maybe| + |MultiVariableCalculusFunctions| |MatrixCommonDenominator| |MachineComplex| + |MultiDictionary| |ModularDistinctDegreeFactorizer| + |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| |MachineFloat| + |ModularHermitianRowReduction| |MachineInteger| |MakeBinaryCompiledFunction| + |MakeFloatCompiledFunction| |MakeFunction| |MakeRecord| + |MakeUnaryCompiledFunction| |MultivariateLifting| |MonogenicLinearOperator| + |MultipleMap| |MathMLFormat| |ModularField| |ModMonic| |ModuleMonomial| + |ModuleOperator| |ModularRing| |Module&| |Module| |MoebiusTransform| |Monad&| + |Monad| |MonadWithUnit&| |MonadWithUnit| |MonogenicAlgebra&| |MonogenicAlgebra| |Monoid&| |Monoid| |MonomialExtensionTools| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MultivariatePolynomial| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MonoidRingFunctions2| |MonoidRing| |Multiset| |MultisetAggregate| |MoreSystemCommands| |MergeThing| |MultivariateTaylorSeriesCategory| |MultivariateFactorize| - |MultivariateSquareFree| |NonAssociativeAlgebra&| - |NonAssociativeAlgebra| |NagPolynomialRootsPackage| - |NagRootFindingPackage| |NagSeriesSummationPackage| - |NagIntegrationPackage| |NagOrdinaryDifferentialEquationsPackage| + |MultivariateSquareFree| |NonAssociativeAlgebra&| |NonAssociativeAlgebra| + |NagPolynomialRootsPackage| |NagRootFindingPackage| + |NagSeriesSummationPackage| |NagIntegrationPackage| + |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagInterpolationPackage| - |NagFittingPackage| |NagOptimisationPackage| - |NagMatrixOperationsPackage| |NagEigenPackage| - |NagLinearEquationSolvingPackage| |NagLapack| - |NagSpecialFunctionsPackage| |NAGLinkSupportPackage| - |NonAssociativeRng&| |NonAssociativeRng| |NonAssociativeRing&| - |NonAssociativeRing| |NumericComplexEigenPackage| - |NumericContinuedFraction| |NonCommutativeOperatorDivision| - |NetworkClientSocket| |NumberFieldIntegralBasis| - |NumericalIntegrationProblem| |NonLinearSolvePackage| - |NonNegativeInteger| |NonLinearFirstOrderODESolver| |None| - |NoneFunctions1| |NormInMonogenicAlgebra| |NormalizationPackage| + |NagFittingPackage| |NagOptimisationPackage| |NagMatrixOperationsPackage| + |NagEigenPackage| |NagLinearEquationSolvingPackage| |NagLapack| + |NagSpecialFunctionsPackage| |NAGLinkSupportPackage| |NonAssociativeRng&| + |NonAssociativeRng| |NonAssociativeRing&| |NonAssociativeRing| + |NumericComplexEigenPackage| |NumericContinuedFraction| + |NonCommutativeOperatorDivision| |NetworkClientSocket| + |NumberFieldIntegralBasis| |NumericalIntegrationProblem| + |NonLinearSolvePackage| |NonNegativeInteger| |NonLinearFirstOrderODESolver| + |None| |NoneFunctions1| |NormInMonogenicAlgebra| |NormalizationPackage| |NormRetractPackage| |NPCoef| |NumericRealEigenPackage| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| - |NewSparseUnivariatePolynomialFunctions2| - |NumberTheoreticPolynomialFunctions| |NormalizedTriangularSetCategory| - |Numeric| |NumberFormats| |NumericalIntegrationCategory| - |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| - |NumericTubePlot| |OrderedAbelianGroup&| |OrderedAbelianGroup| - |OrderedAbelianMonoid&| |OrderedAbelianMonoid| - |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| - |OctonionCategory&| |OctonionCategory| - |OrderedCancellationAbelianMonoid| |Octonion| - |OctonionCategoryFunctions2| - |OrdinaryDifferentialEquationsSolverCategory| |ConstantLODE| - |ElementaryFunctionODESolver| |ODEIntensityFunctionsTable| - |ODEIntegration| |AnnaOrdinaryDifferentialEquationPackage| - |PureAlgebraicLODE| |PrimitiveRatDE| |NumericalODEProblem| - |PrimitiveRatRicDE| |RationalLODE| |ReduceLODE| |RationalRicDE| - |SystemODESolver| |ODETools| |OrderedDirectProduct| - |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| - |OrderlyDifferentialVariable| |OrderedFreeMonoid| - |OrderedIntegralDomain| |OpenMath| |OpenMathConnection| - |OpenMathDevice| |OpenMathEncoding| |OpenMathError| - |OpenMathErrorKind| |ExpressionToOpenMath| - |OppositeMonogenicLinearOperator| |OpenMathPackage| - |OrderedMultisetAggregate| |OpenMathServerPackage| - |OnePointCompletion| |OnePointCompletionFunctions2| |Operator| - |OperatorCategory&| |OperatorCategory| |OperationsQuery| + |NewSparseUnivariatePolynomialFunctions2| |NumberTheoreticPolynomialFunctions| + |NormalizedTriangularSetCategory| |Numeric| |NumberFormats| + |NumericalIntegrationCategory| |NumericalOrdinaryDifferentialEquations| + |NumericalQuadrature| |NumericTubePlot| |OrderedAbelianGroup&| + |OrderedAbelianGroup| |OrderedAbelianMonoid&| |OrderedAbelianMonoid| + |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| |OctonionCategory&| + |OctonionCategory| |OrderedCancellationAbelianMonoid| |Octonion| + |OctonionCategoryFunctions2| |OrdinaryDifferentialEquationsSolverCategory| + |ConstantLODE| |ElementaryFunctionODESolver| |ODEIntensityFunctionsTable| + |ODEIntegration| |AnnaOrdinaryDifferentialEquationPackage| |PureAlgebraicLODE| + |PrimitiveRatDE| |NumericalODEProblem| |PrimitiveRatRicDE| |RationalLODE| + |ReduceLODE| |RationalRicDE| |SystemODESolver| |ODETools| + |OrderedDirectProduct| |OrderlyDifferentialPolynomial| + |OrdinaryDifferentialRing| |OrderlyDifferentialVariable| |OrderedFreeMonoid| + |OrderedIntegralDomain| |OpenMath| |OpenMathConnection| |OpenMathDevice| + |OpenMathEncoding| |OpenMathError| |OpenMathErrorKind| |ExpressionToOpenMath| + |OppositeMonogenicLinearOperator| |OpenMathPackage| |OrderedMultisetAggregate| + |OpenMathServerPackage| |OnePointCompletion| |OnePointCompletionFunctions2| + |Operator| |OperatorCategory&| |OperatorCategory| |OperationsQuery| |OperatorSignature| |NumericalOptimizationCategory| |AnnaNumericalOptimizationPackage| |NumericalOptimizationProblem| |OrderedCompletion| |OrderedCompletionFunctions2| |OrderedFinite| @@ -318,846 +279,755 @@ |OrderedStructure| |OrderedType&| |OrderedType| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial| - |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| - |OrderedSemiGroup| |OrdSetInts| |OutputPackage| |OutputByteConduit&| - |OutputByteConduit| |OutputBinaryFile| |OutputForm| - |OrderedVariableList| |OverloadSet| |OrdinaryWeightedPolynomials| - |PadeApproximants| |PadeApproximantPackage| |PAdicInteger| - |PAdicIntegerCategory| |PAdicRational| |PAdicRationalConstructor| - |Pair| |Palette| |PolynomialAN2Expression| |ParameterAst| - |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve| + |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| |OrderedSemiGroup| + |OrdSetInts| |OutputPackage| |OutputByteConduit&| |OutputByteConduit| + |OutputBinaryFile| |OutputForm| |OrderedVariableList| |OverloadSet| + |OrdinaryWeightedPolynomials| |PadeApproximants| |PadeApproximantPackage| + |PAdicInteger| |PAdicIntegerCategory| |PAdicRational| + |PAdicRationalConstructor| |Pair| |Palette| |PolynomialAN2Expression| + |ParameterAst| |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| |ParametricSpaceCurve| |Parser| - |ParametricSurfaceFunctions2| |ParametricSurface| - |PartitionsAndPermutations| |Patternable| |PatternMatchListResult| - |PatternMatchable| |PatternMatch| |PatternMatchResult| - |PatternMatchResultFunctions2| |Pattern| |PatternFunctions1| - |PatternFunctions2| |PoincareBirkhoffWittLyndonBasis| + |ParametricSurfaceFunctions2| |ParametricSurface| |PartitionsAndPermutations| + |Patternable| |PatternMatchListResult| |PatternMatchable| |PatternMatch| + |PatternMatchResult| |PatternMatchResultFunctions2| |Pattern| + |PatternFunctions1| |PatternFunctions2| |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| |PartialDifferentialDomain&| - |PartialDifferentialDomain| - |PartialDifferentialEquationsSolverCategory| |PolynomialDecomposition| - |AnnaPartialDifferentialEquationPackage| |NumericalPDEProblem| - |PartialDifferentialModule| |PartialDifferentialRing| + |PartialDifferentialDomain| |PartialDifferentialEquationsSolverCategory| + |PolynomialDecomposition| |AnnaPartialDifferentialEquationPackage| + |NumericalPDEProblem| |PartialDifferentialModule| |PartialDifferentialRing| |PartialDifferentialSpace&| |PartialDifferentialSpace| |PendantTree| |Permutation| |Permanent| |PermutationCategory| |PermutationGroup| |PrimeField| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialFactorizationExplicit| - |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| - |PointsOfFiniteOrderTools| |PartialFraction| |PartialFractionPackage| - |PolynomialGcdPackage| |PermutationGroupExamples| |PolyGroebner| - |PositiveInteger| |PiCoercions| |PrincipalIdealDomain| - |PolynomialInterpolation| |PolynomialInterpolationAlgorithms| - |ParametricLinearEquations| |Plot| |PlotFunctions1| |Plot3D| - |PlotTools| |PatternMatchAssertions| |FunctionSpaceAssertions| - |PatternMatchPushDown| |PatternMatchFunctionSpace| + |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| + |PartialFraction| |PartialFractionPackage| |PolynomialGcdPackage| + |PermutationGroupExamples| |PolyGroebner| |PositiveInteger| |PiCoercions| + |PrincipalIdealDomain| |PolynomialInterpolation| + |PolynomialInterpolationAlgorithms| |ParametricLinearEquations| |Plot| + |PlotFunctions1| |Plot3D| |PlotTools| |PatternMatchAssertions| + |FunctionSpaceAssertions| |PatternMatchPushDown| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchPolynomialCategory| |AttachPredicates| |FunctionSpaceAttachPredicates| - |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| - |PatternMatchTools| |PolynomialNumberTheoryFunctions| |Point| - |PolToPol| |RealPolynomialUtilitiesPackage| |Polynomial| - |PolynomialFunctions2| |PolynomialToUnivariatePolynomial| - |PolynomialCategory&| |PolynomialCategory| + |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| |PatternMatchTools| + |PolynomialNumberTheoryFunctions| |Point| |PolToPol| + |RealPolynomialUtilitiesPackage| |Polynomial| |PolynomialFunctions2| + |PolynomialToUnivariatePolynomial| |PolynomialCategory&| |PolynomialCategory| |PolynomialCategoryQuotientFunctions| |PolynomialCategoryLifting| - |PolynomialRoots| |PortNumber| |PlottablePlaneCurveCategory| - |PolynomialRing| |PrecomputedAssociatedEquations| |PrimitiveArray| - |PrimitiveArrayFunctions2| |PrimitiveFunctionCategory| - |PrimitiveElement| |IntegerPrimesPackage| |PrintPackage| |Product| - |Property| |PropositionalFormula| |PropositionalFormulaFunctions1| - |PropositionalFormulaFunctions2| |PropositionalLogic| - |PriorityQueueAggregate| |PseudoRemainderSequence| |PretendAst| - |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| - |PlottableSpaceCurveCategory| |PolynomialSetCategory&| - |PolynomialSetCategory| |PolynomialSetUtilitiesPackage| - |PseudoLinearNormalForm| |PolynomialSquareFree| |PointCategory| - |PointFunctions2| |PointPackage| |PartialTranscendentalFunctions| - |PushVariables| |PAdicWildFunctionFieldIntegralBasis| - |QuasiAlgebraicSet| |QuasiAlgebraicSet2| |QuasiComponentPackage| - |QueryEquation| |QuotientFieldCategory&| |QuotientFieldCategory| - |QuotientFieldCategoryFunctions2| |QuadraticForm| |QuasiquoteAst| - |QueueAggregate| |Quaternion| |QuaternionCategory&| - |QuaternionCategory| |QuaternionCategoryFunctions2| |Queue| - |RadicalCategory&| |RadicalCategory| |RadicalFunctionField| - |RadixExpansion| |RadixUtilities| |RandomNumberSource| - |RationalFactorize| |RationalRetractions| |RecursiveAggregate&| - |RecursiveAggregate| |RealClosedField&| |RealClosedField| - |ElementaryRischDE| |ElementaryRischDESystem| |TranscendentalRischDE| - |TranscendentalRischDESystem| |RandomDistributions| |ReducedDivisor| - |ReduceAst| |RealConstant| |RealZeroPackage| |RealZeroPackageQ| - |RealSolvePackage| |RealClosure| |ReductionOfOrder| |Reference| - |RegularTriangularSet| |RadicalEigenPackage| |RepresentationPackage1| - |RepresentationPackage2| |RepeatedDoubling| |RepeatedSquaring| - |ResolveLatticeCompletion| |ResidueRing| |Result| |ReturnAst| - |RetractableTo&| |RetractableTo| |RetractSolvePackage| + |PolynomialRoots| |PortNumber| |PlottablePlaneCurveCategory| |PolynomialRing| + |PrecomputedAssociatedEquations| |PrimitiveArray| |PrimitiveArrayFunctions2| + |PrimitiveFunctionCategory| |PrimitiveElement| |IntegerPrimesPackage| + |PrintPackage| |Product| |Property| |PropositionalFormula| + |PropositionalFormulaFunctions1| |PropositionalFormulaFunctions2| + |PropositionalLogic| |PriorityQueueAggregate| |PseudoRemainderSequence| + |PretendAst| |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| + |PlottableSpaceCurveCategory| |PolynomialSetCategory&| |PolynomialSetCategory| + |PolynomialSetUtilitiesPackage| |PseudoLinearNormalForm| + |PolynomialSquareFree| |PointCategory| |PointFunctions2| |PointPackage| + |PartialTranscendentalFunctions| |PushVariables| + |PAdicWildFunctionFieldIntegralBasis| |QuasiAlgebraicSet| |QuasiAlgebraicSet2| + |QuasiComponentPackage| |QueryEquation| |QuotientFieldCategory&| + |QuotientFieldCategory| |QuotientFieldCategoryFunctions2| |QuadraticForm| + |QuasiquoteAst| |QueueAggregate| |Quaternion| |QuaternionCategory&| + |QuaternionCategory| |QuaternionCategoryFunctions2| |Queue| |RadicalCategory&| + |RadicalCategory| |RadicalFunctionField| |RadixExpansion| |RadixUtilities| + |RandomNumberSource| |RationalFactorize| |RationalRetractions| + |RecursiveAggregate&| |RecursiveAggregate| |RealClosedField&| + |RealClosedField| |ElementaryRischDE| |ElementaryRischDESystem| + |TranscendentalRischDE| |TranscendentalRischDESystem| |RandomDistributions| + |ReducedDivisor| |ReduceAst| |RealConstant| |RealZeroPackage| + |RealZeroPackageQ| |RealSolvePackage| |RealClosure| |ReductionOfOrder| + |Reference| |RegularTriangularSet| |RadicalEigenPackage| + |RepresentationPackage1| |RepresentationPackage2| |RepeatedDoubling| + |RepeatedSquaring| |ResolveLatticeCompletion| |ResidueRing| |Result| + |ReturnAst| |RetractableTo&| |RetractableTo| |RetractSolvePackage| |RationalFunction| |RandomFloatDistributions| |RationalFunctionFactor| - |RationalFunctionFactorizer| |RGBColorModel| |RGBColorSpace| - |RegularChain| |RandomIntegerDistributions| |Ring&| |Ring| - |RationalInterpolation| |RightLinearSet| |RectangularMatrixCategory&| - |RectangularMatrixCategory| |RectangularMatrix| - |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| + |RationalFunctionFactorizer| |RGBColorModel| |RGBColorSpace| |RegularChain| + |RandomIntegerDistributions| |Ring&| |Ring| |RationalInterpolation| + |RightLinearSet| |RectangularMatrixCategory&| |RectangularMatrixCategory| + |RectangularMatrix| |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| |RangeBinding| |RealNumberSystem&| |RealNumberSystem| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| - |RecursivePolynomialCategory&| |RecursivePolynomialCategory| - |RepeatAst| |RealRootCharacterizationCategory&| - |RealRootCharacterizationCategory| |RegularSetDecompositionPackage| - |RegularTriangularSetCategory&| |RegularTriangularSetCategory| - |RegularTriangularSetGcdPackage| |RestrictAst| |RuntimeValue| - |RewriteRule| |RuleCalled| |Ruleset| + |RecursivePolynomialCategory&| |RecursivePolynomialCategory| |RepeatAst| + |RealRootCharacterizationCategory&| |RealRootCharacterizationCategory| + |RegularSetDecompositionPackage| |RegularTriangularSetCategory&| + |RegularTriangularSetCategory| |RegularTriangularSetGcdPackage| |RestrictAst| + |RuntimeValue| |RewriteRule| |RuleCalled| |Ruleset| |RationalUnivariateRepresentationPackage| |SimpleAlgebraicExtension| |SimpleAlgebraicExtensionAlgFactor| |SAERationalFunctionAlgFactor| |SingletonAsOrderedSet| |SpadSyntaxCategory| |SortedCache| |Scope| |StructuralConstantsPackage| |SequentialDifferentialPolynomial| - |SequentialDifferentialVariable| |Segment| |SegmentFunctions2| - |SegmentAst| |SegmentBinding| |SegmentBindingFunctions2| - |SegmentCategory| |SegmentExpansionCategory| |SequenceAst| |Set| - |SetAggregate&| |SetAggregate| |SetCategory&| |SetCategory| - |SetOfMIntegersInOneToN| |SExpression| |SExpressionCategory| - |SExpressionOf| |SimpleFortranProgram| - |SquareFreeQuasiComponentPackage| - |SquareFreeRegularTriangularSetGcdPackage| - |SquareFreeRegularTriangularSetCategory| - |SymmetricGroupCombinatoricFunctions| |SemiGroup&| |SemiGroup| - |SplitHomogeneousDirectProduct| |SturmHabichtPackage| |Signature| - |SignatureAst| |ElementaryFunctionSign| |RationalFunctionSign| - |SimplifyAlgebraicNumberConvertPackage| |SingleInteger| - |StackAggregate| |SquareMatrixCategory&| |SquareMatrixCategory| - |SmithNormalForm| |SparseMultivariatePolynomial| - |SparseMultivariateTaylorSeries| - |SquareFreeNormalizedTriangularSetCategory| - |PolynomialSolveByFormulas| |RadicalSolvePackage| - |TransSolvePackageService| |TransSolvePackage| |SortPackage| - |ThreeSpace| |ThreeSpaceCategory| |SpadAst| |SpadParser| + |SequentialDifferentialVariable| |Segment| |SegmentFunctions2| |SegmentAst| + |SegmentBinding| |SegmentBindingFunctions2| |SegmentCategory| + |SegmentExpansionCategory| |SequenceAst| |Set| |SetAggregate&| |SetAggregate| + |SetCategory&| |SetCategory| |SetOfMIntegersInOneToN| |SExpression| + |SExpressionCategory| |SExpressionOf| |SimpleFortranProgram| + |SquareFreeQuasiComponentPackage| |SquareFreeRegularTriangularSetGcdPackage| + |SquareFreeRegularTriangularSetCategory| |SymmetricGroupCombinatoricFunctions| + |SemiGroup&| |SemiGroup| |SplitHomogeneousDirectProduct| |SturmHabichtPackage| + |Signature| |SignatureAst| |ElementaryFunctionSign| |RationalFunctionSign| + |SimplifyAlgebraicNumberConvertPackage| |SingleInteger| |StackAggregate| + |SquareMatrixCategory&| |SquareMatrixCategory| |SmithNormalForm| + |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| + |SquareFreeNormalizedTriangularSetCategory| |PolynomialSolveByFormulas| + |RadicalSolvePackage| |TransSolvePackageService| |TransSolvePackage| + |SortPackage| |ThreeSpace| |ThreeSpaceCategory| |SpadAst| |SpadParser| |SpadAstExports| |SpecialOutputPackage| |SpecialFunctionCategory| |SplittingNode| |SplittingTree| |SquareMatrix| |StringAggregate&| |StringAggregate| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SemiRing| |Stack| |StreamAggregate&| |StreamAggregate| |SparseTable| |StepThrough| |StepAst| |StreamInfiniteProduct| |Stream| |StreamFunctions1| |StreamFunctions2| - |StreamFunctions3| |String| |StringTable| - |StreamTaylorSeriesOperations| |StreamTranscendentalFunctions| - |StreamTranscendentalFunctionsNonCommutative| |SubResultantPackage| - |SubSpace| |SuchThat| |SuchThatAst| |SparseUnivariateLaurentSeries| - |FunctionSpaceSum| |RationalFunctionSum| |SparseUnivariatePolynomial| - |SparseUnivariatePolynomialFunctions2| |SupFractionFactorizer| - |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| - |Switch| |Symbol| |SymmetricFunctions| |SymmetricPolynomial| - |TheSymbolTable| |SymbolTable| |Syntax| |SystemInteger| - |SystemNonNegativeInteger| |SystemPointer| |SystemSolvePackage| - |System| |TableauxBumpers| |Table| |Tableau| |TermAlgebraOperator| - |TangentExpansions| |TableAggregate&| |TableAggregate| - |TabulatedComputationPackage| |TemplateUtilities| |TexFormat| - |TexFormat1| |TextFile| |ToolsForSign| |TopLevelThreeSpace| - |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| - |Tree| |TrigonometricFunctionCategory&| + |StreamFunctions3| |String| |StringTable| |StreamTaylorSeriesOperations| + |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| + |SubResultantPackage| |SubSpace| |SuchThat| |SuchThatAst| + |SparseUnivariateLaurentSeries| |FunctionSpaceSum| |RationalFunctionSum| + |SparseUnivariatePolynomial| |SparseUnivariatePolynomialFunctions2| + |SupFractionFactorizer| |SparseUnivariatePuiseuxSeries| + |SparseUnivariateTaylorSeries| |Switch| |Symbol| |SymmetricFunctions| + |SymmetricPolynomial| |TheSymbolTable| |SymbolTable| |Syntax| |SystemInteger| + |SystemNonNegativeInteger| |SystemPointer| |SystemSolvePackage| |System| + |TableauxBumpers| |Table| |Tableau| |TermAlgebraOperator| |TangentExpansions| + |TableAggregate&| |TableAggregate| |TabulatedComputationPackage| + |TemplateUtilities| |TexFormat| |TexFormat1| |TextFile| |ToolsForSign| + |TopLevelThreeSpace| |TranscendentalFunctionCategory&| + |TranscendentalFunctionCategory| |Tree| |TrigonometricFunctionCategory&| |TrigonometricFunctionCategory| |TrigonometricManipulations| - |TriangularMatrixOperations| |TranscendentalManipulations| - |TaylorSeries| |TriangularSetCategory&| |TriangularSetCategory| - |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| |Type| |TypeAst| - |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| - |UniqueFactorizationDomain&| |UniqueFactorizationDomain| |UInt16| - |UInt32| |UInt64| |UInt8| |UnivariateLaurentSeries| - |UnivariateLaurentSeriesFunctions2| |UnivariateLaurentSeriesCategory| + |TriangularMatrixOperations| |TranscendentalManipulations| |TaylorSeries| + |TriangularSetCategory&| |TriangularSetCategory| |TubePlot| |TubePlotTools| + |Tuple| |TwoFactorize| |Type| |TypeAst| |UserDefinedPartialOrdering| + |UserDefinedVariableOrdering| |UniqueFactorizationDomain&| + |UniqueFactorizationDomain| |UInt16| |UInt32| |UInt64| |UInt8| + |UnivariateLaurentSeries| |UnivariateLaurentSeriesFunctions2| + |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesConstructorCategory| - |UnivariateLaurentSeriesConstructor| |UnivariateFactorize| - |UniversalSegment| |UniversalSegmentFunctions2| |UnivariatePolynomial| - |UnivariatePolynomialFunctions2| - |UnivariatePolynomialCommonDenominator| + |UnivariateLaurentSeriesConstructor| |UnivariateFactorize| |UniversalSegment| + |UniversalSegmentFunctions2| |UnivariatePolynomial| + |UnivariatePolynomialFunctions2| |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| - |UnivariatePolynomialMultiplicationPackage| - |UnivariatePolynomialCategory&| |UnivariatePolynomialCategory| - |UnivariatePolynomialCategoryFunctions2| + |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomialCategory&| + |UnivariatePolynomialCategory| |UnivariatePolynomialCategoryFunctions2| |UnivariatePowerSeriesCategory&| |UnivariatePowerSeriesCategory| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesFunctions2| |UnivariatePuiseuxSeriesCategory| |UnivariatePuiseuxSeriesConstructorCategory&| |UnivariatePuiseuxSeriesConstructorCategory| |UnivariatePuiseuxSeriesConstructor| - |UnivariatePuiseuxSeriesWithExponentialSingularity| - |UnaryRecursiveAggregate&| |UnaryRecursiveAggregate| - |UnivariateTaylorSeries| |UnivariateTaylorSeriesFunctions2| - |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesCategory| - |UnivariateTaylorSeriesODESolver| |UTSodetools| |UnionType| |Variable| - |VectorCategory&| |VectorCategory| |Vector| |VectorFunctions2| - |ViewportPackage| |TwoDimensionalViewport| |ThreeDimensionalViewport| - |ViewDefaultsPackage| |Void| |VectorSpace&| |VectorSpace| - |WeierstrassPreparation| |WildFunctionFieldIntegralBasis| |WhereAst| - |WhileAst| |WeightedPolynomials| |WuWenTsunTriangularSet| |XAlgebra| - |XDistributedPolynomial| |XExponentialPackage| |ExtensionField&| + |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnaryRecursiveAggregate&| + |UnaryRecursiveAggregate| |UnivariateTaylorSeries| + |UnivariateTaylorSeriesFunctions2| |UnivariateTaylorSeriesCategory&| + |UnivariateTaylorSeriesCategory| |UnivariateTaylorSeriesODESolver| + |UTSodetools| |UnionType| |Variable| |VectorCategory&| |VectorCategory| + |Vector| |VectorFunctions2| |ViewportPackage| |TwoDimensionalViewport| + |ThreeDimensionalViewport| |ViewDefaultsPackage| |Void| |VectorSpace&| + |VectorSpace| |WeierstrassPreparation| |WildFunctionFieldIntegralBasis| + |WhereAst| |WhileAst| |WeightedPolynomials| |WuWenTsunTriangularSet| + |XAlgebra| |XDistributedPolynomial| |XExponentialPackage| |ExtensionField&| |ExtensionField| |XFreeAlgebra| |XPBWPolynomial| |XPolynomial| - |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| - |YoungDiagram| |ParadoxicalCombinatorsForStreams| - |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| - |Enumeration| |Mapping| |Record| |Union| |bringDown| |s17adf| |nary?| - |pointSizeDefault| |degreePartition| |partialFraction| |laurentRep| - |makeprod| |completeHermite| |dioSolve| |cothIfCan| |extractTop!| - |setFieldInfo| |difference| |symmetricProduct| |minimumDegree| - |partialNumerators| |moebiusMu| |unprotectedRemoveRedundantFactors| - |pointData| |e01bhf| |nextColeman| |entry| |absolutelyIrreducible?| - |getCode| |point?| |maxPoints| |permutationGroup| - |nextNormalPrimitivePoly| |removeSquaresIfCan| |stirling2| |OMputAttr| - |pattern| |log2| |integralBasisAtInfinity| |showRegion| |qinterval| - |radicalOfLeftTraceForm| |d03eef| |makeYoungTableau| |f07fef| - |fixedPoints| |debug3D| |nextLatticePermutation| |qPot| - |shallowExpand| |c05nbf| |algebraicVariables| |identity| - |interactiveEnv| |pow| |e01sff| |OMReadError?| - |createNormalPrimitivePoly| |henselFact| |null| |abs| |localUnquote| - |solveRetract| |rootsOf| |doublyTransitive?| |constantOpIfCan| - |extensionDegree| |genericRightNorm| |palglimint| |partialQuotients| - |complete| |dec| |not| |setelt| |quasiRegular| |createNormalPoly| - |varselect| |tValues| |isOp| |d02cjf| |shiftRight| |integral?| |more?| - |and| |degreeSubResultant| |copy| |f04qaf| |positive?| |c06frf| - |opeval| |beauzamyBound| |part?| |lazyPseudoQuotient| |bernoulliB| - |f04mbf| |or| |discriminantEuclidean| |autoCoerce| |depth| |reduced?| - |tryFunctionalDecomposition?| |associatedSystem| |commaSeparate| - |numberOfFractionalTerms| |identitySquareMatrix| - |mainDefiningPolynomial| |xor| |hspace| |prinshINFO| |medialSet| - |interval| |gethi| |const| |quote| |e02bcf| |tanNa| |case| - |tanh2trigh| |prindINFO| |inR?| |dmpToP| |nextIrreduciblePoly| - |OMputEndBind| |child?| |createPrimitiveElement| |s21bdf| |top| |Zero| - |transcendent?| |polyPart| |setUnion| |iomode| |groebgen| - |useNagFunctions| |linearDependence| |critpOrder| |wordInGenerators| - |One| |subset?| |compdegd| |d02bbf| |flagFactor| |besselI| |c06fuf| - |e01sef| |primeFrobenius| |cardinality| |OMsetEncoding| |asimpson| - |oddInfiniteProduct| |reopen!| |newLine| |dark| |coordinates| |swap| - |coerceImages| |OMputEndApp| |vedf2vef| |tan2trig| |readInt8!| |numer| - |rootNormalize| |union| |rootSimp| |cCosh| |writable?| |critBonD| - |coerceS| |split| |pToDmp| |divideExponents| |ideal| |denom| - |mkIntegral| |complex?| |iCompose| |factor| |charthRoot| - |makeViewport3D| |reduceBasisAtInfinity| |addPoint| |triangular?| - |less?| |cyclicEntries| |pdf2df| |listexp| |sqrt| |errorKind| - |zeroDimPrime?| |separateFactors| |elt| |rightDiscriminant| - |cyclicGroup| |d01alf| |digits| |qqq| |pi| |getMultiplicationMatrix| - |real| |initiallyReduced?| |rightFactorIfCan| |resultantEuclidean| - |completeSmith| |deepestInitial| |triangularSystems| |bumptab| - |pomopo!| |cCoth| |linearlyDependent?| |imag| - |selectSumOfSquaresRoutines| |factorAndSplit| |any?| |minPoints3D| - |eigenvector| |unitNormal| |infRittWu?| |directProduct| |OMgetEndBVar| - |mainMonomials| |lineColorDefault| |getButtonValue| |powern| - |splitConstant| |s17acf| |cycleTail| |rdHack1| |resultant| |mkAnswer| - |removeIrreducibleRedundantFactors| |fi2df| |purelyTranscendental?| - |s17dlf| |bracket| |htrigs| |fortranInteger| |dualSignature| - |exponentialOrder| |leftCharacteristicPolynomial| |brace| |block| - |rdregime| |points| |cSin| |optional?| |f04maf| |groebner?| |makeEq| - |destruct| |contractSolve| |bat1| |trigs2explogs| |mainVariable?| - |stronglyReduced?| |internalDecompose| |possiblyInfinite?| - |signAround| |type| |updatD| |multiple?| |debug| |minPoints| |graphs| - |pdf2ef| |Si| |basisOfRightNucloid| |constantRight| |open| - |zeroMatrix| |copy!| |critM| D |divide| |probablyZeroDim?| - |quasiRegular?| |adaptive| |bivariate?| |writeByte!| |drawStyle| - |bfEntry| |singularAtInfinity?| |addBadValue| |exportedOperators| - |setrest!| |stiffnessAndStabilityFactor| |f02awf| |intcompBasis| - |void| |stop| |replace| |isList| |maxColIndex| |repSq| |setImagSteps| - |integralAtInfinity?| |simplifyPower| |monomial| |checkForZero| - |c06gcf| |zeroOf| |mapdiv| |An| |besselJ| |characteristicSet| - |leftRegularRepresentation| |e01bff| |multivariate| - |removeRoughlyRedundantFactorsInContents| |polyRDE| |exactQuotient| - |newline| |generalizedEigenvector| |operations| |s20acf| |predicates| - |leftTrace| |create3Space| |variables| |clearTheIFTable| |OMclose| - |eigenMatrix| |LazardQuotient| |dictionary| |index?| |Nul| |variable?| - |decompose| |f02ajf| |nthRootIfCan| |setRow!| |reflect| - |infiniteProduct| |dot| |printCode| |shufflein| |exptMod| |in?| - |d01anf| |routines| |stFunc1| |ScanFloatIgnoreSpacesIfCan| - |removeSinSq| |sorted?| |LazardQuotient2| |airyBi| - |expenseOfEvaluationIF| |edf2ef| |double?| |e01bgf| |tree| |f04asf| - |value| |resetBadValues| |prepareDecompose| |sturmVariationsOf| - |negative?| |removeRedundantFactorsInContents| |clearCache| - |imaginary| |putColorInfo| |s13aaf| |bindings| |phiCoord| |iiasec| - |entry?| |coefChoose| |generalInfiniteProduct| |plus!| - |palginfieldint| |f02axf| |cAcosh| |lazyResidueClass| |setprevious!| - |sPol| |taylor| |print| |extract!| |maxrow| |maxrank| |rootKerSimp| - |zeroSetSplitIntoTriangularSystems| |numericalOptimization| - |divideIfCan!| |resolve| |cCos| |s01eaf| |laurent| |iiperm| |mkcomm| - |read!| |prinb| |npcoef| |plotPolar| |setvalue!| |repeating?| - |aspFilename| |puiseux| |sech2cosh| |createMultiplicationTable| - |LiePoly| |edf2fi| |squareFreeLexTriangular| |meshFun2Var| - |laurentIfCan| |changeWeightLevel| |definingEquations| |rotate| - |safeCeiling| |pseudoQuotient| |removeRedundantFactors| |computeInt| - |cAsech| |fintegrate| |e02akf| |resultantEuclideannaif| |constructor| - |generalizedInverse| |representationType| |nextPrimitivePoly| |inv| - |outputSpacing| |minset| |algintegrate| |rightUnit| - |subResultantGcdEuclidean| |cyclicParents| |cSech| |ground?| |iiGamma| - |mapBivariate| |nsqfree| |outputAsTex| |alphabetic?| |extension| - |hermiteH| |setPosition| |midpoints| |ground| |space| |flexibleArray| - |jvmPublic| |polynomialZeros| |denominators| |solve1| |character?| - |recip| |divisorCascade| |linearAssociatedLog| |leadingMonomial| - |even?| |push!| |critT| |expintegrate| |numerators| |normalDenom| - |toseLastSubResultant| |leftRecip| |symmetricTensors| - |numberOfComputedEntries| |listBranches| |leadingCoefficient| - |upperCase?| |euclideanSize| |hdmpToDmp| |getConstant| - |numberOfNormalPoly| |jacobiIdentity?| |OMUnknownCD?| |leftRemainder| - |leftUnit| |iiexp| |fixedPoint| |rightTrace| |primitiveMonomials| - |logpart| |imagj| |genericRightTraceForm| |rewriteSetWithReduction| - |comparison| |removeCosSq| |carriageReturn| |hasoln| |gensym| - |reductum| |positiveSolve| |bright| |s18adf| |modularGcdPrimitive| - |diagonal?| |separateDegrees| |traceMatrix| |lifting1| |e02ahf| - |rootPoly| |hyperelliptic| |generalLambert| |arity| - |quasiAlgebraicSet| |lastSubResultant| |acoshIfCan| |argscript| - |rectangularMatrix| |mainExpression| |leadingIdeal| |returnTypeOf| - |incrementKthElement| |quasiMonic?| |bumptab1| |selectODEIVPRoutines| - |jvmUTF8ConstantTag| |d01gaf| |cycle| |iiacosh| |c05adf| |fTable| - |diagonalProduct| |outlineRender| |leftExtendedGcd| |rootBound| - |infinityNorm| |rightPower| |factorSFBRlcUnit| |tower| - |factorGroebnerBasis| |janko2| |SturmHabichtCoefficients| - |particularSolution| |quoByVar| |iFTable| |s17agf| |s18def| - |branchIfCan| |countRealRootsMultiple| |cosh2sech| |jvmSuper| |e04ucf| - |moduleSum| |changeName| |cyclotomicDecomposition| |OMputInteger| - |var1Steps| |shape| |interpolate| |eof?| |LagrangeInterpolation| - |f02xef| |complexExpand| |aromberg| |hexDigit?| |symmetricSquare| - |setLength!| |lhs| |quotientByP| |viewWriteAvailable| |removeSinhSq| - |ridHack1| |style| |getMeasure| |bipolarCylindrical| |s13acf| - |remove!| |figureUnits| |rhs| |testModulus| |getDatabase| |iidprod| - |jvmTransient| |matrix| |qualifier| |close| |vertConcat| - |bivariateSLPEBR| |nextItem| |loadNativeModule| |e| |sup| - |primextintfrac| |e04ycf| |endSubProgram| |formfeed| |readIfCan!| - |taylorRep| |eulerE| |linearDependenceOverZ| |complexNumeric| - |OMgetEndObject| |jvmStrict| |exprex| |laplacian| |quadraticNorm| - |display| |rootProduct| |overset?| |basisOfCenter| |callForm?| |cache| - |writeLine!| |hclf| |lifting| |LyndonBasis| |logGamma| |cAcsch| - |identityMatrix| |limitedint| |shuffle| |kernels| |s15aef| |top!| - |empty?| |expIfCan| |rightAlternative?| |factorSquareFreeByRecursion| - |reseed| |monomialIntegrate| |mathieu22| |operator| |scripted?| - |linkToFortran| |normalizeIfCan| |lowerBound| |infix| |rational| - |setEpilogue!| |vark| |imagE| |univariate| |resetNew| |irDef| - |leftLcm| |separate| |declare| |localIntegralBasis| |mapGen| - |monicRightDivide| |horizConcat| |OMsend| |cn| |unitVector| |ignore?| - |expt| |iidsum| |apply| |output| |sylvesterMatrix| |cons| |maxint| - |rischDEsys| |writeUInt8!| |idealSimplify| |width| |setValue!| - |graphImage| |jvmStringConstantTag| |isobaric?| |test| |first| - |f01rdf| |e02ddf| |resize| |unparse| |complexNormalize| - |idealiserMatrix| |jvmFieldrefConstantTag| |roughSubIdeal?| - |createGenericMatrix| |rest| |OMsupportsSymbol?| |mr| |padecf| - |squareFree| |myDegree| |mathieu24| |fortran| |component| |ptFunc| - |adaptive3D?| |setIntersection| |uncouplingMatrices| - |leftRankPolynomial| |meshPar1Var| |addMatch| |gderiv| |empty| |low| - |size?| |OMgetEndError| |horizontalTab| |leader| |prod| |source| - |deref| |constant?| |f01qcf| |internal?| |one?| |iicosh| |minPol| - |intensity| |message| |mapUp!| |setClosed| |expenseOfEvaluation| - |fortranCharacter| |setLabelValue| |vspace| |printTypes| |elem?| - |trim| |leftMinimalPolynomial| |setProperty| |iter| |listOfLists| - |writeInt8!| |internalLastSubResultant| |countable?| |rationalIfCan| - |optional| |reducedDiscriminant| |pointLists| |getPickedPoints| - |unitsColorDefault| |iisqrt2| |target| |digit| |complement| |cAtan| - |optpair| |evenInfiniteProduct| |linGenPos| |slex| |critMTonD1| - |f04jgf| |assign| |shiftLeft| |elRow1!| |cyclic?| |substring?| |fmecg| - |getVariableOrder| |multiplyExponents| |triangSolve| |e01baf| - |singleFactorBound| |member?| |denomLODE| |meatAxe| |setPredicates| - |iifact| |hostByteOrder| |OMencodingXML| |explicitlyFinite?| - |radicalEigenvector| |initTable!| |shrinkable| |countRealRoots| - |suffix?| |rename| |mulmod| |octon| |ef2edf| |dn| |e02bef| - |lastSubResultantEuclidean| |curveColor| |anfactor| |update| - |selectPolynomials| |interReduce| |secIfCan| |flatten| |invmultisect| - |monicDivide| |sechIfCan| |lazyPquo| |isMult| |quotient| |prefix?| - |root?| |subtractIfCan| |numberOfHues| |imagK| |interpret| - |graphStates| |coerceListOfPairs| |removeZero| |pToHdmp| |column| - |log10| |tableForDiscreteLogarithm| |f04adf| |realEigenvalues| - |extendedint| |recolor| |minPoly| |clipPointsDefault| - |SturmHabichtSequence| |tube| |script| |bitand| |polygamma| - |elementary| |delete!| |tanintegrate| |printStatement| - |coercePreimagesImages| |scalarMatrix| |bitCoef| |restorePrecision| - |bitior| |mantissa| |linearAssociatedOrder| |colorFunction| - |unrankImproperPartitions1| |rationalPoint?| |setAttributeButtonStep| - |binaryTournament| |df2mf| |escape| |cPower| |fortranComplex| - |nthCoef| |unit| |parseString| |central?| |unary?| |write!| - |normalizedAssociate| |chiSquare1| |tex| |decreasePrecision| - |reducedContinuedFraction| |iiasin| |digamma| |complexNumericIfCan| - |bfKeys| |interpretString| |insertionSort!| |subspace| |infix?| - |unvectorise| |leviCivitaSymbol| |rightRecip| |entries| |rem| - |normalForm| |corrPoly| |lexico| |principal?| |odd?| |mask| - |showFortranOutputStack| |sncndn| |goodnessOfFit| |tanSum| - |perfectSquare?| |quo| |createMultiplicationMatrix| |increment| - |anticoord| |sh| |d02raf| |integerBound| |explicitlyEmpty?| |bounds| - |result| |resultantReduit| |e02bbf| |realSolve| |palglimint0| - |doubleDisc| |coordinate| |bandedJacobian| |OMconnOutDevice| - |leftExactQuotient| |copies| |div| |harmonic| |measure| - |exactQuotient!| |mapSolve| |readLineIfCan!| |leftReducedSystem| - |ScanRoman| |quasiMonicPolynomials| |gcdcofact| |exquo| |match?| - |expextendedint| |cAsinh| |oneDimensionalArray| |roman| |child| - |e04naf| |addiag| |ode| |outerProduct| ~= |satisfy?| |readUInt8!| - |enqueue!| |externalList| |epilogue| |colorDef| |problemPoints| - |headRemainder| |reduction| |e02aef| |#| |fibonacci| |showTheIFTable| - |factorials| |pack!| |gcdcofactprim| |integrate| |degree| - |certainlySubVariety?| ~ |slash| |makeMulti| |changeMeasure| - |alphabetic| |e02gaf| |ricDsolve| |iisec| |s17dhf| |binary| - |argumentListOf| |arrayStack| |digit?| |rotatex| |realEigenvectors| - |fullDisplay| |eigenvalues| |rubiksGroup| |round| |localReal?| - |complementaryBasis| |fortranReal| |startStats!| |karatsubaDivide| - |makeGraphImage| |nthExponent| |fractionFreeGauss!| |inverseColeman| - |leadingBasisTerm| |compile| |/\\| |e04dgf| |extendedResultant| - |denomRicDE| |center| |factorByRecursion| |jvmFinal| |symmetric?| - |subresultantSequence| |nthExpon| |\\/| |f01ref| |lazyPseudoDivide| - |orbits| |semiResultantEuclideannaif| |monomial?| |inRadical?| - |vectorise| |OMputObject| |wordsForStrongGenerators| |sqfree| - |setOfMinN| |zerosOf| |dimensionOfIrreducibleRepresentation| |d03edf| - |equality| |nonSingularModel| |OMputSymbol| |axes| - |semiIndiceSubResultantEuclidean| |true| |hue| |inverse| |pointColor| - |e04gcf| |minRowIndex| |lookupFunction| |antisymmetric?| - |chineseRemainder| |s18aef| |binaryTree| |userOrdered?| - |monicRightFactorIfCan| |changeNameToObjf| |getOperands| |sinIfCan| - |typeLists| |oblateSpheroidal| |roughBasicSet| |retractable?| - |rootRadius| |expandTrigProducts| |leastPower| |closedCurve?| - |mapCoef| |rootSplit| |conjug| |rquo| |elaboration| |primlimintfrac| - |conditionP| |iiatan| |enterInCache| |redPo| |position| |edf2efi| - |traverse| |lflimitedint| |OMputFloat| |fillPascalTriangle| |saturate| - |noLinearFactor?| |HenselLift| |subst| |insert| |makeViewport2D| - |inspect| |iiasinh| |d01ajf| |showScalarValues| |cTanh| - |solveLinearPolynomialEquationByRecursion| |normDeriv2| |powerSum| - |dihedral| |table| |palgRDE0| |halfExtendedSubResultantGcd2| - |multiEuclideanTree| |f01maf| |e04jaf| |startTableGcd!| |trapezoidalo| - |addmod| |jvmInterfaceMethodConstantTag| |se2rfi| |perspective| - |jvmClassConstantTag| |changeVar| |errorInfo| |sts2stst| - |compactFraction| |cAcot| |wholeRagits| |s18acf| - |differentialVariables| |inputBinaryFile| |LyndonWordsList1| - |pushuconst| |doubleRank| |pushdown| |musserTrials| |objects| |mesh| - |e01bef| |outputBinaryFile| |integralMatrixAtInfinity| |euler| - |paraboloidal| |linearlyDependentOverZ?| |base| |UpTriBddDenomInv| - |readBytes!| |closeComponent| |isAbsolutelyIrreducible?| - |clipWithRanges| |iibinom| |f04arf| |iitan| |latex| |iiabs| |polyred| - |nullity| |mirror| |initial| |linears| |putProperty| |sqfrFactor| - |complexSolve| |open?| |safetyMargin| |appendPoint| - |halfExtendedSubResultantGcd1| |relationsIdeal| |bezoutResultant| - |solveLinear| |categories| |OMgetError| |s19adf| - |getSyntaxFormsFromFile| |zCoord| |intermediateResultsIF| - |primPartElseUnitCanonical!| |algDsolve| |irreducible?| |overbar| - |integralRepresents| |splitNodeOf!| |OMwrite| |new| - |semiResultantEuclidean2| |ldf2vmf| |setTopPredicate| |log| |Is| - |pile| |numericIfCan| |getZechTable| |symmetricRemainder| |mkPrim| - |monicCompleteDecompose| |smith| |compiledFunction| - |semiDiscriminantEuclidean| |autoReduced?| |contours| |build| - |zeroDimensional?| |s21bbf| |noValueMode| |OMserve| |extractBottom!| - |f02aef| |superscript| |topPredicate| |rCoord| |string?| - |roughEqualIdeals?| |uniform| |f02agf| |df2ef| |setAdaptive3D| - |listYoungTableaus| |lazyIrreducibleFactors| |set| |primeFactor| - |connect| |bezoutDiscriminant| |exponential1| |minus!| |swapRows!| - |crushedSet| |f02fjf| |rationalApproximation| |setleft!| |crest| - |aQuadratic| |composites| |f04mcf| |sparsityIF| |frst| |acscIfCan| - |jvmMethodrefConstantTag| |coerceL| |squareFreeFactors| - |derivationCoordinates| |acothIfCan| |approxNthRoot| |drawComplex| - |removeSuperfluousCases| |multiEuclidean| |region| |retract| - |reducedForm| |makeCrit| |logical?| |expressIdealMember| |previous| - |randnum| |solveInField| |nextSublist| |genericLeftTraceForm| |sort!| - |xCoord| |imagi| |list?| |c06ebf| |left| |power!| |getExplanations| - |extractClosed| |internalSubPolSet?| |inverseLaplace| |terms| - |swapColumns!| |d01amf| |f02adf| |right| |repeatUntilLoop| - |putProperties| |evaluateInverse| |OMmakeConn| |qelt| |rotate!| - |scaleRoots| |invertIfCan| |OMgetEndAtp| |bernoulli| RF2UTS - |radicalRoots| |internalAugment| |level| |putGraph| - |generalizedContinuumHypothesisAssumed| |qsetelt| - |solveLinearPolynomialEquationByFractions| |bottom!| - |ScanFloatIgnoreSpaces| |getProperty| |cdr| |filename| - |groebnerFactorize| |useEisensteinCriterion| |nodes| |OMputString| - |ord| |xRange| |removeCoshSq| |pushNewContour| |cot2trig| |nextPrime| - |isOr| |radPoly| |linear?| |OMopenFile| |indiceSubResultant| - |exteriorDifferential| |setMaxPoints3D| |yRange| |point| |irCtor| - |wronskianMatrix| |evenlambert| |reset| |LyndonCoordinates| |showAll?| - |stack| |innerSolve1| |parse| |modifyPoint| |setScreenResolution| - |pointPlot| |B1solve| |zRange| |isOpen?| |moebius| |overlabel| - |iiacsch| |roughUnitIdeal?| |sin?| |eulerPhi| |att2Result| |isImplies| - |distance| |map!| |calcRanges| |inputOutputBinaryFile| |geometric| - |square?| |write| |binomThmExpt| |diagonal| |makeop| |skewSFunction| - |numberOfPrimitivePoly| |qsetelt!| |nextsubResultant2| |makeUnit| - |series| |save| |scale| |jvmInterface| |viewPhiDefault| |polyRicDE| - |OMputError| |mapDown!| |screenResolution| |move| |reduceLODE| |last| - |OMgetSymbol| |computeCycleLength| |realRoots| |headReduced?| - |firstUncouplingMatrix| |internalSubQuasiComponent?| |btwFact| - |semiSubResultantGcdEuclidean1| |baseRDE| |assoc| |simplify| |updatF| - |taylorQuoByVar| |d01fcf| |s17ahf| |keys| |unrankImproperPartitions0| - |arg1| |maxRowIndex| |norm| |setlast!| |palgextint0| |rischDE| - |conditionsForIdempotents| |laplace| |simpleBounds?| - |stoseInternalLastSubResultant| |arg2| |cExp| |completeEval| - |subHeight| |simpson| |min| |virtualDegree| |SturmHabicht| - |totalfract| |OMParseError?| |tanh2coth| |key| |shift| - |genericLeftMinimalPolynomial| |isTimes| |solveLinearlyOverQ| |rk4| - |acsch| |factor1| |invertibleElseSplit?| |complexEigenvalues| - |ceiling| |allRootsOf| |symbol| |conditions| |d01asf| |backOldPos| - |quotedOperators| |createRandomElement| |failed| |multinomial| - |OMlistCDs| |reducedSystem| |redpps| |OMreceive| |expression| |match| - |badValues| |underscore| |OMgetEndApp| |range| |mightHaveRoots| - |removeZeroes| |property| |lastSubResultantElseSplit| |expr| |integer| - |tubePointsDefault| |useSingleFactorBound?| |index| |eval| - |linearPolynomials| |f07fdf| |float?| |createPrimitivePoly| - |ListOfTerms| |clipParametric| |minordet| |rightOne| |antiCommutator| - |normFactors| |froot| |areEquivalent?| |extractSplittingLeaf| - |fortranDoubleComplex| |curve?| |stopMusserTrials| |deepestTail| - |unitNormalize| |s19abf| ** |rotatez| |critMonD1| |semicolonSeparate| - |inGroundField?| |insertRoot!| |rule| |transform| |rowEch| |nlde| - |oddlambert| |coefficients| |pseudoRemainder| - |genericLeftDiscriminant| |fortranTypeOf| |algSplitSimple| - |jvmProtected| |morphism| |splitSquarefree| |dmp2rfi| |diagonalMatrix| - |fixedDivisor| |prepareSubResAlgo| |multiplyCoefficients| - |leftQuotient| |lex| |changeThreshhold| |bezoutMatrix| |iflist2Result| - |patternVariable| |stopTableGcd!| |extractPoint| |stopTable!| - |var2StepsDefault| |OMputEndBVar| |setProperties| |newSubProgram| - |extractProperty| |realZeros| |setErrorBound| |composite| |multMonom| - |iExquo| |separant| |s19aaf| |tensorProduct| - |semiResultantReduitEuclidean| |sign| |readInt32!| |c06ecf| - |univariateSolve| |birth| |leftFactorIfCan| |fortranCarriageReturn| - |plenaryPower| |messagePrint| |basisOfLeftAnnihilator| - |removeSuperfluousQuasiComponents| |setleaves!| |macroExpand| |size| - |lazyIntegrate| |unravel| |conical| |exprToGenUPS| |integer?| - |headAst| |irVar| |frobenius| |mat| |mainCoefficients| |chiSquare| - |s17ajf| |getMultiplicationTable| |setMinPoints3D| |rightExtendedGcd| - |symbol?| |UnVectorise| |maxdeg| |OMgetAtp| |characteristicPolynomial| - |symmetricGroup| |fixPredicate| |padicFraction| - |resetAttributeButtons| |iicos| |lieAlgebra?| |complexRoots| - |doubleFloatFormat| |baseRDEsys| |basisOfCentroid| |sub| - |factorPolynomial| |basicSet| |leastMonomial| |ratPoly| |charClass| - |parts| |standardBasisOfCyclicSubmodule| |ramifiedAtInfinity?| - |leftPower| |nullary?| |primintfldpoly| |cSec| |toseInvertible?| - |rightNorm| |limitPlus| |flexible?| |monomRDEsys| |createZechTable| - |pastel| |convergents| |OMgetBind| |cyclePartition| |asinhIfCan| - |iiacoth| |rangeIsFinite| |nil| |genericRightDiscriminant| - |OMUnknownSymbol?| |generalPosition| |permutations| |pmintegrate| - |listOfMonoms| |initializeGroupForWordProblem| |viewpoint| - |setPrologue!| |monic?| |trace2PowMod| |prevPrime| |Gamma| |clikeUniv| - |semiLastSubResultantEuclidean| |makeSketch| |polCase| |df2st| - |simplifyExp| |option?| |quadratic?| |ran| |OMputEndAttr| - |pointColorDefault| |subQuasiComponent?| |discriminant| |thenBranch| - |safeFloor| |approximate| |ocf2ocdf| |nthr| |generic?| |isNot| - |principalAncestors| |d02gaf| |symmetricDifference| |prem| |node| - |complex| |primextendedint| |tubePoints| |ParCondList| - |totalDifferential| |symmetricPower| |setOrder| |setRealSteps| - |numberOfChildren| |showIntensityFunctions| |curryRight| |quatern| - |stFuncN| |permutation| |insertMatch| |tanhIfCan| - |exprHasAlgebraicWeight| |s17def| |pade| |yellow| |innerint| |gbasis| - |makeFloatFunction| |cup| |coleman| |noKaratsuba| |gradient| - |cylindrical| |normalizedDivide| |derivative| |approximants| |lintgcd| - |cycleRagits| |clipSurface| |module| |datalist| |unaryFunction| - |e04fdf| |newReduc| |s18dcf| |s21baf| |physicalLength| |currentScope| - |selectFiniteRoutines| |trailingCoefficient| |writeBytes!| |checkRur| - |upDateBranches| |bitLength| |trapezoidal| |singular?| - |euclideanNormalForm| |constDsolve| |ode2| |isAtom| |sinhcosh| - |curryLeft| |optAttributes| |hasTopPredicate?| |mindeg| |cosSinInfo| - |createNormalElement| |shellSort| |hcrf| |useSingleFactorBound| - |fortranLinkerArgs| |retractIfCan| |OMencodingBinary| - |genericRightTrace| |monicModulo| |unmakeSUP| |BasicMethod| - |leftTraceMatrix| |identification| |complexEigenvectors| - |showArrayValues| |leftDivide| |integralLastSubResultant| |rightTrim| - |PollardSmallFactor| |primintegrate| |lquo| |OMbindTCP| |ip4Address| - |comp| |sturmSequence| |leftTrim| |lambert| |deepExpand| |totalDegree| - |exponential| |ipow| |close!| |polarCoordinates| |addPointLast| |inf| - |integralDerivationMatrix| |loopPoints| |rightUnits| |omError| - |e02def| |parent| |findConstructor| |Lazard| |d02ejf| - |nextPrimitiveNormalPoly| |createThreeSpace| |getCurve| |content| - |measure2Result| |primitivePart| |find| |linearAssociatedExp| |ranges| - |generator| |equation| |lp| |zero?| |Hausdorff| |youngGroup| - |rowEchLocal| |primitivePart!| |s19acf| |OMgetAttr| |companionBlocks| - |cAcos| |selectIntegrationRoutines| |bigEndian| |lyndon| |readable?| - |normalise| |solveLinearPolynomialEquation| |product| |OMgetString| - |po| |finiteBound| |c06gsf| UP2UTS |rk4a| |setAdaptive| - |withPredicates| |leaves| |exprToUPS| |selectPDERoutines| - |palgintegrate| |makeTerm| |condition| |map| |leftGcd| |f02abf| - |returnType!| |host| |leftDiscriminant| |applyRules| |multiset| - |rightMult| |minGbasis| |factorFraction| |varList| |taylorIfCan| |is?| - |linear| |toScale| |duplicates?| |startPolynomial| |OMcloseConn| - |iicsc| |continuedFraction| |rationalPower| |doubleComplex?| - |dmpToHdmp| |optimize| |laguerreL| |iroot| |iisinh| |e02baf| - |OMreadFile| |divisors| |polar| |acosIfCan| |scan| |fractionPart| - |endOfFile?| |polynomial| |normalizeAtInfinity| |OMputEndAtp| - |makeVariable| |cTan| |elements| |exists?| |asinIfCan| |outputGeneral| - |indices| |mainMonomial| |cos2sec| |capacity| |OMgetInteger| |cap| - |zeroVector| |cCsc| |convert| |ptree| |maxPoints3D| |plus| |dequeue!| - |OMputBind| |outputMeasure| |dimensionsOf| |parabolicCylindrical| - |setPoly| |reduceByQuasiMonic| |bubbleSort!| |initiallyReduce| - |numberOfIrreduciblePoly| |lllip| |leftFactor| |rk4f| |normal01| - |elaborateFile| |coth2trigh| |weights| |redPol| |high| |times| |incr| - |cyclotomic| |numberOfComponents| |buildSyntax| |generic| |imagI| - |minIndex| |stoseSquareFreePart| |validExponential| |besselK| - |jordanAlgebra?| |setStatus!| |rightTraceMatrix| |hi| |rightRank| - |perfectNthRoot| |direction| |balancedBinaryTree| |determinant| - |cschIfCan| |characteristic| |supersub| |stoseInvertibleSetreg| - |submod| |lowerCase| |chebyshevT| |cscIfCan| |compound?| - |brillhartTrials| |rightRemainder| |Vectorise| |partialDenominators| - |setColumn!| |lexGroebner| |internalIntegrate0| |extend| - |sortConstraints| |increase| |stoseInvertible?sqfreg| |tracePowMod| - |addMatchRestricted| |littleEndian| |schwerpunkt| - |rightRankPolynomial| |isConnected?| |collect| |viewZoomDefault| - |monom| |constant| |charpol| |shanksDiscLogAlgorithm| |nonQsign| - |cCot| |univcase| |powerAssociative?| |lyndonIfCan| |normalElement| - |ParCond| |atanhIfCan| |showClipRegion| |generateIrredPoly| - |removeRoughlyRedundantFactorsInPols| |back| - |rewriteIdealWithRemainder| |upperBound| |linearElement| |mappingAst| - |prinpolINFO| |conjugate| |d02kef| - |rewriteIdealWithQuasiMonicGenerators| |createIrreduciblePoly| - |mapExpon| |cycleLength| |f04atf| |ref| |members| |common| |cot2tan| - |integral| |enterPointData| |color| |findCycle| |contains?| - |minimumExponent| |c06eaf| |systemSizeIF| |fortranDouble| |tableau| - |innerSolve| |bsolve| |nativeModuleExtension| |integralMatrix| - |c05pbf| |next| |jvmAbstract| |concat!| |rombergo| |abelianGroup| - |perfectNthPower?| |postfix| |rootPower| |rank| |status| |leftOne| - |readUInt16!| |mergeFactors| |nthFractionalTerm| |lowerPolynomial| - |tan2cot| |setchildren!| |sin2csc| |jvmStatic| |redmat| - |basisOfLeftNucloid| |weakBiRank| |createLowComplexityNormalBasis| - |atanIfCan| |irreducibleFactor| |powers| |mainSquareFreePart| - |rightExactQuotient| |rightFactorCandidate| |GospersMethod| |queue| - |zeroDim?| |finite?| |reducedQPowers| |newTypeLists| |parabolic| - |maxIndex| |assert| |uniform01| |getOperator| |lazyEvaluate| |pr2dmp| - |divisor| |permutationRepresentation| |numberOfOperations| |setEmpty!| - |palgRDE| |univariatePolynomialsGcds| |explicitEntries?| - |zeroSetSplit| |linefeed| |nil?| |makingStats?| |encodingDirectory| - |solveid| |blankSeparate| |BumInSepFFE| |generate| |stronglyReduce| - |checkPrecision| |extractIfCan| |stFunc2| |variable| |categoryFrame| - |pushup| |enumerate| |basisOfRightAnnihilator| |cAtanh| |binding| - |nthFlag| |d01akf| |dim| |say| |testDim| |iterators| |headReduce| - |leftMult| |selectOptimizationRoutines| |radicalSimplify| - |incrementBy| |var1StepsDefault| |jvmNative| |infLex?| |inconsistent?| - |algebraicOf| |screenResolution3D| |coHeight| |iicoth| |setTex!| - |scalarTypeOf| |lists| |fracPart| |getStream| |jvmFloatConstantTag| - |rationalFunction| |expand| |lazyGintegrate| |getIdentifier| - |tubeRadiusDefault| |invertibleSet| |polygon?| |setelt!| |pair| - |bombieriNorm| |rightLcm| |e01daf| |filterWhile| |lazyVariations| - |selectAndPolynomials| |isQuotient| |adaptive?| |squareMatrix| - |clearTheFTable| |limit| |stopTableInvSet!| |internalIntegrate| - |rk4qc| |firstNumer| |isEquiv| |filterUntil| |componentUpperBound| - |fortranLiteral| |node?| |consnewpol| |recoverAfterFail| |quartic| - |generalizedContinuumHypothesisAssumed?| |cartesian| |ksec| - |numberOfVariables| |select| |wholeRadix| |pquo| |delay| - |getProperties| |invmod| |homogeneous?| |noncommutativeJordanAlgebra?| - |lSpaceBasis| |outputFloating| |scanOneDimSubspaces| |RittWuCompare| - |makeFR| |trunc| |innerEigenvectors| |s14baf| |jvmSynchronized| - |mapUnivariate| |s20adf| |pair?| |knownInfBasis| |s17dcf| |singRicDE| - |blue| |nand| |primitiveElement| |atom?| |completeEchelonBasis| - |numFunEvals3D| |oddintegers| |expint| |RemainderList| |properties| EQ - |edf2df| |height| |e02agf| |getMatch| |lfunc| |stoseLastSubResultant| - |solid| |mix| |lookup| |infinite?| |middle| |viewSizeDefault| - |quasiComponent| |translate| |LyndonWordsList| |initials| - |basisOfLeftNucleus| |resetVariableOrder| |fprindINFO| |fglmIfCan| - |s17akf| |selectNonFiniteRoutines| |exprHasWeightCosWXorSinWX| - |normalized?| |showAllElements| |alphanumeric?| |elliptic| |modTree| - |symbolIfCan| |nextPartition| |presub| |lfextlimint| |Ci| - |genericRightMinimalPolynomial| |rightScalarTimes!| - |indicialEquationAtInfinity| |aLinear| |zeroSquareMatrix| |f02aff| - |functorData| |c06gqf| |OMgetEndBind| |leaf?| |computePowers| - |minColIndex| |showSummary| |sumOfKthPowerDivisors| |palgextint| - |updateStatus!| |f04faf| |infinity| |inc| |swap!| |imports| |d02bhf| - |associatedEquations| |torsionIfCan| |functionIsFracPolynomial?| - |viewPosDefault| |trueEqual| |isPlus| |rewriteIdealWithHeadRemainder| - |concat| |getBadValues| |mapmult| |contract| |viewDefaults| - |showAttributes| |mesh?| |revert| |mainVariables| |sec2cos| |ravel| - |nullary| |graeffe| |f01qef| |insertBottom!| |support| |SFunction| - |accuracyIF| |maximumExponent| |kernel| |removeDuplicates!| |distFact| - |reshape| |setright!| |discreteLog| |resultantReduitEuclidean| - |lazyPrem| |freeOf?| |rename!| |gramschmidt| |list| |printHeader| - |iisqrt3| |mdeg| |sort| |transcendenceDegree| |algint| |constantIfCan| - |draw| |isAnd| |mpsode| |increasePrecision| |ODESolve| |exp1| - |highCommonTerms| |subSet| |lfintegrate| |prefixRagits| |e02adf| - |generalSqFr| |critB| |nodeOf?| |functionIsContinuousAtEndPoints| - |yCoordinates| |max| |random| |genus| |antiCommutative?| |byte| - |KrullNumber| |viewThetaDefault| |leadingTerm| |OMputVariable| - |monicDecomposeIfCan| |cSinh| |OMconnectTCP| |cAsec| - |characteristicSerie| |weight| |deleteRoutine!| |palgint0| |mainForm| - |linSolve| |Beta| |real?| |complexZeros| |coord| |backspace| |iitanh| - |id| |subResultantChain| |makeObject| |credPol| |comment| - |integralBasis| |tail| |rightMinimalPolynomial| |lyndon?| - |whatInfinity| |randomR| |cLog| |coef| |lo| |cubic| |roughBase?| - |fractRadix| |groebnerIdeal| |replaceKthElement| |airyAi| |elaborate| - |mainContent| |var2Steps| |step| |aQuartic| |jordanAdmissible?| - |choosemon| |call| |nor| |sdf2lst| |bytes| |branchPointAtInfinity?| - |matrixDimensions| |unitCanonical| |viewport2D| |heapSort| - |algebraic?| |row| |numericalIntegration| |stoseInvertibleSet| - |clipBoolean| |romberg| |iiacot| |generalizedEigenvectors| - |completeHensel| |title| |erf| |sylvesterSequence| |super| - |mainKernel| |OMsupportsCD?| |s17dgf| |splitDenominator| |iiasech| - |mapMatrixIfCan| |stosePrepareSubResAlgo| |int| |mainCharacterization| - |LowTriBddDenomInv| |char| |rst| |collectUpper| |getlo| |OMgetEndAttr| - |universe| |llprop| |matrixConcat3D| |cyclicEqual?| |sum| - |controlPanel| |pointColorPalette| |numberOfImproperPartitions| |push| - |principalIdeal| |iicot| |dilog| |stoseInvertible?| |e02ajf| - |defineProperty| |linearMatrix| |leadingIndex| |commutativeEquality| - |reindex| |external?| |lfinfieldint| |currentCategoryFrame| |sin| - |lazyPremWithDefault| |systemCommand| |makeResult| - |stoseInvertibleSetsqfreg| |genericLeftTrace| |f01rcf| |shiftRoots| - |tab| |explimitedint| |semiResultantEuclidean1| |cos| |f02bbf| - |before?| |seriesToOutputForm| |numberOfCycles| |solve| |float| - |linearForm| |indiceSubResultantEuclidean| - |degreeSubResultantEuclidean| |tan| |LiePolyIfCan| |f02wef| |normal| - |irForm| F2FG |tablePow| |outputForm| |has?| |cotIfCan| |setMinPoints| - |bivariatePolynomials| |cot| |iipow| |copyInto!| |hasPredicate?| - |prolateSpheroidal| |printInfo| |sn| |augment| |chebyshevU| - |clearTable!| |sec| |singularitiesOf| |e01saf| |rur| |fortranLogical| - |partitions| |radicalSolve| |graphState| |decrease| |alphanumeric| - |csc| |selectMultiDimensionalRoutines| |iisin| |diophantineSystem| - |commutator| |univariate?| |basisOfCommutingElements| - |transcendentalDecompose| |dom| |constantToUnaryFunction| |asin| - |viewWriteDefault| |algebraicSort| |showTheFTable| - |halfExtendedResultant1| |basis| |hasHi| |elliptic?| |monomialIntPoly| - |obj| |iisech| |subscript| |ratDenom| |expintfldpoly| |setMaxPoints| - |pop!| |rotatey| |bit?| |null?| |mindegTerm| |permanent| LODO2FUN - |radix| |polygon| |typeForm| |fill!| |e04mbf| |byteBuffer| |jacobi| - |d02gbf| |extendedSubResultantGcd| |OMunhandledSymbol| |op| - |predicate| |options| |biRank| |mainPrimitivePart| |pushucoef| - |simpsono| |processTemplate| |primes| GE |rischNormalize| - |OMgetObject| |distribute| |asecIfCan| |unknown| |deriv| |e01sbf| - 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|radicalEigenvectors| |patternMatchTimes| |closedCurve| |units| - |fortranCompilerName| |order| |iiacsc| |karatsubaOnce| - |fullPartialFraction| |cycles| |associates?| |asec| |parameters| - |search| |csubst| |zero| |alternative?| |readUInt32!| |rational?| - |intersect| |regime| |sample| |evaluate| |over| |toseInvertibleSet| - |acsc| |stirling1| |returns| |acschIfCan| |finiteBasis| |jacobian| - |arbitrary| |untab| |subResultantGcd| |diagonals| |subNode?| |sinh| - |genericPosition| |And| |f01brf| |f02akf| |s14abf| - |univariatePolynomials| |c06fqf| |sinhIfCan| |clearFortranOutputStack| - |cAcoth| |adjoint| |cosh| |deleteProperty!| |cCsch| |Or| - |jvmDoubleConstantTag| |resultantnaif| |factorial| - |primPartElseUnitCanonical| |makeRecord| |basisOfNucleus| |exponents| - |iteratedInitials| |rangePascalTriangle| |coth2tanh| |tanh| |trigs| - |error| |f2df| |Not| |check| |code| |univariatePolynomial| |hermite| - |addPoint2| |verticalTab| |closed| |isExpt| |UP2ifCan| |iterationVar| - |powmod| |coth| |droot| |schema| |eigenvectors| |df2fi| |f04axf| - |OMputApp| |OMencodingSGML| |currentSubProgram| |function| - |hypergeometric0F1| |iilog| |setref| |pdct| |outputList| |modulus| - |possiblyNewVariety?| |sech| |input| |definingPolynomial| - |computeCycleEntry| |eisensteinIrreducible?| |associative?| - |lexTriangular| |someBasis| |binomial| |hex| |numberOfMonomials| - |weighted| |hash| |constantCoefficientRicDE| |shallowCopy| |green| - |csch| |library| |atrapezoidal| |squareFreePrim| |shade| |rroot| - |makeSUP| |cyclicSubmodule| |refine| |sizeLess?| |explogs2trigs| - |getOrder| |count| |elColumn2!| |factorsOfDegree| |asinh| - |integralCoordinates| |subNodeOf?| |compBound| |sequences| |mathieu23| - |repeating| |continue| |rightRegularRepresentation| |complexIntegrate| - |double| |key?| |mainValue| |seed| |acosh| |primitive?| |packageCall| - |complexForm| |quoted?| |cross| |coerceP| |dAndcExp| |OMopenString| - |internalZeroSetSplit| |minimize| |atanh| |commutative?| |cycleEntry| - |associatorDependence| |whitePoint| |argument| |root| |reorder| - |removeConstantTerm| |f01mcf| |belong?| |prefix| |e02dff| |acoth| - |solid?| |totalLex| |wordInStrongGenerators| |squareFreePart| - |insertTop!| |getGoodPrime| |parents| |directory| |raisePolynomial| - |fractRagits| |OMputEndObject| |stoseIntegralLastSubResultant| - |toseSquareFreePart| |asech| |dfRange| |precision| |equiv| |cAcsc| - |mvar| |ldf2lst| |wrregime| |basisOfMiddleNucleus| |jokerMode| - |Lazard2| |f01qdf| |s17aff| |relerror| |inverseIntegralMatrix| - |modularFactor| |internalInfRittWu?| |constantOperator| |seriesSolve| - |arguments| |transpose| |summation| |parametersOf| |normalDeriv| - |variationOfParameters| |outputArgs| |multiple| |cAsin| - |cyclotomicFactorization| |bothWays| |lepol| |factorSquareFree| - |front| |eq?| |jvmIntegerConstantTag| |OMgetFloat| |disjunction| - |applyQuote| |factorset| |exp| |quickSort| |computeBasis| - |mergeDifference| |lowerCase?| |nextsousResultant2| |iicsch| - |hostPlatform| |scopes| |declare!| |exprToXXP| |hdmpToP| |bat| - |plusInfinity| |positiveRemainder| |OMlistSymbols| |cycleSplit!| - |selectOrPolynomials| |printingInfo?| |lcm| |acotIfCan| |integers| - |asechIfCan| |Frobenius| |laguerre| |minusInfinity| |OMread| |makeCos| - |stripCommentsAndBlanks| FG2F |clearDenominator| - |factorsOfCyclicGroupSize| |SturmHabichtMultiple| |dflist| |d01aqf| - |totalGroebner| |ruleset| |bipolar| |ramified?| |torsion?| - |decomposeFunc| |karatsuba| |gcd| |OMconnInDevice| |upperCase!| - |setsubMatrix!| |PDESolve| |youngDiagram| BY |nextNormalPoly| - |numeric| |changeBase| |coshIfCan| |generalTwoFactor| |c02aff| - |legendre| |false| |selectsecond| |commonDenominator| |rightQuotient| - |logIfCan| |radical| |insert!| |squareTop| |show| |d01apf| - |gcdPolynomial| |nothing| |setScreenResolution3D| |orthonormalBasis| - |prime?| |stiffnessAndStabilityOfODEIF| |extendedEuclidean| - |cRationalPower| |prime| |randomLC| |suchThat| |lift| |findBinding| - |subTriSet?| |indicialEquations| |nullSpace| |leftUnits| |moduloP| - |alternating| |just| |prologue| |drawCurves| |symbolTable| |dimension| - |reduce| |trace| |f02bjf| |ratpart| |merge!| - |exprHasLogarithmicWeights| |leadingExponent| |components| |segment| - |zoom| |reify| |leftAlternative?| |goto| |plot| |factors| - |squareFreePolynomial| |categoryMode| |c06gbf| |extendedIntegrate| - |ratDsolve| |setFormula!| |pol| |pushFortranOutputStack| - |infieldIntegrate| |preprocess| |binarySearchTree| - |chainSubResultants| |tubePlot| |rightCharacteristicPolynomial| - |imagk| |trivialIdeal?| |leftNorm| |irreducibleFactors| - |popFortranOutputStack| |totolex| |any| |realElementary| - |pleskenSplit| |HermiteIntegrate| |jvmPrivate| |e02zaf| NOT - |environment| |quadraticForm| |domainTemplate| |c06fpf| |triangulate| - |outputAsFortran| |bitTruth| |leadingSupport| |red| |setButtonValue| - |f07aef| OR |chvar| |physicalLength!| - |setLegalFortranSourceExtensions| |hitherPlane| |mathieu12| |bag| - |strongGenerators| |invertible?| |psolve| |currentEnv| |duplicates| - AND |notelem| |selectfirst| |tanQ| |curry| |factorOfDegree| |implies| - |combineFeatureCompatibility| |FormatArabic| |iprint| - |halfExtendedResultant2| |useEisensteinCriterion?| |reverse| - |position!| |orbit| |meshPar2Var| |second| |operation| |csch2sinh| - |kind| |palgLODE| |dihedralGroup| |rootOf| |badNum| - |purelyAlgebraicLeadingMonomial?| |cycleElt| |reverse!| |gcdprim| - |OMreadStr| |palgint| |third| |ReduceOrder| |floor| |iiatanh| - |partition| |select!| |createLowComplexityTable| |bits| - |listConjugateBases| |structuralConstants| |functionIsOscillatory| - |d01gbf| |weierstrass| |clip| |sumOfSquares| |imagJ| |children| F - |upperCase| |operators| |append| |minimalPolynomial| |exQuo| - |distdfact| |zeroDimPrimary?| |extractIndex| |subCase?| |iiacos| - |OMencodingUnknown| |readInt16!| |relativeApprox| |nthFactor| - |constantLeft| |modifyPointData| |hessian| |padicallyExpand| - |cyclicCopy| |curveColorPalette| |tRange| |showTheRoutinesTable| - |radicalEigenvalues| |cosIfCan| |car| |signature| |pascalTriangle| - |elseBranch| |light| |outputAsScript| |xn| |leftZero| |presuper| - |typeList| |deepCopy| |eyeDistance| |semiSubResultantGcdEuclidean2| - |signatureAst| |substitute| |reverseLex| |rspace| |connectTo| - |complexElementary| |f07adf| |outputFixed| |lazy?| |f01bsf| |tab1| - |removeDuplicates| |clearTheSymbolTable| |antisymmetricTensors| - |rowEchelon| |setnext!| |kovacic| |leftRank| |vector| |goodPoint| - |twoFactor| |socf2socdf| |sumSquares| |pole?| |superHeight| |init| - |listLoops| * |setDifference| |midpoint| |symbolTableOf| |c02agf| - |rewriteSetByReducingWithParticularGenerators| |balancedFactorisation| - |differentiate| |e02bdf| |mapUnivariateIfCan| |fixedPointExquo| - |curve| |drawToScale| |normal?| |alternatingGroup| |purelyAlgebraic?| - Y |patternMatch| |collectQuasiMonic| |create| |truncate| |hexDigit| - |normInvertible?| |semiDegreeSubResultantEuclidean| |graphCurves| - |matrixGcd| |rarrow| |wreath| |lagrange| |subPolSet?| |bumprow| - |unknownEndian| |legendreP| |ellipticCylindrical| = |nthRoot| UTS2UP - |nilFactor| |surface| |diff| |largest| - |inverseIntegralMatrixAtInfinity| |heap| |numberOfDivisors| - |numberOfComposites| |remove| |represents| |s14aaf| |voidMode| - |startTable!| |category| |tanIfCan| |axesColorDefault| |forLoop| - |expPot| |f02aaf| |power| < |subResultantsChain| |definingInequation| - |s17aef| |tubeRadius| |length| |domain| |infieldint| |supRittWu?| - |boundOfCauchy| |rightZero| > |createPrimitiveNormalPoly| - |rowEchelonLocal| |isPower| |attributeData| |aCubic| |besselY| - |scripts| |package| |overlap| |element?| |kmax| <= |euclideanGroebner| - |viewDeltaYDefault| |head| |sizeMultiplication| |merge| |expandPower| - |number?| |cond| |firstSubsetGray| |rules| |pushdterm| >= - |indicialEquation| |OMgetType| |jvmVolatile| |nonLinearPart| - |constantKernel| |magnitude| |perfectSqrt| |monicLeftDivide| - |OMputEndError| |rightGcd| |minrank| |construct| |twist| |mathieu11| - |removeRoughlyRedundantFactorsInPol| |t| |tanAn| |OMputAtp| - |hasSolution?| |atoms| |idealiser| |setCondition!| |kroneckerDelta| - |conjugates| |delta| |factorSquareFreePolynomial| |numerator| |label| - |coefficient| + |algebraicDecompose| |closed?| |printStats!| - |collectUnder| |associator| |poisson| |lfextendedint| |ode1| - |branchPoint?| |elRow2!| - |FormatRoman| |argumentList!| - |setVariableOrder| |expandLog| |subscriptedVariables| |splitLinear| - |name| |fortranLiteralLine| |jvmLongConstantTag| / |diag| |generators| - |nextSubsetGray| |drawComplexVectorField| SEGMENT GF2FG |e02dcf| - |mappingMode| |directSum| |body| |lieAdmissible?| |ScanArabic| - |setStatus| |stoseInvertible?reg| |dual| |regularRepresentation| - |hconcat| |algebraicCoefficients?| |rationalPoints| |dominantTerm| - |lighting| |unit?| |viewport3D| |normalize| |localAbs| - |leadingCoefficientRicDE| |supDimElseRittWu?| |startTableInvSet!| - |s13adf| |rootDirectory| |modularGcd| |subMatrix| |cfirst| - |linearPart| |whileLoop| |readByte!| |usingTable?| |sinh2csch| - |extendIfCan| |option| |e02daf| |zag| |wholePart| |sincos| - |sizePascalTriangle| |lambda| |Ei| |palgLODE0| |setfirst!| - |pmComplexintegrate| |listRepresentation| |makeSeries| - |antiAssociative?| |irreducibleRepresentation| |integerIfCan| - |makeSin| |s21bcf| |showTheSymbolTable| |firstDenom| |unexpand| - |s15adf| |coerce| |decimal| |divideIfCan| |brillhartIrreducible?| - |simplifyLog| |sayLength| |gcdPrimitive| |dequeue| |specialTrigs| - |exponent| |spherical| |mapExponents| |denominator| |printInfo!| - |pureLex| |lllp| |times!| |numFunEvals| |port| |thetaCoord| - |intPatternMatch| |OMgetApp| |inHallBasis?| |getGraph| - |tryFunctionalDecomposition| |hMonic| |leftScalarTimes!| |lprop| - |toroidal| |recur| |ddFact| |pseudoDivide| |reciprocalPolynomial| |eq| - |nil| |infinite| |arbitraryExponent| |approximate| |complex| - |shallowMutable| |canonical| |noetherian| |central| - |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| - |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| - |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| - |finiteAggregate| |shallowlyMutable| |commutative|)
\ No newline at end of file + |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| + |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| + |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| |Record| + |Union| |zeroOf| |rootsOf| |makeSketch| |inrootof| |droot| |iroot| |eq?| + |assoc| |doublyTransitive?| |knownInfBasis| |rootSplit| |ratDenom| |ratPoly| + |rootPower| |rootProduct| |rootSimp| |rootKerSimp| |leftRank| |rightRank| + |doubleRank| |weakBiRank| |biRank| |basisOfCommutingElements| + |basisOfLeftAnnihilator| |basisOfRightAnnihilator| |basisOfLeftNucleus| + |basisOfRightNucleus| |basisOfMiddleNucleus| |basisOfNucleus| |basisOfCenter| + |basisOfLeftNucloid| |basisOfRightNucloid| |basisOfCentroid| + |radicalOfLeftTraceForm| |obj| |dom| |any| |applyRules| |localUnquote| + |arbitrary| |setColumn!| |setRow!| |oneDimensionalArray| |associatedSystem| + |uncouplingMatrices| |associatedEquations| |arrayStack| |setButtonValue| + |setAttributeButtonStep| |resetAttributeButtons| |getButtonValue| |decrease| + |increase| |morphism| |balancedFactorisation| |before?| |mapDown!| |mapUp!| + |setleaves!| |balancedBinaryTree| |sylvesterMatrix| |bezoutMatrix| + |bezoutResultant| |bezoutDiscriminant| |bfEntry| |bfKeys| |inspect| |extract!| + |bag| |binding| |test| |setProperties| |setProperty| |deleteProperty!| |has?| + |comparison| |equality| |nary?| |unary?| |nullary?| |properties| |derivative| + |constantOperator| |constantOpIfCan| |integerBound| |setright!| |setleft!| + |brillhartIrreducible?| |brillhartTrials| |noLinearFactor?| |insertRoot!| + |binarySearchTree| |nor| |nand| |node| |binaryTournament| |binaryTree| |byte| + |setLength!| |capacity| |byteBuffer| |unknownEndian| |bigEndian| + |littleEndian| |subtractIfCan| |setPosition| + |generalizedContinuumHypothesisAssumed| + |generalizedContinuumHypothesisAssumed?| |countable?| |Aleph| |unravel| + |ravel| |leviCivitaSymbol| |kroneckerDelta| |reindex| |parents| + |principalAncestors| |exportedOperators| |alphanumeric| |alphabetic| + |hexDigit| |digit| |charClass| |alphanumeric?| |lowerCase?| |upperCase?| + |alphabetic?| |hexDigit?| |digit?| |escape| |verticalTab| |horizontalTab| + |backspace| |formfeed| |linefeed| |carriageReturn| |newline| |underscore| + |char| |ord| |mkIntegral| |radPoly| |rootPoly| |goodPoint| |chvar| + |removeDuplicates| |find| |e| |clipParametric| |clipWithRanges| |numberOfHues| + |yellow| |iifact| |iibinom| |iiperm| |iipow| |iidsum| |iidprod| |ipow| + |factorial| |multinomial| |permutation| |stirling1| |stirling2| |summation| + |factorials| |mkcomm| |polarCoordinates| |complex| |imaginary| |elaborateFile| + |elaborate| |macroExpand| |solid| |solid?| |denominators| |numerators| + |convergents| |approximants| |reducedForm| |partialQuotients| + |partialDenominators| |partialNumerators| |reducedContinuedFraction| |push| + |bindings| |cartesian| |polar| |cylindrical| |spherical| |parabolic| + |parabolicCylindrical| |paraboloidal| |ellipticCylindrical| + |prolateSpheroidal| |oblateSpheroidal| |bipolar| |bipolarCylindrical| + |toroidal| |conical| |modTree| |multiEuclideanTree| |complexZeros| + |divisorCascade| |graeffe| |pleskenSplit| |reciprocalPolynomial| |rootRadius| + |schwerpunkt| |setErrorBound| |startPolynomial| |cycleElt| + |computeCycleLength| |computeCycleEntry| |findConstructor| |arguments| + |operations| |dualSignature| |kind| |package| |domain| |category| |coerceP| + |powerSum| |elementary| |alternating| |cyclic| |dihedral| |cap| |cup| |wreath| + |SFunction| |skewSFunction| |cyclotomicDecomposition| + |cyclotomicFactorization| |rangeIsFinite| |functionIsContinuousAtEndPoints| + |functionIsOscillatory| |changeName| |exprHasWeightCosWXorSinWX| + |exprHasAlgebraicWeight| |exprHasLogarithmicWeights| + |combineFeatureCompatibility| |sparsityIF| |stiffnessAndStabilityFactor| + |stiffnessAndStabilityOfODEIF| |systemSizeIF| |expenseOfEvaluationIF| + |accuracyIF| |intermediateResultsIF| |subscriptedVariables| |central?| + |elliptic?| |qsetelt| |doubleResultant| |distdfact| |separateDegrees| + |trace2PowMod| |tracePowMod| |irreducible?| |decimal| |innerint| + |exteriorDifferential| |totalDifferential| |homogeneous?| |leadingBasisTerm| + |ignore?| |computeInt| |checkForZero| |nan?| |logGamma| |hypergeometric0F1| + |rotatez| |rotatey| |rotatex| |identity| |dictionary| |dioSolve| + |directProduct| |newLine| |copies| |say| |sayLength| |setnext!| |setprevious!| + |next| |previous| |datalist| |shanksDiscLogAlgorithm| |showSummary| |reflect| + |reify| |constructor| |functorData| |separant| |initial| |leader| |isobaric?| + |weights| |differentialVariables| |extractBottom!| |extractTop!| + |insertBottom!| |insertTop!| |bottom!| |top!| |dequeue| |makeObject| |recolor| + |drawComplex| |drawComplexVectorField| |setRealSteps| |setImagSteps| + |setClipValue| |draw| |option?| |range| |colorFunction| |curveColor| + |pointColor| |clip| |clipBoolean| |style| |toScale| |pointColorPalette| + |curveColorPalette| |var1Steps| |var2Steps| |space| |tubePoints| |tubeRadius| + |option| |weight| |makeVariable| |finiteBound| |sortConstraints| + |sumOfSquares| |splitLinear| |simpleBounds?| |linearMatrix| |linearPart| + |nonLinearPart| |quadratic?| |changeNameToObjf| |optAttributes| |Nul| + |exponents| |iisqrt2| |iisqrt3| |iiexp| |iilog| |iisin| |iicos| |iitan| + |iicot| |iisec| |iicsc| |iiasin| |iiacos| |iiatan| |iiacot| |iiasec| |iiacsc| + |iisinh| |iicosh| |iitanh| |iicoth| |iisech| |iicsch| |iiasinh| |iiacosh| + |iiatanh| |iiacoth| |iiasech| |iiacsch| |specialTrigs| |localReal?| + |rischNormalize| |realElementary| |validExponential| |rootNormalize| |tanQ| + |callForm?| |getIdentifier| |variable?| |getConstant| |type| |environment| + |typeForm| |irForm| |elaboration| |select!| |delete!| |sn| |cn| |dn| |sncndn| + |qsetelt!| |categoryFrame| |interactiveEnv| |currentEnv| |putProperties| + |getProperties| |putProperty| |getProperty| |scopes| |eigenvalues| + |eigenvector| |generalizedEigenvector| |generalizedEigenvectors| + |eigenvectors| |factorAndSplit| |rightOne| |leftOne| |rightZero| |leftZero| + |swap| |error| |minPoly| |freeOf?| |operators| |tower| |kernels| |mainKernel| + |distribute| |subst| |functionIsFracPolynomial?| |problemPoints| |zerosOf| + |singularitiesOf| |polynomialZeros| |f2df| |ef2edf| |ocf2ocdf| |socf2socdf| + |df2fi| |edf2fi| |edf2df| |expenseOfEvaluation| |numberOfOperations| |edf2efi| + |dfRange| |dflist| |df2mf| |ldf2vmf| |edf2ef| |vedf2vef| |df2st| |f2st| + |ldf2lst| |sdf2lst| |getlo| |gethi| |outputMeasure| |measure2Result| + |att2Result| |iflist2Result| |pdf2ef| |pdf2df| |df2ef| |fi2df| |mat| |neglist| + |multiEuclidean| |extendedEuclidean| |euclideanSize| |sizeLess?| + |simplifyPower| |number?| |seriesSolve| |constantToUnaryFunction| |tubePlot| + |exponentialOrder| |completeEval| |lowerPolynomial| |raisePolynomial| + |normalDeriv| |ran| |highCommonTerms| |mapCoef| |nthCoef| |binomThmExpt| + |pomopo!| |mapExponents| |linearAssociatedLog| |linearAssociatedOrder| + |linearAssociatedExp| |createNormalElement| |setLabelValue| |getCode| + |printCode| |code| |operation| |common| |printStatement| |save| |stop| |block| + |cond| |returns| |call| |comment| |continue| |goto| |repeatUntilLoop| + |whileLoop| |forLoop| |sin?| |zeroVector| |zeroSquareMatrix| + |identitySquareMatrix| |lookupFunction| |encodingDirectory| |attributeData| + |domainTemplate| |lSpaceBasis| |finiteBasis| |principal?| |divisor| + |useNagFunctions| |rationalPoints| |nonSingularModel| |algSplitSimple| + |hyperelliptic| |elliptic| |integralDerivationMatrix| |integralRepresents| + |integralCoordinates| |yCoordinates| |inverseIntegralMatrixAtInfinity| + |integralMatrixAtInfinity| |inverseIntegralMatrix| |integralMatrix| + |reduceBasisAtInfinity| |normalizeAtInfinity| |complementaryBasis| |integral?| + |integralAtInfinity?| |integralBasisAtInfinity| |ramified?| + |ramifiedAtInfinity?| |singular?| |singularAtInfinity?| |branchPoint?| + |branchPointAtInfinity?| |rationalPoint?| |absolutelyIrreducible?| |genus| + |getZechTable| |createZechTable| |createMultiplicationTable| + |createMultiplicationMatrix| |createLowComplexityTable| + |createLowComplexityNormalBasis| |representationType| |createPrimitiveElement| + |tableForDiscreteLogarithm| |factorsOfCyclicGroupSize| |sizeMultiplication| + |getMultiplicationMatrix| |getMultiplicationTable| |primitive?| + |numberOfIrreduciblePoly| |numberOfPrimitivePoly| |numberOfNormalPoly| + |createIrreduciblePoly| |createPrimitivePoly| |createNormalPoly| + |createNormalPrimitivePoly| |createPrimitiveNormalPoly| |nextIrreduciblePoly| + |nextPrimitivePoly| |nextNormalPoly| |nextNormalPrimitivePoly| + |nextPrimitiveNormalPoly| |leastAffineMultiple| |reducedQPowers| + |rootOfIrreduciblePoly| |write!| |read!| |iomode| |close!| |reopen!| |open| + |rightUnit| |leftUnit| |rightMinimalPolynomial| |leftMinimalPolynomial| + |associatorDependence| |lieAlgebra?| |jordanAlgebra?| + |noncommutativeJordanAlgebra?| |jordanAdmissible?| |lieAdmissible?| + |jacobiIdentity?| |powerAssociative?| |alternative?| |flexible?| + |rightAlternative?| |leftAlternative?| |antiAssociative?| |associative?| + |antiCommutative?| |commutative?| |rightCharacteristicPolynomial| + |leftCharacteristicPolynomial| |rightNorm| |leftNorm| |rightTrace| |leftTrace| + |someBasis| |sort!| |copyInto!| |sorted?| |LiePoly| |quickSort| |heapSort| + |shellSort| |outputSpacing| |outputGeneral| |outputFixed| |outputFloating| + |exp1| |log10| |log2| |rationalApproximation| |relerror| |complexSolve| + |complexRoots| |realRoots| |leadingTerm| |overlap| |hcrf| |hclf| |writable?| + |readable?| |exists?| |extension| |directory| |filename| |shallowExpand| + |deepExpand| |clearFortranOutputStack| |showFortranOutputStack| + |popFortranOutputStack| |pushFortranOutputStack| |topFortranOutputStack| + |setFormula!| |formula| |linkToFortran| |setLegalFortranSourceExtensions| + |fracPart| |polyPart| |fullPartialFraction| |primeFrobenius| |discreteLog| + |decreasePrecision| |increasePrecision| |bits| |unitNormalize| |unit| + |flagFactor| |sqfrFactor| |primeFactor| |nthFlag| |nthExponent| + |irreducibleFactor| |factors| |nilFactor| |regularRepresentation| + |traceMatrix| |randomLC| |minimize| |module| |rightRegularRepresentation| + |leftRegularRepresentation| |rightTraceMatrix| |leftTraceMatrix| + |rightDiscriminant| |leftDiscriminant| |represents| |mergeFactors| |isMult| + |applyQuote| |ground| |ground?| |exprToXXP| |exprToUPS| |exprToGenUPS| + |localAbs| |universe| |complement| |cardinality| |internalIntegrate0| + |makeCos| |makeSin| |iiGamma| |iiabs| |bringDown| |newReduc| |logical?| + |character?| |doubleComplex?| |complex?| |double?| |ffactor| |qfactor| + |UP2ifCan| |anfactor| |fortranCharacter| |fortranDoubleComplex| + |fortranComplex| |fortranLogical| |fortranInteger| |fortranDouble| + |fortranReal| |external?| |scalarTypeOf| |fortranCarriageReturn| + |fortranLiteral| |fortranLiteralLine| |processTemplate| |makeFR| + |musserTrials| |stopMusserTrials| |numberOfFactors| |modularFactor| + |useSingleFactorBound?| |useSingleFactorBound| |useEisensteinCriterion?| + |useEisensteinCriterion| |eisensteinIrreducible?| + |tryFunctionalDecomposition?| |tryFunctionalDecomposition| |btwFact| + |beauzamyBound| |bombieriNorm| |rootBound| |singleFactorBound| |quadraticNorm| + |infinityNorm| |scaleRoots| |shiftRoots| |degreePartition| |factorOfDegree| + |factorsOfDegree| |pascalTriangle| |rangePascalTriangle| |sizePascalTriangle| + |fillPascalTriangle| |safeCeiling| |safeFloor| |safetyMargin| |sumSquares| + |euclideanNormalForm| |euclideanGroebner| |factorGroebnerBasis| + |groebnerFactorize| |credPol| |redPol| |gbasis| |critT| |critM| |critB| + |critBonD| |critMTonD1| |critMonD1| |redPo| |hMonic| |updatF| |sPol| |updatD| + |minGbasis| |lepol| |prinshINFO| |prindINFO| |fprindINFO| |prinpolINFO| + |prinb| |critpOrder| |makeCrit| |virtualDegree| |lcm| + |conditionsForIdempotents| |genericRightDiscriminant| |genericRightTraceForm| + |genericLeftDiscriminant| |genericLeftTraceForm| |genericRightNorm| + |genericRightTrace| |genericRightMinimalPolynomial| |rightRankPolynomial| + |genericLeftNorm| |genericLeftTrace| |genericLeftMinimalPolynomial| + |leftRankPolynomial| |generic| |rightUnits| |leftUnits| |compBound| |tablePow| + |solveid| |testModulus| |HenselLift| |completeHensel| |multMonom| |build| + |leadingIndex| |leadingExponent| |GospersMethod| |nextSubsetGray| + |firstSubsetGray| |clipPointsDefault| |drawToScale| |adaptive| |figureUnits| + |putColorInfo| |appendPoint| |component| |ranges| |pointLists| + |makeGraphImage| |graphImage| |groebSolve| |testDim| |genericPosition| |lfunc| + |inHallBasis?| |reorder| |parameters| |headAst| |heap| |gcdprim| |gcdcofact| + |gcdcofactprim| |lintgcd| |hex| |count| |every?| |any?| |map!| |host| + |trueEqual| |factorList| |listConjugateBases| |matrixGcd| |divideIfCan!| + |leastPower| |idealiser| |idealiserMatrix| |moduleSum| |mapUnivariate| + |mapUnivariateIfCan| |mapMatrixIfCan| |mapBivariate| |fullDisplay| + |relationsIdeal| |saturate| |groebner?| |groebnerIdeal| |ideal| |leadingIdeal| + |backOldPos| |generalPosition| |quotient| |zeroDim?| |inRadical?| |in?| + |element?| |zeroDimPrime?| |zeroDimPrimary?| |radical| |primaryDecomp| + |contract| |gensym| |leadingSupport| |shrinkable| |physicalLength!| + |physicalLength| |flexibleArray| |elseBranch| |thenBranch| + |generalizedInverse| |imports| |sequence| |readBytes!| |readUInt32!| + |readInt32!| |readUInt16!| |readInt16!| |readUInt8!| |readInt8!| |readByte!| + |setFieldInfo| |pol| |xn| |dAndcExp| |repSq| |expPot| |qPot| |lookup| + |normal?| |basis| |normalElement| |minimalPolynomial| |position!| |eof?| + |inputBinaryFile| |increment| |incrementBy| |charpol| |solve1| + |innerEigenvectors| |compile| |declare| |parseString| |unparse| |flatten| + |lambda| |binary| |packageCall| |interpret| |innerSolve1| |innerSolve| + |makeEq| |modularGcdPrimitive| |modularGcd| |reduction| |signAround| |invmod| + |powmod| |mulmod| |submod| |addmod| |mask| |dec| |inc| |symmetricRemainder| + |positiveRemainder| |bit?| |algint| |algintegrate| |palgintegrate| + |palginfieldint| |bitLength| |bitCoef| |bitTruth| |contains?| |inf| + |qinterval| |interval| |unit?| |associates?| |unitCanonical| |unitNormal| + |lfextendedint| |lflimitedint| |lfinfieldint| |lfintegrate| |lfextlimint| + |BasicMethod| |PollardSmallFactor| |showTheFTable| |clearTheFTable| |fTable| + |showAttributes| |entry| |palgint0| |palgextint0| |palglimint0| |palgRDE0| + |palgLODE0| |chineseRemainder| |divisors| |eulerPhi| |fibonacci| |harmonic| + |jacobi| |moebiusMu| |numberOfDivisors| |sumOfDivisors| + |sumOfKthPowerDivisors| |HermiteIntegrate| |palgint| |palgextint| |palglimint| + |palgRDE| |palgLODE| |splitConstant| |pmComplexintegrate| |pmintegrate| + |infieldint| |extendedint| |limitedint| |integerIfCan| |internalIntegrate| + |infieldIntegrate| |limitedIntegrate| |extendedIntegrate| |varselect| |kmax| + |ksec| |vark| |removeConstantTerm| |mkPrim| |intPatternMatch| |primintegrate| + |expintegrate| |tanintegrate| |primextendedint| |expextendedint| + |primlimitedint| |explimitedint| |primextintfrac| |primlimintfrac| + |primintfldpoly| |expintfldpoly| |monomialIntegrate| |monomialIntPoly| + |inverseLaplace| |inputOutputBinaryFile| |closed| |bothWays| |input| |resolve| + |bytes| |ip4Address| |iprint| |elem?| |notelem| |logpart| |ratpart| |mkAnswer| + |irDef| |irCtor| |irVar| |perfectNthPower?| |perfectNthRoot| |approxNthRoot| + |perfectSquare?| |perfectSqrt| |approxSqrt| |generateIrredPoly| + |complexExpand| |complexIntegrate| |dimensionOfIrreducibleRepresentation| + |irreducibleRepresentation| |checkRur| |cAcsch| |cAsech| |cAcoth| |cAtanh| + |cAcosh| |cAsinh| |cCsch| |cSech| |cCoth| |cTanh| |cCosh| |cSinh| |cAcsc| + |cAsec| |cAcot| |cAtan| |cAcos| |cAsin| |cCsc| |cSec| |cCot| |cTan| |cCos| + |cSin| |cLog| |cExp| |cRationalPower| |cPower| |seriesToOutputForm| |iCompose| + |taylorQuoByVar| |iExquo| |getStream| |getRef| |makeSeries| |mappingMode| + |categoryMode| |voidMode| |noValueMode| |jokerMode| GF2FG FG2F F2FG + |explogs2trigs| |trigs2explogs| |swap!| |fill!| |minIndex| |maxIndex| |entry?| + |indices| |index?| |entries| |categories| |jvmInterface| |jvmSuper| + |jvmNameAndTypeConstantTag| |jvmInterfaceMethodConstantTag| + |jvmMethodrefConstantTag| |jvmFieldrefConstantTag| |jvmStringConstantTag| + |jvmClassConstantTag| |jvmDoubleConstantTag| |jvmLongConstantTag| + |jvmFloatConstantTag| |jvmIntegerConstantTag| |jvmUTF8ConstantTag| + |jvmTransient| |jvmVolatile| |jvmStrict| |jvmAbstract| |jvmNative| + |jvmSynchronized| |jvmFinal| |jvmStatic| |jvmProtected| |jvmPrivate| + |jvmPublic| |search| |key?| |symbolIfCan| |kernel| |argument| |constantKernel| + |constantIfCan| |kovacic| |unknown| |laplace| |trailingCoefficient| + |normalizeIfCan| |polCase| |distFact| |identification| |LyndonCoordinates| + |LyndonBasis| |zeroDimensional?| |fglmIfCan| |groebner| |lexTriangular| + |squareFreeLexTriangular| |belong?| |erf| |dilog| |li| |Ci| |Si| |Ei| + |linGenPos| |groebgen| |totolex| |minPol| |computeBasis| |coord| |anticoord| + |intcompBasis| |choosemon| |transform| |pack!| |library| |complexLimit| + |limit| |linearlyDependent?| |linearDependence| |solveLinear| |linearElement| + |reducedSystem| |leftReducedSystem| |linearForm| |setDifference| + |setIntersection| |setUnion| |append| |null| |nil| |substitute| |duplicates?| + |mapGen| |mapExpon| |commutativeEquality| |leftMult| |rightMult| |makeUnit| + |reverse!| |reverse| |nthFactor| |nthExpon| |makeMulti| |makeTerm| + |listOfMonoms| |insert| |delete| |symmetricSquare| |factor1| + |symmetricProduct| |symmetricPower| |directSum| |\\/| |/\\| ~ + |solveLinearPolynomialEquationByFractions| |hasSolution?| |linSolve| + |LyndonWordsList| |LyndonWordsList1| |lyndonIfCan| |lyndon| |lyndon?| + |numberOfComputedEntries| |rst| |frst| |lazyEvaluate| |lazy?| + |explicitlyEmpty?| |explicitEntries?| |matrixDimensions| |matrixConcat3D| + |setelt!| |plus| |identityMatrix| |zeroMatrix| |iter| |arg1| |arg2| |comp| + |mappingAst| |nullary| |fixedPoint| |id| |recur| |const| |curry| |diag| + |curryRight| |curryLeft| |constantRight| |constantLeft| |twist| + |setsubMatrix!| |subMatrix| |swapColumns!| |swapRows!| |vertConcat| + |horizConcat| |squareTop| |elRow1!| |elRow2!| |elColumn2!| + |fractionFreeGauss!| |invertIfCan| |copy!| |plus!| |minus!| |leftScalarTimes!| + |rightScalarTimes!| |times!| |power!| |nothing| |just| |gradient| |divergence| + |laplacian| |hessian| |bandedHessian| |jacobian| |bandedJacobian| |duplicates| + |removeDuplicates!| |linears| |ddFact| |separateFactors| |exptMod| + |meshPar2Var| |meshFun2Var| |meshPar1Var| |ptFunc| |minimumExponent| + |maximumExponent| |precision| |mantissa| |rowEch| |rowEchLocal| + |rowEchelonLocal| |normalizedDivide| |maxint| |binaryFunction| + |makeFloatFunction| |function| |makeRecord| |unaryFunction| |compiledFunction| + |corrPoly| |lifting| |lifting1| |exprex| |coerceL| |coerceS| |frobenius| + |computePowers| |pow| |An| |UnVectorise| |Vectorise| |setPoly| |index| + |exponent| |exQuo| |moebius| |rightRecip| |leftRecip| |leftPower| |rightPower| + |derivationCoordinates| |generator| |one?| |splitSquarefree| |normalDenom| + |reshape| |totalfract| |pushdterm| |pushucoef| |pushuconst| + |numberOfMonomials| |multiset| |systemCommand| |mergeDifference| + |squareFreePrim| |compdegd| |univcase| |consnewpol| |nsqfree| |intChoose| + |coefChoose| |myDegree| |normDeriv2| |plenaryPower| |c02aff| |c02agf| |c05adf| + |c05nbf| |c05pbf| |c06eaf| |c06ebf| |c06ecf| |c06ekf| |c06fpf| |c06fqf| + |c06frf| |c06fuf| |c06gbf| |c06gcf| |c06gqf| |c06gsf| |d01ajf| |d01akf| + |d01alf| |d01amf| |d01anf| |d01apf| |d01aqf| |d01asf| |d01bbf| |d01fcf| + |d01gaf| |d01gbf| |d02bbf| |d02bhf| |d02cjf| |d02ejf| |d02gaf| |d02gbf| + |d02kef| |d02raf| |d03edf| |d03eef| |d03faf| |e01baf| |e01bef| |e01bff| + |e01bgf| |e01bhf| |e01daf| |e01saf| |e01sbf| |e01sef| |e01sff| |e02adf| + |e02aef| |e02agf| |e02ahf| |e02ajf| |e02akf| |e02baf| |e02bbf| |e02bcf| + |e02bdf| |e02bef| |e02daf| |e02dcf| |e02ddf| |e02def| |e02dff| |e02gaf| + |e02zaf| |e04dgf| |e04fdf| |e04gcf| |e04jaf| |e04mbf| |e04naf| |e04ucf| + |e04ycf| |f01brf| |f01bsf| |f01maf| |f01mcf| |f01qcf| |f01qdf| |f01qef| + |f01rcf| |f01rdf| |f01ref| |f02aaf| |f02abf| |f02adf| |f02aef| |f02aff| + |f02agf| |f02ajf| |f02akf| |f02awf| |f02axf| |f02bbf| |f02bjf| |f02fjf| + |f02wef| |f02xef| |f04adf| |f04arf| |f04asf| |f04atf| |f04axf| |f04faf| + |f04jgf| |f04maf| |f04mbf| |f04mcf| |f04qaf| |f07adf| |f07aef| |f07fdf| + |f07fef| |s01eaf| |s13aaf| |s13acf| |s13adf| |s14aaf| |s14abf| |s14baf| + |s15adf| |s15aef| |s17acf| |s17adf| |s17aef| |s17aff| |s17agf| |s17ahf| + |s17ajf| |s17akf| |s17dcf| |s17def| |s17dgf| |s17dhf| |s17dlf| |s18acf| + |s18adf| |s18aef| |s18aff| |s18dcf| |s18def| |s19aaf| |s19abf| |s19acf| + |s19adf| |s20acf| |s20adf| |s21baf| |s21bbf| |s21bcf| |s21bdf| + |fortranCompilerName| |fortranLinkerArgs| |aspFilename| |dimensionsOf| + |checkPrecision| |restorePrecision| |antiCommutator| |commutator| |associator| + |complexEigenvalues| |complexEigenvectors| |isConnected?| |connectTo| |shift| + |normalizedAssociate| |normalize| |outputArgs| |normInvertible?| |normFactors| + |npcoef| |listexp| |characteristicPolynomial| |realEigenvalues| + |realEigenvectors| |halfExtendedResultant2| |halfExtendedResultant1| + |extendedResultant| |subResultantsChain| |lazyPseudoQuotient| + |lazyPseudoRemainder| |bernoulliB| |eulerE| |numeric| |complexNumeric| + |numericIfCan| |complexNumericIfCan| |FormatArabic| |ScanArabic| |FormatRoman| + |ScanRoman| |ScanFloatIgnoreSpaces| |ScanFloatIgnoreSpacesIfCan| + |numericalIntegration| |rk4| |rk4a| |rk4qc| |rk4f| |aromberg| |asimpson| + |atrapezoidal| |romberg| |simpson| |trapezoidal| |rombergo| |simpsono| + |trapezoidalo| |sup| |inv| |imagE| |imagk| |imagj| |imagi| |octon| |ODESolve| + |constDsolve| |showTheIFTable| |clearTheIFTable| |keys| |iFTable| + |showIntensityFunctions| |expint| |diff| |algDsolve| |denomLODE| + |indicialEquations| |indicialEquation| |denomRicDE| |leadingCoefficientRicDE| + |constantCoefficientRicDE| |changeVar| |ratDsolve| + |indicialEquationAtInfinity| |reduceLODE| |singRicDE| |polyRicDE| |ricDsolve| + |triangulate| |solveInField| |wronskianMatrix| |variationOfParameters| + |lexico| |OMmakeConn| |OMcloseConn| |OMconnInDevice| |OMconnOutDevice| + |OMconnectTCP| |OMbindTCP| |OMopenFile| |OMopenString| |OMclose| + |OMsetEncoding| |OMputApp| |OMputAtp| |OMputAttr| |OMputBind| |OMputBVar| + |OMputError| |OMputObject| |OMputEndApp| |OMputEndAtp| |OMputEndAttr| + |OMputEndBind| |OMputEndBVar| |OMputEndError| |OMputEndObject| |OMputInteger| + |OMputFloat| |OMputVariable| |OMputString| |OMputSymbol| |OMgetApp| |OMgetAtp| + |OMgetAttr| |OMgetBind| |OMgetBVar| |OMgetError| |OMgetObject| |OMgetEndApp| + |OMgetEndAtp| |OMgetEndAttr| |OMgetEndBind| |OMgetEndBVar| |OMgetEndError| + |OMgetEndObject| |OMgetInteger| |OMgetFloat| |OMgetVariable| |OMgetString| + |OMgetSymbol| |OMgetType| |OMencodingBinary| |OMencodingSGML| |OMencodingXML| + |OMencodingUnknown| |omError| |errorInfo| |errorKind| |OMReadError?| + |OMUnknownSymbol?| |OMUnknownCD?| |OMParseError?| |OMwrite| |po| |op| |OMread| + |OMreadFile| |OMreadStr| |OMlistCDs| |OMlistSymbols| |OMsupportsCD?| + |OMsupportsSymbol?| |OMunhandledSymbol| |OMreceive| |OMsend| |OMserve| + |infinity| |makeop| |opeval| |evaluateInverse| |evaluate| |conjug| |adjoint| + |arity| |getDatabase| |numericalOptimization| |optimize| |goodnessOfFit| + |whatInfinity| |infinite?| |finite?| |minusInfinity| |plusInfinity| |pureLex| + |totalLex| |reverseLex| |min| |leftLcm| |rightExtendedGcd| |rightGcd| + |rightExactQuotient| |rightRemainder| |rightQuotient| |rightLcm| + |leftExtendedGcd| |leftGcd| |leftExactQuotient| |leftRemainder| |leftQuotient| + |times| |apply| |monicLeftDivide| |monicRightDivide| |leftDivide| + |rightDivide| |hermiteH| |laguerreL| |legendreP| |outputList| |writeBytes!| + |writeUInt8!| |writeInt8!| |writeByte!| |isOpen?| |outputBinaryFile| |not| + |or| |and| |quo| |rem| |div| >= > ~= |blankSeparate| |semicolonSeparate| + |commaSeparate| |pile| |paren| |bracket| |prod| |overlabel| |overbar| |prime| + |quote| |supersub| |presuper| |presub| |super| |sub| |rarrow| |assign| |slash| + |over| |zag| |box| |label| |infix?| |postfix| |infix| |prefix| |vconcat| + |hconcat| |rspace| |vspace| |hspace| |superHeight| |subHeight| |height| + |width| |doubleFloatFormat| |messagePrint| |message| |members| |padecf| |pade| + |root| |quotientByP| |moduloP| |modulus| |digits| |continuedFraction| |pair| + |light| |pastel| |bright| |dim| |dark| |getSyntaxFormsFromFile| |surface| + |coordinate| |conjugates| |shuffle| |shufflein| |sequences| |permutations| + |lists| |makeResult| |is?| |Is| |addMatchRestricted| |insertMatch| |addMatch| + |getMatch| |failed| |failed?| |optpair| |getBadValues| |resetBadValues| + |hasTopPredicate?| |topPredicate| |setTopPredicate| |patternVariable| + |withPredicates| |setPredicates| |predicates| |hasPredicate?| |optional?| + |multiple?| |generic?| |quoted?| |inR?| |isList| |isQuotient| |isOp| |Zero| + |satisfy?| |addBadValue| |badValues| |retractable?| |ListOfTerms| |One| + |PDESolve| |leftFactor| |rightFactorCandidate| |measure| D |ptree| + |coerceImages| |fixedPoints| |odd?| |even?| |numberOfCycles| |cyclePartition| + |coerceListOfPairs| |coercePreimagesImages| |listRepresentation| |permanent| + |cycles| |cycle| |initializeGroupForWordProblem| <= < |support| + |wordInGenerators| |wordInStrongGenerators| |orbits| |orbit| + |permutationGroup| |wordsForStrongGenerators| |strongGenerators| |base| + |generators| |bivariateSLPEBR| |solveLinearPolynomialEquationByRecursion| + |factorByRecursion| |factorSquareFreeByRecursion| |randomR| |factorSFBRlcUnit| + |charthRoot| |conditionP| |solveLinearPolynomialEquation| + |factorSquareFreePolynomial| |factorPolynomial| |squareFreePolynomial| + |gcdPolynomial| |torsion?| |torsionIfCan| |getGoodPrime| |badNum| |mix| + |doubleDisc| |polyred| |padicFraction| |padicallyExpand| + |numberOfFractionalTerms| |nthFractionalTerm| |firstNumer| |firstDenom| + |compactFraction| |partialFraction| |gcdPrimitive| |symmetricGroup| + |alternatingGroup| |abelianGroup| |cyclicGroup| |dihedralGroup| |mathieu11| + |mathieu12| |mathieu22| |mathieu23| |mathieu24| |janko2| |rubiksGroup| + |youngGroup| |lexGroebner| |totalGroebner| |expressIdealMember| + |principalIdeal| |LagrangeInterpolation| |psolve| |wrregime| |rdregime| + |bsolve| |dmp2rfi| |se2rfi| |pr2dmp| |hasoln| |ParCondList| |redpps| |B1solve| + |factorset| |maxrank| |minrank| |minset| |nextSublist| |overset?| |ParCond| + |redmat| |regime| |sqfree| |inconsistent?| |debug| |numFunEvals| |setAdaptive| + |adaptive?| |setScreenResolution| |screenResolution| |setMaxPoints| + |maxPoints| |setMinPoints| |minPoints| |parametric?| |plotPolar| |debug3D| + |numFunEvals3D| |setAdaptive3D| |adaptive3D?| |setScreenResolution3D| + |screenResolution3D| |setMaxPoints3D| |maxPoints3D| |setMinPoints3D| + |minPoints3D| |tValues| |tRange| |plot| |pointPlot| |calcRanges| |assert| + |optional| |multiple| |fixPredicate| |patternMatch| |patternMatchTimes| + |bernoulli| |chebyshevT| |chebyshevU| |cyclotomic| |euler| |fixedDivisor| + |laguerre| |legendre| |dmpToHdmp| |hdmpToDmp| |pToHdmp| |hdmpToP| |dmpToP| + |pToDmp| |sylvesterSequence| |sturmSequence| |boundOfCauchy| + |sturmVariationsOf| |lazyVariations| |content| |primitiveMonomials| + |totalDegree| |minimumDegree| |monomials| |isPlus| |isTimes| |isExpt| + |isPower| |rroot| |qroot| |froot| |nthr| |port| |firstUncouplingMatrix| + |integral| |primitiveElement| |nextPrime| |prevPrime| |primes| |print| + |selectsecond| |selectfirst| |makeprod| |property| |disjunction| |conjunction| + |isEquiv| |isImplies| |isOr| |isAnd| |isNot| |isAtom| |atoms| |dual| |equiv| + |implies| |false| |true| |merge!| |max| |resultantEuclidean| + |semiResultantEuclidean2| |semiResultantEuclidean1| |indiceSubResultant| + |indiceSubResultantEuclidean| |semiIndiceSubResultantEuclidean| + |degreeSubResultant| |degreeSubResultantEuclidean| + |semiDegreeSubResultantEuclidean| |lastSubResultantEuclidean| + |semiLastSubResultantEuclidean| |subResultantGcdEuclidean| + |semiSubResultantGcdEuclidean2| |semiSubResultantGcdEuclidean1| + |discriminantEuclidean| |semiDiscriminantEuclidean| |chainSubResultants| + |schema| |resultantReduit| |resultantReduitEuclidean| + |semiResultantReduitEuclidean| |divide| |Lazard| |Lazard2| + |nextsousResultant2| |resultantnaif| |resultantEuclideannaif| + |semiResultantEuclideannaif| |pdct| |powers| |partitions| |parts| |partition| + |complete| |pole?| |monomial| |leadingMonomial| |zRange| |yRange| |xRange| + |listBranches| |triangular?| |rewriteIdealWithRemainder| + |rewriteIdealWithHeadRemainder| |remainder| |headRemainder| |roughUnitIdeal?| + |roughEqualIdeals?| |roughSubIdeal?| |roughBase?| |trivialIdeal?| |sort| + |collectUpper| |collect| |collectUnder| |mainVariable?| |mainVariables| + |removeSquaresIfCan| |unprotectedRemoveRedundantFactors| + |removeRedundantFactors| |certainlySubVariety?| |possiblyNewVariety?| + |probablyZeroDim?| |selectPolynomials| |selectOrPolynomials| + |selectAndPolynomials| |quasiMonicPolynomials| |univariate?| + |univariatePolynomials| |linear?| |linearPolynomials| |bivariate?| + |bivariatePolynomials| |removeRoughlyRedundantFactorsInPols| + |removeRoughlyRedundantFactorsInPol| |interReduce| |roughBasicSet| + |crushedSet| |rewriteSetByReducingWithParticularGenerators| + |rewriteIdealWithQuasiMonicGenerators| |squareFreeFactors| + |univariatePolynomialsGcds| |removeRoughlyRedundantFactorsInContents| + |removeRedundantFactorsInContents| |removeRedundantFactorsInPols| + |irreducibleFactors| |lazyIrreducibleFactors| + |removeIrreducibleRedundantFactors| |normalForm| |changeBase| + |companionBlocks| |xCoord| |yCoord| |zCoord| |rCoord| |thetaCoord| |phiCoord| + |color| |hue| |shade| |nthRootIfCan| |expIfCan| |logIfCan| |sinIfCan| + |cosIfCan| |tanIfCan| |cotIfCan| |secIfCan| |cscIfCan| |asinIfCan| |acosIfCan| + |atanIfCan| |acotIfCan| |asecIfCan| |acscIfCan| |sinhIfCan| |coshIfCan| + |tanhIfCan| |cothIfCan| |sechIfCan| |cschIfCan| |asinhIfCan| |acoshIfCan| + |atanhIfCan| |acothIfCan| |asechIfCan| |acschIfCan| |pushdown| |pushup| + |reducedDiscriminant| |idealSimplify| |definingInequation| |definingEquations| + |setStatus| |quasiAlgebraicSet| |radicalSimplify| |random| |denominator| + |numerator| |denom| |numer| |quadraticForm| |back| |front| |rotate!| + |dequeue!| |enqueue!| |quatern| |imagK| |imagJ| |imagI| |conjugate| |queue| + |nthRoot| |fractRadix| |wholeRadix| |cycleRagits| |prefixRagits| |fractRagits| + |wholeRagits| |radix| |randnum| |reseed| |seed| |rational| |rational?| + |rationalIfCan| |setvalue!| |setchildren!| |node?| |child?| |distance| + |leaves| |nodes| |rename| |rename!| |mainValue| |mainDefiningPolynomial| + |mainForm| |sqrt| |rischDE| |rischDEsys| |monomRDE| |baseRDE| |polyRDE| + |monomRDEsys| |baseRDEsys| |weighted| |rdHack1| |midpoint| |midpoints| + |realZeros| |mainCharacterization| |algebraicOf| |ReduceOrder| = |setref| + |deref| |ref| |radicalEigenvectors| |radicalEigenvector| |radicalEigenvalues| + |eigenMatrix| |normalise| |gramschmidt| |orthonormalBasis| + |antisymmetricTensors| |createGenericMatrix| |symmetricTensors| + |tensorProduct| |permutationRepresentation| |completeEchelonBasis| + |createRandomElement| |cyclicSubmodule| |standardBasisOfCyclicSubmodule| + |areEquivalent?| |isAbsolutelyIrreducible?| |meatAxe| |scanOneDimSubspaces| + |double| |expt| |lift| |showArrayValues| |showScalarValues| |solveRetract| + |variables| |mainVariable| |univariate| |multivariate| |uniform01| |normal01| + |exponential1| |chiSquare1| |normal| |exponential| |chiSquare| F |t| + |factorFraction| |componentUpperBound| |blue| |green| |red| |whitePoint| + |uniform| |binomial| |poisson| |geometric| |ridHack1| |interpolate| + |nullSpace| |nullity| |rank| |rowEchelon| |column| |row| |qelt| |ncols| + |nrows| |maxColIndex| |minColIndex| |maxRowIndex| |minRowIndex| + |antisymmetric?| |symmetric?| |diagonal?| |square?| |matrix| + |rectangularMatrix| |characteristic| |round| |fractionPart| |wholePart| + |floor| |ceiling| |norm| |mightHaveRoots| |refine| |middle| |size| |right| + |left| |roman| |recoverAfterFail| |showTheRoutinesTable| |deleteRoutine!| + |getExplanations| |getMeasure| |changeMeasure| |changeThreshhold| + |selectMultiDimensionalRoutines| |selectNonFiniteRoutines| + |selectSumOfSquaresRoutines| |selectFiniteRoutines| |selectODEIVPRoutines| + |selectPDERoutines| |selectOptimizationRoutines| |selectIntegrationRoutines| + |routines| |mainSquareFreePart| |mainPrimitivePart| |mainContent| + |primitivePart!| |gcd| |nextsubResultant2| |LazardQuotient2| |LazardQuotient| + |subResultantChain| |halfExtendedSubResultantGcd2| + |halfExtendedSubResultantGcd1| |extendedSubResultantGcd| |exactQuotient!| + |exactQuotient| |primPartElseUnitCanonical!| |primPartElseUnitCanonical| + |retract| |retractIfCan| |lazyResidueClass| |monicModulo| |lazyPseudoDivide| + |lazyPremWithDefault| |lazyPquo| |lazyPrem| |pquo| |prem| |supRittWu?| + |RittWuCompare| |mainMonomials| |mainCoefficients| |leastMonomial| + |mainMonomial| |quasiMonic?| |monic?| |leadingCoefficient| |deepestInitial| + |iteratedInitials| |deepestTail| |head| |mdeg| |mvar| |iterators| + |relativeApprox| |rootOf| |allRootsOf| |definingPolynomial| |positive?| + |negative?| |zero?| |augment| |lastSubResultant| |lastSubResultantElseSplit| + |invertibleSet| |invertible?| |invertibleElseSplit?| + |purelyAlgebraicLeadingMonomial?| |algebraicCoefficients?| + |purelyTranscendental?| |purelyAlgebraic?| |prepareSubResAlgo| + |internalLastSubResultant| |integralLastSubResultant| |toseLastSubResultant| + |toseInvertible?| |toseInvertibleSet| |toseSquareFreePart| |expression| + |quotedOperators| |pattern| |suchThat| |rule| |rules| |ruleset| |rur| |create| + |clearCache| |cache| |enterInCache| |currentCategoryFrame| |currentScope| + |pushNewContour| |findBinding| |contours| |structuralConstants| |coordinates| + |bounds| |equation| |incr| |high| |low| |hi| |lo| BY |body| |union| |subset?| + |symmetricDifference| |difference| |intersect| |set| |brace| |part?| |latex| + |hash| |delta| |member?| |enumerate| |setOfMinN| |elements| + |replaceKthElement| |incrementKthElement| |cdr| |car| |expr| |float| |integer| + |symbol| |destruct| |float?| |integer?| |symbol?| |string?| |list?| |pair?| + |atom?| |null?| |eq| |fortran| |startTable!| |stopTable!| |supDimElseRittWu?| + |algebraicSort| |moreAlgebraic?| |subTriSet?| |subPolSet?| + |internalSubPolSet?| |internalInfRittWu?| |internalSubQuasiComponent?| + |subQuasiComponent?| |removeSuperfluousQuasiComponents| |subCase?| + |removeSuperfluousCases| |prepareDecompose| |branchIfCan| |startTableGcd!| + |stopTableGcd!| |startTableInvSet!| |stopTableInvSet!| + |stosePrepareSubResAlgo| |stoseInternalLastSubResultant| + |stoseIntegralLastSubResultant| |stoseLastSubResultant| + |stoseInvertible?sqfreg| |stoseInvertibleSetsqfreg| |stoseInvertible?reg| + |stoseInvertibleSetreg| |stoseInvertible?| |stoseInvertibleSet| + |stoseSquareFreePart| |coleman| |inverseColeman| |listYoungTableaus| + |makeYoungTableau| |nextColeman| |nextLatticePermutation| |nextPartition| + |numberOfImproperPartitions| |subSet| |unrankImproperPartitions0| + |unrankImproperPartitions1| |subresultantSequence| |SturmHabichtSequence| + |SturmHabichtCoefficients| |SturmHabicht| |countRealRoots| + |SturmHabichtMultiple| |countRealRootsMultiple| |source| |target| |signature| + |signatureAst| |Or| |And| |Not| |xor| |depth| |top| |pop!| |push!| |minordet| + |determinant| |diagonalProduct| |trace| |diagonal| |diagonalMatrix| + |scalarMatrix| |hermite| |completeHermite| |smith| |completeSmith| + |diophantineSystem| |csubst| |particularSolution| |mapSolve| |linear| + |quadratic| |cubic| |quartic| |aLinear| |aQuadratic| |aCubic| |aQuartic| + |radicalSolve| |radicalRoots| |contractSolve| |decomposeFunc| |unvectorise| + |bubbleSort!| |insertionSort!| |check| |objects| |lprop| |llprop| |lllp| + |lllip| |lp| |mesh?| |mesh| |polygon?| |polygon| |closedCurve?| |closedCurve| + |curve?| |curve| |point?| |enterPointData| |composites| |components| + |numberOfComposites| |numberOfComponents| |create3Space| |parse| + |outputAsFortran| |outputAsScript| |outputAsTex| |abs| |Beta| |digamma| + |polygamma| |Gamma| |besselJ| |besselY| |besselI| |besselK| |airyAi| |airyBi| + |subNode?| |infLex?| |setEmpty!| |setStatus!| |setCondition!| |setValue!| + |copy| |status| |value| |empty?| |splitNodeOf!| |remove!| |remove| + |subNodeOf?| |nodeOf?| |result| |conditions| |updateStatus!| + |extractSplittingLeaf| |squareMatrix| |transpose| |rightTrim| |leftTrim| + |trim| |split| |position| |replace| |match?| |match| |substring?| |suffix?| + |prefix?| |upperCase!| |upperCase| |lowerCase!| |lowerCase| |KrullNumber| + |numberOfVariables| |algebraicDecompose| |transcendentalDecompose| + |internalDecompose| |decompose| |upDateBranches| |printInfo| |preprocess| + |internalZeroSetSplit| |internalAugment| |stack| |size?| |possiblyInfinite?| + |explicitlyFinite?| |nextItem| |init| |step| |upperBound| |lowerBound| + |iterationVar| |infiniteProduct| |evenInfiniteProduct| |oddInfiniteProduct| + |generalInfiniteProduct| |filterUntil| |filterWhile| |generate| |showAll?| + |showAllElements| |output| |cons| |delay| |findCycle| |repeating?| |repeating| + |exquo| |recip| |integers| |oddintegers| |int| |mapmult| |deriv| |gderiv| + |compose| |addiag| |lazyIntegrate| |nlde| |powern| |mapdiv| |lazyGintegrate| + |power| |sincos| |sinhcosh| |asin| |acos| |atan| |acot| |asec| |acsc| |sinh| + |cosh| |tanh| |coth| |sech| |csch| |asinh| |acosh| |atanh| |acoth| |asech| + |acsch| |subresultantVector| |primitivePart| |pointData| |parent| |level| + |extractProperty| |extractClosed| |extractIndex| |extractPoint| |traverse| + |defineProperty| |closeComponent| |modifyPoint| |addPointLast| |addPoint2| + |addPoint| |merge| |deepCopy| |shallowCopy| |numberOfChildren| |children| + |child| |birth| |internal?| |root?| |leaf?| |rhs| |lhs| |construct| + |predicate| |sum| |outputForm| NOT AND EQ OR GE LE GT LT |list| |string| + |argscript| |superscript| |subscript| |script| |scripts| |scripted?| |name| + |resetNew| |symFunc| |symbolTableOf| |argumentListOf| |returnTypeOf| + |printHeader| |returnType!| |argumentList!| |endSubProgram| + |currentSubProgram| |newSubProgram| |clearTheSymbolTable| |showTheSymbolTable| + |symbolTable| |printTypes| |newTypeLists| |typeLists| |externalList| + |typeList| |parametersOf| |fortranTypeOf| |declare!| |empty| |case| + |compound?| |getOperands| |getOperator| |nil?| |buildSyntax| |autoCoerce| + |solve| |triangularSystems| |loadNativeModule| |nativeModuleExtension| + |hostByteOrder| |hostPlatform| |rootDirectory| |bumprow| |bumptab| |bumptab1| + |untab| |bat1| |bat| |tab1| |tab| |lex| |slex| |inverse| |maxrow| |mr| + |tableau| |listOfLists| |operator| |tanSum| |tanAn| |tanNa| |table| + |initTable!| |printInfo!| |startStats!| |printStats!| |clearTable!| + |usingTable?| |printingInfo?| |makingStats?| |extractIfCan| |insert!| + |interpretString| |stripCommentsAndBlanks| |setPrologue!| |setTex!| + |setEpilogue!| |prologue| |new| |tex| |epilogue| |display| |endOfFile?| + |readIfCan!| |readLineIfCan!| |readLine!| |writeLine!| |sign| |nonQsign| + |direction| |createThreeSpace| |pi| |cyclicParents| |cyclicEqual?| + |cyclicEntries| |cyclicCopy| |tree| |cyclic?| |cos| |cot| |csc| |sec| |sin| + |tan| |complexNormalize| |complexElementary| |trigs| |real| |imag| |real?| + |complexForm| |UpTriBddDenomInv| |LowTriBddDenomInv| |simplify| |htrigs| + |simplifyExp| |simplifyLog| |expandPower| |expandLog| |cos2sec| |cosh2sech| + |cot2trig| |coth2trigh| |csc2sin| |csch2sinh| |sec2cos| |sech2cosh| |sin2csc| + |sinh2csch| |tan2trig| |tanh2trigh| |tan2cot| |tanh2coth| |cot2tan| + |coth2tanh| |removeCosSq| |removeSinSq| |removeCoshSq| |removeSinhSq| + |expandTrigProducts| |fintegrate| |coefficient| |coHeight| |extendIfCan| + |algebraicVariables| |zeroSetSplitIntoTriangularSystems| |zeroSetSplit| + |reduceByQuasiMonic| |collectQuasiMonic| |removeZero| |initiallyReduce| + |headReduce| |stronglyReduce| |rewriteSetWithReduction| |autoReduced?| + |initiallyReduced?| |headReduced?| |stronglyReduced?| |reduced?| |normalized?| + |quasiComponent| |initials| |basicSet| |infRittWu?| |getCurve| |listLoops| + |closed?| |open?| |setClosed| |tube| |point| |unitVector| |cosSinInfo| + |loopPoints| |select| |generalTwoFactor| |generalSqFr| |twoFactor| |setOrder| + |getOrder| |less?| |userOrdered?| |largest| |more?| |setVariableOrder| + |getVariableOrder| |resetVariableOrder| |prime?| |sample| |bitior| |bitand| + |rationalFunction| |taylorIfCan| |taylor| |removeZeroes| |taylorRep| |factor| + |factorSquareFree| |henselFact| |hasHi| |segment| SEGMENT |fmecg| + |commonDenominator| |clearDenominator| |splitDenominator| + |monicRightFactorIfCan| |rightFactorIfCan| |leftFactorIfCan| + |monicDecomposeIfCan| |monicCompleteDecompose| |divideIfCan| |noKaratsuba| + |karatsubaOnce| |karatsuba| |separate| |pseudoDivide| |pseudoQuotient| + |composite| |subResultantGcd| |resultant| |discriminant| |differentiate| + |pseudoRemainder| |shiftLeft| |shiftRight| |karatsubaDivide| |monicDivide| + |divideExponents| |unmakeSUP| |makeSUP| |vectorise| |eval| |extend| + |approximate| |truncate| |order| |center| |terms| |squareFreePart| + |BumInSepFFE| |multiplyExponents| |laurentIfCan| |laurent| |laurentRep| + |rationalPower| |puiseux| |dominantTerm| |limitPlus| |split!| |setlast!| + |setrest!| |setelt| |setfirst!| |cycleSplit!| |concat!| |cycleTail| + |cycleLength| |cycleEntry| |third| |second| |tail| |last| |rest| |elt| |first| + |concat| |invmultisect| |multisect| |revert| |generalLambert| |evenlambert| + |oddlambert| |lambert| |lagrange| |univariatePolynomial| |integrate| ** + |polynomial| |multiplyCoefficients| |quoByVar| |coefficients| |series| + |stFunc1| |stFunc2| |stFuncN| |fixedPointExquo| |ode1| |ode2| |ode| |mpsode| + UP2UTS UTS2UP LODO2FUN RF2UTS |variable| |magnitude| |length| |cross| + |outerProduct| |dot| - |zero| + |vector| |scan| |reduce| |graphCurves| + |drawCurves| |update| |show| |scale| |connect| |region| |points| |units| + |getGraph| |putGraph| |graphs| |graphStates| |graphState| |makeViewport2D| + |viewport2D| |getPickedPoints| |key| |close| |write| |colorDef| |reset| + |intensity| |lighting| |clipSurface| |showClipRegion| |showRegion| + |hitherPlane| |eyeDistance| |perspective| |translate| |zoom| |rotate| + |drawStyle| |outlineRender| |diagonals| |axes| |controlPanel| |viewpoint| + |dimensions| |title| |resize| |move| |options| |modifyPointData| |subspace| + |makeViewport3D| |viewport3D| |viewDeltaYDefault| |viewDeltaXDefault| + |viewZoomDefault| |viewPhiDefault| |viewThetaDefault| |pointColorDefault| + |lineColorDefault| |axesColorDefault| |unitsColorDefault| |pointSizeDefault| + |viewPosDefault| |viewSizeDefault| |viewDefaults| |viewWriteDefault| + |viewWriteAvailable| |var1StepsDefault| |var2StepsDefault| |tubePointsDefault| + |tubeRadiusDefault| |void| |dimension| |crest| |cfirst| |sts2stst| |clikeUniv| + |weierstrass| |qqq| |integralBasis| |localIntegralBasis| |qualifier| + |mainExpression| |condition| |changeWeightLevel| |characteristicSerie| + |characteristicSet| |medialSet| |Hausdorff| |Frobenius| |transcendenceDegree| + |extensionDegree| |inGroundField?| |transcendent?| |algebraic?| |varList| |sh| + |mirror| |monomial?| |monom| |rquo| |lquo| |mindegTerm| |log| |exp| |product| + |LiePolyIfCan| |coerce| |trunc| |degree| / |quasiRegular| |quasiRegular?| + |constant| |constant?| |coef| |mindeg| |maxdeg| |#| |map| |reductum| * + |RemainderList| |unexpand| |expand| |shape| |youngDiagram| Y |triangSolve| + |univariateSolve| |realSolve| |positiveSolve| |squareFree| |convert| + |linearlyDependentOverZ?| |linearDependenceOverZ| |solveLinearlyOverQ| |nil| + |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| + |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| + |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| + |additiveValuation| |unitsKnown| |canonicalUnitNormal| + |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| |commutative|)
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T) ((-321 #1#) -12 (|has| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (-321 (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)))) (|has| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (-1133))) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-294 #1#) . T) ((-385 #1#) . T) ((-503 #1#) . T) ((-503 |#2|) . T) ((-618 #2# #1#) . T) ((-618 |#1| |#2|) . T) ((-528 #1# #1#) -12 (|has| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (-321 (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)))) (|has| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (-1133))) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-629 |#1| |#2|) . T) ((-673 #1#) . T) ((-688 #1#) . T) ((-872) |has| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (-872)) ((-875) |has| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (-872)) ((-1042 #1#) . T) ((-1133) -4128 (|has| |#2| (-1133)) (|has| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (-1133)) (|has| (-2 (|:| -2654 |#1|) (|:| -1356 |#2|)) (-872))) ((-1182 #1#) . T) ((-1226 |#1| |#2|) . T) ((-1249) . T) ((-1288 #1#) . 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T) ((-107 #1=(-2 (|:| -4376 |#1|) (|:| -2300 |#2|))) . T) ((-102) -4043 (|has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-1133)) (|has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-872)) (|has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-102)) (|has| |#2| (-1133)) (|has| |#2| (-102))) ((-632 (-888)) -4043 (|has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-1133)) (|has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-872)) (|has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-632 (-888))) (|has| |#2| (-1133)) (|has| |#2| (-632 (-888)))) ((-153 #2=(-2 (|:| -4376 |#1|) (|:| -2300 |#2|))) . T) ((-633 (-549)) |has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-633 (-549))) ((-233 #1#) . T) ((-242 #1#) . T) ((-298 #3=(-560) #2#) . T) ((-298 (-1266 (-560)) $) . T) ((-298 |#1| |#2|) . T) ((-300 #3# #2#) . T) ((-300 |#1| |#2|) . T) ((-321 #2#) -12 (|has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-321 (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)))) (|has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-1133))) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-294 #2#) . T) ((-385 #2#) . T) ((-503 #2#) . T) ((-503 |#2|) . T) ((-618 #3# #2#) . T) ((-618 |#1| |#2|) . T) ((-528 #2# #2#) -12 (|has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-321 (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)))) (|has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-1133))) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-629 |#1| |#2|) . T) ((-673 #2#) . T) ((-688 #2#) . T) ((-872) |has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-872)) ((-875) |has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-872)) ((-1042 #2#) . T) ((-1133) -4043 (|has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-1133)) (|has| (-2 (|:| -4376 |#1|) (|:| -2300 |#2|)) (-872)) (|has| |#2| (-1133))) ((-1182 #2#) . T) ((-1226 |#1| |#2|) . T) ((-1249) . T) ((-1288 #2#) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -4128 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -4128 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1235)) ((-95) |has| |#1| (-1235)) ((-102) . T) ((-111 #0# #0#) -4128 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -4128 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -4128 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -4128 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-888)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1052)) ((-633 (-171 (-391))) |has| |#1| (-1052)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-916 (-391))) |has| |#1| (-633 (-916 (-391)))) ((-633 (-916 (-560))) |has| |#1| (-633 (-916 (-560)))) ((-633 #1=(-1203 |#1|)) . 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T) ((-23) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1235)) ((-95) |has| |#1| (-1235)) ((-102) . T) ((-111 #1# #1#) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -4043 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #1#) -4043 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-888)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1052)) ((-633 (-171 (-391))) |has| |#1| (-1052)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-916 (-391))) |has| |#1| (-633 (-916 (-391)))) ((-633 (-916 (-560))) |has| |#1| (-633 (-916 (-560)))) ((-633 #2=(-1203 |#1|)) . T) ((-236 $) -4043 (|has| |#1| (-363)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) -4043 (|has| |#1| (-363)) (|has| |#1| (-240))) ((-239) -4043 (|has| |#1| (-363)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-250) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-296) |has| |#1| (-1235)) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) -4043 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-319) -4043 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-376) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-416) |has| |#1| (-363)) ((-381) -4043 (|has| |#1| (-363)) (|has| |#1| (-381))) ((-363) |has| |#1| (-363)) ((-383 |#1| #2#) . T) ((-424 |#1| #2#) . T) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-414 |#1|) . T) ((-426 |#1|) . T) ((-466) -4043 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-507) |has| |#1| (-1235)) ((-528 (-1209) |#1|) |has| |#1| (-528 (-1209) |#1|)) ((-528 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-571) -4043 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-668 #1#) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-662 |#1|) . T) ((-662 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-739 |#1|) . T) ((-739 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-746 |#1| #2#) . T) ((-748) . T) ((-922 $ #4=(-1209)) -4043 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #4#) -4043 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) |has| |#1| (-912 (-391))) ((-912 (-560)) |has| |#1| (-912 (-560))) ((-910 |#1|) . T) ((-940) -12 (|has| |#1| (-319)) (|has| |#1| (-940))) ((-951) -4043 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1034) -12 (|has| |#1| (-1034)) (|has| |#1| (-1235))) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1083 #1#) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1083 |#1|) . T) ((-1083 $) . T) ((-1088 #1#) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1088 |#1|) . T) ((-1088 $) . T) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-363)) ((-1235) |has| |#1| (-1235)) ((-1238) |has| |#1| (-1235)) ((-1249) . 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(-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-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"))) (-5 *1 (-195)))) (-1569 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-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 (-195))))) +(-10 -7 (-15 -1569 ((-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")) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1570 ((-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")) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1785 ((-229) (-1121 (-866 (-229))))) (-15 -1786 ((-229) (-1121 (-866 (-229))))) (-15 -1571 ((-391) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1761 ((-663 (-229)) (-326 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(|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -1650 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3746 (((-1191) $) NIL T ELT)) (-3747 (((-1152) $) NIL T ELT)) (-4462 (((-888) $) NIL T ELT)) (-1389 (((-114) $ $) NIL T ELT)) (-3540 (((-114) $ $) NIL T ELT))) (((-196) (-809)) (T -196)) NIL (-809) -((-2226 (((-114) $ $) NIL T ELT)) (-3530 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -2683 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 66 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -2683 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-2207 (((-2 (|:| -2207 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -2683 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -2207 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -2683 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-2405 (((-1191) $) NIL T ELT)) (-3875 (((-1152) $) NIL T ELT)) (-4457 (((-888) $) NIL T ELT)) (-3591 (((-114) $ $) NIL T ELT)) (-4286 (((-114) $ $) NIL T ELT))) +((-3053 (((-114) $ $) NIL T ELT)) (-2873 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 66 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -1650 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-3155 (((-2 (|:| -3155 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -3155 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -1650 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3746 (((-1191) $) NIL T ELT)) (-3747 (((-1152) $) NIL T ELT)) (-4462 (((-888) $) NIL T ELT)) (-1389 (((-114) $ $) NIL T ELT)) (-3540 (((-114) $ $) NIL T ELT))) (((-197) (-809)) (T -197)) NIL (-809) -((-2226 (((-114) $ $) NIL T ELT)) (-3530 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -2683 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 80 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -2683 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-2207 (((-2 (|:| -2207 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -2683 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 46 T ELT) (((-2 (|:| -2207 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 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(-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3746 (((-1191) $) NIL T ELT)) (-3747 (((-1152) $) NIL T ELT)) (-4462 (((-888) $) NIL T ELT)) (-1389 (((-114) $ $) NIL T ELT)) (-3540 (((-114) $ $) NIL T ELT))) (((-198) (-809)) (T -198)) NIL (-809) -((-2226 (((-114) $ $) NIL T ELT)) (-3530 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -2683 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 63 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -2683 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-2207 (((-2 (|:| -2207 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -2683 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 36 T ELT) (((-2 (|:| -2207 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -2683 (-663 (-1121 (-866 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(-229)))) NIL T ELT)) (-3746 (((-1191) $) NIL T ELT)) (-3747 (((-1152) $) NIL T ELT)) (-4462 (((-888) $) NIL T ELT)) (-1389 (((-114) $ $) NIL T ELT)) (-3540 (((-114) $ $) NIL T ELT))) (((-199) (-809)) (T -199)) NIL (-809) -((-2226 (((-114) $ $) NIL T ELT)) (-3530 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -2683 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 76 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -2683 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-2207 (((-2 (|:| -2207 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -2683 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 40 T ELT) (((-2 (|:| -2207 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -2683 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-2405 (((-1191) $) NIL T ELT)) (-3875 (((-1152) $) NIL T ELT)) (-4457 (((-888) $) NIL T ELT)) (-3591 (((-114) $ $) NIL T ELT)) (-4286 (((-114) $ $) NIL T ELT))) +((-3053 (((-114) $ $) NIL T ELT)) (-2873 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 76 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -1650 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-3155 (((-2 (|:| -3155 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 40 T ELT) (((-2 (|:| -3155 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -1650 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3746 (((-1191) $) NIL T ELT)) (-3747 (((-1152) $) NIL T ELT)) (-4462 (((-888) $) NIL T ELT)) (-1389 (((-114) $ $) NIL T ELT)) (-3540 (((-114) $ $) NIL T ELT))) (((-200) (-809)) (T -200)) NIL (-809) -((-2226 (((-114) $ $) NIL T ELT)) (-3530 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -2683 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 93 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -2683 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-2207 (((-2 (|:| -2207 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -2683 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 49 T ELT) (((-2 (|:| -2207 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -2683 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-2405 (((-1191) $) NIL T ELT)) (-3875 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(|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -4043 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -4043 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -4043 (|has| |#2| (-1081)) (|has| |#2| (-817)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-635 #1=(-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ((-635 (-560)) -4043 (|has| |#2| (-1081)) (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133)))) ((-635 |#2|) |has| |#2| (-1133)) ((-632 (-888)) -4043 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-632 (-888))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-632 (-1299 |#2|)) . T) ((-236 $) -4043 (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1081)))) ((-234 |#2|) |has| |#2| (-1081)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1081))) ((-239) -4043 (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1081)))) ((-274 |#2|) |has| |#2| (-1081)) ((-298 #2=(-560) |#2|) . T) ((-300 #2# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1081)) ((-426 |#2|) |has| |#2| (-1133)) ((-503 |#2|) . T) ((-618 #2# |#2|) . T) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-668 (-560)) -4043 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-668 |#2|) -4043 (|has| |#2| (-1081)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1081)) ((-670 #3=(-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081))) ((-670 |#2|) -4043 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-670 $) |has| |#2| (-1081)) ((-662 |#2|) -4043 (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-660 #3#) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081))) ((-660 |#2|) |has| |#2| (-1081)) ((-739 |#2|) -4043 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-748) |has| |#2| (-1081)) ((-816) |has| |#2| (-817)) ((-817) |has| |#2| (-817)) ((-818) |has| |#2| (-817)) ((-821) |has| |#2| (-817)) ((-872) -4043 (|has| |#2| (-872)) (|has| |#2| (-817))) ((-875) -4043 (|has| |#2| (-872)) (|has| |#2| (-817))) ((-922 $ #4=(-1209)) -4043 (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081)))) ((-928 (-1209)) -12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081))) ((-930 #4#) -4043 (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081)))) ((-1070 #1#) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ((-1070 (-560)) -12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) ((-1070 |#2|) |has| |#2| (-1133)) ((-1083 |#2|) -4043 (|has| |#2| (-1081)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1088 |#2|) -4043 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1081) |has| |#2| (-1081)) ((-1089) |has| |#2| (-1081)) ((-1144) |has| |#2| (-1081)) ((-1133) -4043 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1249) . T) ((-1307 |#2|) |has| |#2| (-376))) +((-3053 (((-114) $ $) NIL (|has| |#2| (-102)) ELT)) (-3692 (((-114) $) NIL (|has| |#2| (-23)) ELT)) (-4223 (($ (-949)) 63 (|has| |#2| (-1081)) ELT)) (-2427 (((-1305) $ (-560) (-560)) NIL (|has| $ (-6 -4512)) ELT)) (-2887 (($ $ $) 69 (|has| |#2| (-817)) ELT)) (-1438 (((-3 $ "failed") $ $) 54 (|has| |#2| (-133)) ELT)) (-3624 (((-793)) NIL (|has| |#2| (-381)) ELT)) (-4304 ((|#2| $ (-560) |#2|) NIL (|has| $ (-6 -4512)) ELT)) (-4240 (($) NIL T CONST)) (-3661 (((-3 (-560) #1="failed") $) NIL (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) ELT) (((-3 (-421 (-560)) #1#) $) NIL (-12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ELT) (((-3 |#2| #1#) $) 31 (|has| |#2| (-1133)) ELT)) (-3660 (((-560) $) NIL (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) ELT) (((-421 (-560)) $) NIL (-12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ELT) ((|#2| $) 29 (|has| |#2| (-1133)) ELT)) (-2507 (((-711 (-560)) (-711 $)) NIL (-12 (|has| 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -4128 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-888)) . T) ((-175) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-633 (-916 (-391)))) (|has| |#3| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-633 (-916 (-560)))) (|has| |#3| (-633 (-916 (-560))))) ((-236 $) -4128 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -4128 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -4128 (|has| |#1| (-940)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-922 $ #2=(-1209)) -4128 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-922 $ |#3|) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-928 |#3|) . T) ((-930 #2#) -4128 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-930 |#3|) . T) ((-912 (-391)) -12 (|has| |#1| (-912 (-391))) (|has| |#3| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-912 (-560))) (|has| |#3| (-912 (-560)))) ((-980 |#1| |#4| |#3|) . T) ((-940) |has| |#1| (-940)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1070 |#2|) . T) ((-1070 |#3|) . T) ((-1083 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1088 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . T) ((-1254) |has| |#1| (-940))) -((-2226 (((-114) $ $) 19 (|has| |#1| (-102)) ELT)) (-1937 ((|#1| $) 58 T ELT)) (-1456 ((|#1| $) 48 T ELT)) (-3789 (($) 7 T CONST)) (-2529 (($ $) 64 T ELT)) (-4166 (($ $) 52 T ELT)) (-1780 ((|#1| |#1| $) 50 T ELT)) (-3656 ((|#1| $) 49 T ELT)) (-2810 (((-663 |#1|) $) 30 (|has| $ (-6 -4510)) ELT)) (-3169 (((-663 |#1|) $) 29 (|has| $ (-6 -4510)) ELT)) (-2073 (((-114) |#1| $) 27 (-12 (|has| |#1| (-1133)) (|has| $ (-6 -4510))) ELT)) (-2590 (($ (-1 |#1| |#1|) $) 34 (|has| $ (-6 -4511)) ELT)) (-3016 (($ (-1 |#1| |#1|) $) 35 T ELT)) (-4314 (((-793) $) 65 T ELT)) (-2405 (((-1191) $) 22 (|has| |#1| (-1133)) ELT)) (-2352 ((|#1| $) 43 T ELT)) (-3937 ((|#1| |#1| $) 56 T ELT)) (-3427 ((|#1| |#1| $) 55 T ELT)) (-4047 (($ |#1| $) 44 T ELT)) (-3352 (((-793) $) 59 T ELT)) (-3875 (((-1152) $) 21 (|has| |#1| (-1133)) ELT)) (-3978 ((|#1| $) 66 T ELT)) (-1345 ((|#1| $) 54 T ELT)) (-2457 ((|#1| $) 53 T ELT)) (-1706 ((|#1| $) 45 T ELT)) (-3729 (((-114) (-1 (-114) |#1|) $) 32 (|has| $ (-6 -4510)) ELT)) (-2693 (($ $ (-663 (-305 |#1|))) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ (-305 |#1|)) 25 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ |#1| |#1|) 24 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 23 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT)) (-3979 (((-114) $ $) 11 T ELT)) (-2229 ((|#1| |#1| $) 62 T ELT)) (-1938 (((-114) $) 8 T ELT)) (-2012 (($) 9 T ELT)) (-3073 ((|#1| $) 63 T ELT)) (-4464 (($) 61 T ELT) (($ (-663 |#1|)) 60 T ELT)) (-1428 (((-793) $) 47 T ELT)) (-3891 (((-793) (-1 (-114) |#1|) $) 31 (|has| $ (-6 -4510)) ELT) (((-793) |#1| $) 28 (-12 (|has| |#1| (-1133)) (|has| $ (-6 -4510))) ELT)) (-1415 (($ $) 10 T ELT)) (-4457 (((-888) $) 17 (|has| |#1| (-632 (-888))) ELT)) (-2542 ((|#1| $) 57 T ELT)) (-3591 (((-114) $ $) 20 (|has| |#1| (-102)) ELT)) (-4134 (($ (-663 |#1|)) 46 T ELT)) (-3155 ((|#1| $) 67 T ELT)) (-1542 (((-114) (-1 (-114) |#1|) $) 33 (|has| $ (-6 -4510)) ELT)) (-4286 (((-114) $ $) 18 (|has| |#1| (-102)) ELT)) (-2237 (((-793) $) 6 (|has| $ (-6 -4510)) ELT))) +((-1667 (*1 *2 *3) (-12 (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *4 *3 *5 *6)))) (-1633 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-663 *4)))) (-4288 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-793)))) (-4288 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-793)))) (-4464 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-793)))) (-1632 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-663 (-793))))) (-1666 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-793)))) (-1632 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-663 (-793))))) (-1666 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-793)))) (-1631 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-114)))) (-1630 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *2 *5)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-817)) (-4 *2 (-277 *4)))) (-1629 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1081)) (-4 *3 (-872)) (-4 *4 (-277 *3)) (-4 *5 (-817)))) (-1628 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1081)) (-4 *3 (-872)) (-4 *4 (-277 *3)) (-4 *5 (-817)))) (-1667 (*1 *2 *1) (-12 (-4 *3 (-240)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *3 *4 *5 *6))))) +(-13 (-980 |t#1| |t#4| |t#3|) (-234 |t#1|) (-1070 |t#2|) (-10 -8 (-15 -1667 ((-1 $ (-793)) |t#2|)) (-15 -1633 ((-663 |t#2|) $)) (-15 -4288 ((-793) $ |t#2|)) (-15 -4288 ((-793) $)) (-15 -4464 ((-793) $ |t#2|)) (-15 -1632 ((-663 (-793)) $)) (-15 -1666 ((-793) $)) (-15 -1632 ((-663 (-793)) $ |t#2|)) (-15 -1666 ((-793) $ |t#2|)) (-15 -1631 ((-114) $)) (-15 -1630 (|t#3| $)) (-15 -1629 ($ $)) (-15 -1628 ($ $)) (IF (|has| |t#1| (-240)) (PROGN (-6 (-528 |t#2| |t#1|)) (-6 (-528 |t#2| $)) (-6 (-321 $)) (-15 -1667 ((-1 $ (-793)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -4043 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-888)) . T) ((-175) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-633 (-916 (-391)))) (|has| |#3| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-633 (-916 (-560)))) (|has| |#3| (-633 (-916 (-560))))) ((-236 $) -4043 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -4043 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -4043 (|has| |#1| (-940)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #2=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #2#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-922 $ #3=(-1209)) -4043 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-922 $ |#3|) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-928 |#3|) . T) ((-930 #3#) -4043 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-930 |#3|) . T) ((-912 (-391)) -12 (|has| |#1| (-912 (-391))) (|has| |#3| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-912 (-560))) (|has| |#3| (-912 (-560)))) ((-980 |#1| |#4| |#3|) . T) ((-940) |has| |#1| (-940)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1070 |#2|) . T) ((-1070 |#3|) . T) ((-1083 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1088 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . 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T) ((-951) |has| |#1| (-571)) ((-1070 (-421 (-560))) -4128 (|has| |#1| (-1070 (-421 (-560)))) (-12 (|has| |#1| (-571)) (|has| |#1| (-1070 (-560))))) ((-1070 #1#) |has| |#1| (-571)) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 #3#) |has| |#1| (-1081)) ((-1070 #4#) . T) ((-1070 |#1|) . T) ((-1083 #0#) |has| |#1| (-571)) ((-1083 |#1|) |has| |#1| (-175)) ((-1083 $) |has| |#1| (-571)) ((-1088 #0#) |has| |#1| (-571)) ((-1088 |#1|) |has| |#1| (-175)) ((-1088 $) |has| |#1| (-571)) ((-1081) -4128 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1089) -4128 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1144) -4128 (|has| |#1| (-1144)) (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-487)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1133) . T) ((-1249) . 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(|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) $) 31 T ELT)) (-4123 (($ (-2 (|:| -4376 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2300 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) 28 T ELT)) (-2298 (($ (-663 (-2 (|:| -4376 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2300 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) 26 T ELT)) (-2300 (((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 38 T ELT)) (-2434 (((-663 (-2 (|:| -4376 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2300 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) $) 36 T ELT)) (-2297 (((-1305)) 11 T ELT))) +(((-574) (-10 -8 (-15 -2296 ($)) (-15 -2297 ((-1305))) (-15 -2898 ((-663 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) $)) (-15 -2298 ($ (-663 (-2 (|:| -4376 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2300 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| -1650 (-3 (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="Range not yet evaluated"))))))))) (-15 -4123 ($ (-2 (|:| -4376 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2300 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) (-15 -2299 ((-3 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) "failed") (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -2434 ((-663 (-2 (|:| -4376 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2300 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) $)) (-15 -2300 ((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))))) (T -574)) +((-2300 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| -1650 (-3 (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="Range not yet evaluated"))))) (-5 *1 (-574)))) (-2434 (*1 *2 *1) (-12 (-5 *2 (-663 (-2 (|:| -4376 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2300 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) 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(|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2300 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) (-5 *1 (-574)))) (-2298 (*1 *1 *2) (-12 (-5 *2 (-663 (-2 (|:| -4376 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2300 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) (-5 *1 (-574)))) (-2898 (*1 *2 *1) (-12 (-5 *2 (-663 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-5 *1 (-574)))) (-2297 (*1 *2) (-12 (-5 *2 (-1305)) (-5 *1 (-574)))) (-2296 (*1 *1) (-5 *1 (-574)))) +(-10 -8 (-15 -2296 ($)) (-15 -2297 ((-1305))) (-15 -2898 ((-663 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) $)) (-15 -2298 ($ (-663 (-2 (|:| -4376 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2300 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| -1650 (-3 (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="Range not yet evaluated"))))))))) (-15 -4123 ($ (-2 (|:| -4376 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2300 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) (-15 -2299 ((-3 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) "failed") (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -2434 ((-663 (-2 (|:| -4376 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2300 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) $)) (-15 -2300 ((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| #6#))) (|:| -1650 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) +((-3572 (((-1203 (-421 (-1203 |#2|))) |#2| (-630 |#2|) (-630 |#2|) (-1203 |#2|)) 35 T ELT)) (-2303 (((-3 (-2 (|:| |mainpart| |#2|) (|:| |limitedlogs| (-663 (-2 (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #1="failed") |#2| (-630 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -4128 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -4128 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-102) . T) ((-111 #0# #0#) -4128 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -4128 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -4128 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -4128 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) . T) ((-633 |#2|) . 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T) ((-23) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -4043 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #1#) -4043 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -4043 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) . T) ((-633 |#2|) . 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T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #2=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #2#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-922 $ |#3|) . T) ((-928 |#3|) . T) ((-930 |#3|) . T) ((-912 (-391)) -12 (|has| |#1| (-912 (-391))) (|has| |#3| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-912 (-560))) (|has| |#3| (-912 (-560)))) ((-980 |#1| |#2| |#3|) . T) ((-940) |has| |#1| (-940)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1070 |#3|) . T) ((-1083 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1088 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . 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T) ((-662 #1#) -4128 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4128 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -4128 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4128 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2=(-1209)) -12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) -12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))) ((-930 #2#) -12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))) ((-1005 |#1| #0# (-1114)) . T) ((-951) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1083 #1#) -4128 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 $) -4128 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -4128 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 $) -4128 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1278 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -4128 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -4128 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -4128 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -4128 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -4128 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -4128 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -4128 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1209)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . 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T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1144)) ((-302) -4128 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -4128 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -4128 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -4128 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -4128 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -4128 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -4128 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -4128 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-818) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-821) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-844) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-871) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-872) -4128 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-875) -4128 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-922 $ #4=(-1209)) -4128 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-928 (-1209)) -4128 (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-930 #4#) -4128 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-912 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-560)))) ((-910 |#2|) |has| |#1| (-376)) ((-940) -12 (|has| |#1| (-376)) (|has| |#2| (-940))) ((-1005 |#1| #0# (-1114)) . 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T) ((-23) . T) ((-47 |#1| #1=(-560)) . T) ((-25) . T) ((-38 #2=(-421 (-560))) -4043 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #2# #2#) -4043 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -4043 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -4043 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -4043 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #2#) -4043 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #3=(-1209)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -4043 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-549)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-560))))) ((-236 $) -4043 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -4043 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-239) -4043 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #1# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1144)) ((-302) -4043 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -4043 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #2#) -4043 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #2#) -4043 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #4=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #2#) -4043 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #4#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #2#) -4043 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-818) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-821) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-844) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-871) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-872) -4043 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-875) -4043 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-922 $ #5=(-1209)) -4043 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209))))) ((-928 (-1209)) -4043 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209))))) ((-930 #5#) -4043 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209))))) ((-912 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-560)))) ((-910 |#2|) |has| |#1| (-376)) ((-940) -12 (|has| |#1| (-376)) (|has| |#2| (-940))) ((-1005 |#1| #1# (-1114)) . T) ((-951) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1052) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-1070 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-1070 |#2|) . T) ((-1083 #2#) -4043 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 |#2|) |has| |#1| (-376)) ((-1083 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #2#) -4043 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 |#2|) |has| |#1| (-376)) ((-1088 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) -12 (|has| |#1| (-376)) (|has| |#2| (-1184))) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1261 |#1|) . T) ((-1278 |#1| #1#) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -4128 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1114)) . T) ((-635 |#1|) . T) ((-635 $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1114) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| (-1114) (-633 (-916 (-391)))) (|has| |#1| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| (-1114) (-633 (-916 (-560)))) (|has| |#1| (-633 (-916 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -4128 (|has| |#1| (-940)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2#) . T) ((-922 $ #4=(-1209)) -4128 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #2#) . T) ((-930 #4#) -4128 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) -12 (|has| (-1114) (-912 (-391))) (|has| |#1| (-912 (-391)))) ((-912 (-560)) -12 (|has| (-1114) (-912 (-560))) (|has| |#1| (-912 (-560)))) ((-980 |#1| #0# #2#) . T) ((-940) |has| |#1| (-940)) ((-951) |has| |#1| (-376)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 |#1|) . T) ((-1083 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4128 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-1184)) ((-1249) . 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(-663 (-1209)) (-663 (-793))) 109 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $) 107 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT) (($ $ (-793)) 105 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT)) (-4286 (((-114) $ $) 8 T ELT)) (-4395 (($ $ |#1|) 75 (|has| |#1| (-376)) ELT)) (-4385 (($ $) 28 T ELT) (($ $ $) 27 T ELT)) (-4374 (($ $ $) 18 T ELT)) (** (($ $ (-949)) 33 T ELT) (($ $ (-793)) 41 T ELT)) (* (($ (-949) $) 17 T ELT) (($ (-793) $) 20 T ELT) (($ (-560) $) 29 T ELT) (($ $ $) 32 T ELT) (($ $ |#1|) 85 T ELT) (($ |#1| $) 84 T ELT) (($ (-421 (-560)) $) 73 (|has| |#1| (-38 (-421 (-560)))) ELT) (($ $ (-421 (-560))) 72 (|has| |#1| (-38 (-421 (-560)))) ELT))) +((-4283 (*1 *2 *1 *3) (-12 (-5 *3 (-793)) (-4 *1 (-1275 *4)) (-4 *4 (-1081)) (-5 *2 (-1299 *4)))) (-4282 (*1 *2 *1) (-12 (-4 *1 (-1275 *3)) (-4 *3 (-1081)) (-5 *2 (-1203 *3)))) (-4281 (*1 *1 *2) (-12 (-5 *2 (-1203 *3)) (-4 *3 (-1081)) (-4 *1 (-1275 *3)))) (-4293 (*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-4280 (*1 *1 *1 *2) (|partial| -12 (-5 *2 (-793)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-4279 (*1 *2 *1 *1) (-12 (-4 *3 (-1081)) (-5 *2 (-2 (|:| -2198 *1) (|:| -3389 *1))) (-4 *1 (-1275 *3)))) (-4278 (*1 *2 *1 *3) (-12 (-5 *3 (-793)) (-4 *4 (-1081)) (-5 *2 (-2 (|:| -2198 *1) (|:| -3389 *1))) (-4 *1 (-1275 *4)))) (-4277 (*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-4276 (*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-4275 (*1 *1 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)))) (-4274 (*1 *1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-4273 (*1 *2 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-175)))) (-4272 (*1 *2 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-175)))) (-4316 (*1 *2 *2 *2) (-12 (-5 *2 (-421 *1)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)) (-4 *3 (-571)))) (-4288 (*1 *2 *1 *1) (-12 (-4 *1 (-1275 *3)) (-4 *3 (-1081)) (-4 *3 (-571)) (-5 *2 (-793)))) (-4271 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$ (-793))) (-15 -4280 ((-3 $ "failed") $ (-793))) (-15 -4279 ((-2 (|:| -2198 $) (|:| -3389 $)) $ $)) (-15 -4278 ((-2 (|:| -2198 $) (|:| -3389 $)) $ (-793))) (-15 -4277 ($ $ (-793))) (-15 -4276 ($ $ (-793))) (-15 -4275 ($ $ $)) (-15 -4274 ($ $ (-1 |t#1| |t#1|) $)) (IF (|has| |t#1| (-1184)) (-6 (-1184)) |%noBranch|) (IF (|has| |t#1| (-175)) (PROGN (-15 -4273 (|t#1| $)) (-15 -4272 (|t#1| $ $))) |%noBranch|) (IF (|has| |t#1| (-571)) (PROGN (-6 (-298 (-421 $) (-421 $))) (-15 -4316 ((-421 $) (-421 $) (-421 $))) (-15 -4288 ((-793) $ $)) (-15 -4271 ($ $ $)) (-15 -4270 ((-3 $ "failed") $ $)) (-15 -4270 ((-3 (-421 $) "failed") (-421 $) $)) (-15 -4269 ($ $ $)) (-15 -4268 ((-2 (|:| -4470 |t#1|) (|:| -2198 $) (|:| -3389 $)) $ $))) |%noBranch|) (IF (|has| |t#1| (-466)) (-15 -4267 ((-2 (|:| |primePart| $) (|:| |commonPart| $)) $ $)) |%noBranch|) (IF (|has| |t#1| (-376)) (PROGN (-6 (-319)) (-6 -4507) (-15 -4316 (|t#1| (-421 $) |t#1|))) |%noBranch|) (IF (|has| |t#1| (-38 (-421 (-560)))) (-15 -4328 ($ $)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #1=(-793)) . T) ((-25) . T) ((-38 #2=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #2# #2#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #2#) -4043 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #3=(-1114)) . T) ((-635 |#1|) . T) ((-635 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| (-1114) (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-633 (-916 (-391)))) (|has| (-1114) (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-633 (-916 (-560)))) (|has| (-1114) (-633 (-916 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #1#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -4043 (|has| |#1| (-940)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #3# |#1|) . T) ((-528 #3# $) . T) ((-528 $ $) . T) ((-571) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #2#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #2#) |has| |#1| (-38 (-421 (-560)))) ((-670 #4=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #2#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #4#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #2#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #3#) . T) ((-922 $ #5=(-1209)) -4043 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 #3#) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #3#) . T) ((-930 #5#) -4043 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) -12 (|has| |#1| (-912 (-391))) (|has| (-1114) (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-912 (-560))) (|has| (-1114) (-912 (-560)))) ((-980 |#1| #1# #3#) . T) ((-940) |has| |#1| (-940)) ((-951) |has| |#1| (-376)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #3#) . T) ((-1070 |#1|) . T) ((-1083 #2#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #2#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4043 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-1184)) ((-1249) . T) ((-1254) |has| |#1| (-940))) +((-4474 ((|#4| (-1 |#3| |#1|) |#2|) 22 T ELT))) +(((-1276 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -4474 (|#4| (-1 |#3| |#1|) |#2|))) (-1081) (-1275 |#1|) (-1081) (-1275 |#3|)) (T -1276)) +((-4474 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1081)) (-4 *6 (-1081)) (-4 *2 (-1275 *6)) (-5 *1 (-1276 *5 *4 *6 *2)) (-4 *4 (-1275 *5))))) +(-10 -7 (-15 -4474 (|#4| (-1 |#3| |#1|) |#2|))) +((-3570 (((-663 (-1114)) $) 34 T ELT)) (-4475 (($ $) 31 T ELT)) (-3380 (($ |#2| |#3|) NIL T ELT) (($ $ (-1114) |#3|) 28 T ELT) (($ $ (-663 (-1114)) (-663 |#3|)) 27 T ELT)) (-3381 (($ $) 14 T ELT)) (-3678 ((|#2| $) 12 T ELT)) (-4464 ((|#3| $) 10 T ELT))) +(((-1277 |#1| |#2| |#3|) (-10 -8 (-15 -3570 ((-663 (-1114)) |#1|)) (-15 -3380 (|#1| |#1| (-663 (-1114)) (-663 |#3|))) (-15 -3380 (|#1| |#1| (-1114) |#3|)) (-15 -4475 (|#1| |#1|)) (-15 -3380 (|#1| |#2| |#3|)) (-15 -4464 (|#3| |#1|)) (-15 -3381 (|#1| |#1|)) (-15 -3678 (|#2| |#1|))) (-1278 |#2| |#3|) (-1081) (-816)) (T -1277)) +NIL 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T) ((-23) . T) ((-47 |#1| #1=(-421 (-560))) . T) ((-25) . T) ((-38 #2=(-421 (-560))) -4043 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #2# #2#) -4043 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4043 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #2#) -4043 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-888)) . 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T) ((-1083 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1088 #2#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4043 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1278 |#1| #1#) . 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T T T) -7 NIL NIL NIL) (-1315 3416903 3419012 3419108 "XDPOLY" 3419113 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1314 3415558 3416296 3416339 "XALG" 3416344 NIL XALG (NIL T) -9 NIL 3416455 NIL) (-1313 3408582 3413535 3414029 "WUTSET" 3415150 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1312 3406684 3407634 3407957 "WP" 3408393 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1311 3406232 3406506 3406576 "WHILEAST" 3406636 T WHILEAST (NIL) -8 NIL NIL NIL) (-1310 3405644 3405949 3406043 "WHEREAST" 3406160 T WHEREAST (NIL) -8 NIL NIL NIL) (-1309 3404518 3404728 3405023 "WFFINTBS" 3405441 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1308 3402386 3402849 3403311 "WEIER" 3404090 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1307 3401310 3401868 3401910 "VSPACE" 3402046 NIL VSPACE (NIL T) -9 NIL 3402120 NIL) (-1306 3401142 3401175 3401266 "VSPACE-" 3401271 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1305 3400939 3400993 3401061 "VOID" 3401096 T VOID (NIL) -8 NIL NIL NIL) (-1304 3397207 3398002 3398739 "VIEWDEF" 3400224 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1303 3386151 3388755 3390928 "VIEW3D" 3395056 T VIEW3D (NIL) -8 NIL NIL NIL) (-1302 3378168 3380062 3381641 "VIEW2D" 3384594 T VIEW2D (NIL) -8 NIL NIL NIL) (-1301 3376268 3376663 3377069 "VIEW" 3377784 T VIEW (NIL) -7 NIL NIL NIL) (-1300 3374821 3375104 3375422 "VECTOR2" 3375998 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1299 3369841 3374591 3374683 "VECTOR" 3374764 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1298 3362900 3367545 3367588 "VECTCAT" 3368583 NIL VECTCAT (NIL T) -9 NIL 3369170 NIL) (-1297 3361842 3362168 3362558 "VECTCAT-" 3362563 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1296 3361248 3361493 3361613 "VARIABLE" 3361757 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1295 3361181 3361186 3361216 "UTYPE" 3361221 T UTYPE (NIL) -9 NIL NIL NIL) (-1294 3359989 3360165 3360427 "UTSODETL" 3361007 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1293 3357381 3357889 3358413 "UTSODE" 3359530 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1292 3347391 3353314 3353357 "UTSCAT" 3354469 NIL UTSCAT (NIL T) -9 NIL 3355227 NIL) (-1291 3344517 3345461 3346450 "UTSCAT-" 3346455 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1290 3344138 3344187 3344320 "UTS2" 3344468 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1289 3335455 3341899 3342379 "UTS" 3343716 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1288 3329433 3332265 3332308 "URAGG" 3334378 NIL URAGG (NIL T) -9 NIL 3335101 NIL) (-1287 3326465 3327433 3328457 "URAGG-" 3328462 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1286 3321841 3325100 3325565 "UPXSSING" 3326129 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1285 3314270 3321745 3321817 "UPXSCONS" 3321822 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1284 3303028 3310472 3310534 "UPXSCCA" 3311108 NIL UPXSCCA (NIL T T) -9 NIL 3311341 NIL) (-1283 3302648 3302751 3302925 "UPXSCCA-" 3302930 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1282 3291306 3298475 3298518 "UPXSCAT" 3299166 NIL UPXSCAT (NIL T) -9 NIL 3299775 NIL) (-1281 3290730 3290815 3290994 "UPXS2" 3291221 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1280 3282222 3290112 3290376 "UPXS" 3290524 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1279 3280858 3281129 3281480 "UPSQFREE" 3281965 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1278 3273689 3277124 3277179 "UPSCAT" 3278259 NIL UPSCAT (NIL T T) -9 NIL 3279025 NIL) (-1277 3272845 3273100 3273427 "UPSCAT-" 3273432 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1276 3272466 3272515 3272648 "UPOLYC2" 3272796 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1275 3256614 3265593 3265636 "UPOLYC" 3267737 NIL UPOLYC (NIL T) -9 NIL 3268958 NIL) (-1274 3247483 3250382 3253522 "UPOLYC-" 3253527 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1273 3246804 3246929 3247093 "UPMP" 3247372 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1272 3246351 3246438 3246577 "UPDIVP" 3246717 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1271 3244889 3245168 3245484 "UPDECOMP" 3246100 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1270 3244102 3244232 3244418 "UPCDEN" 3244773 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1269 3243615 3243690 3243839 "UP2" 3244027 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1268 3234211 3243298 3243427 "UP" 3243534 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1267 3233416 3233553 3233758 "UNISEG2" 3234054 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1266 3231769 3232620 3232897 "UNISEG" 3233174 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1265 3230811 3231009 3231235 "UNIFACT" 3231585 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1264 3217542 3230715 3230787 "ULSCONS" 3230792 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1263 3197359 3210622 3210684 "ULSCCAT" 3211322 NIL ULSCCAT (NIL T T) -9 NIL 3211611 NIL) (-1262 3196355 3196654 3197042 "ULSCCAT-" 3197047 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3184810 3191901 3191944 "ULSCAT" 3192807 NIL ULSCAT (NIL T) -9 NIL 3193538 NIL) (-1260 3184234 3184319 3184498 "ULS2" 3184725 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1259 3166065 3183546 3183788 "ULS" 3184050 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1258 3164984 3165684 3165798 "UINT8" 3165909 T UINT8 (NIL) -8 NIL NIL 3166001) (-1257 3163902 3164602 3164716 "UINT64" 3164827 T UINT64 (NIL) -8 NIL NIL 3164919) (-1256 3162820 3163520 3163634 "UINT32" 3163745 T UINT32 (NIL) -8 NIL NIL 3163837) (-1255 3161738 3162438 3162552 "UINT16" 3162663 T UINT16 (NIL) -8 NIL NIL 3162755) (-1254 3159817 3160984 3161014 "UFD" 3161226 T UFD (NIL) -9 NIL 3161340 NIL) (-1253 3159599 3159657 3159752 "UFD-" 3159757 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1252 3158657 3158864 3159080 "UDVO" 3159405 T UDVO (NIL) -7 NIL NIL NIL) (-1251 3156423 3156882 3157353 "UDPO" 3158221 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1250 3156135 3156378 3156409 "TYPEAST" 3156414 T TYPEAST (NIL) -8 NIL NIL NIL) (-1249 3156068 3156073 3156103 "TYPE" 3156108 T TYPE (NIL) -9 NIL NIL NIL) (-1248 3155021 3155241 3155481 "TWOFACT" 3155862 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1247 3153996 3154430 3154665 "TUPLE" 3154821 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1246 3151633 3152206 3152745 "TUBETOOL" 3153479 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1245 3150439 3150680 3150922 "TUBE" 3151426 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1244 3138688 3143196 3143293 "TSETCAT" 3148562 NIL TSETCAT (NIL T T T T) -9 NIL 3150094 NIL) (-1243 3133156 3135020 3136911 "TSETCAT-" 3136916 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1242 3127342 3132128 3132411 "TS" 3132908 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3121815 3122828 3123757 "TRMANIP" 3126478 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1240 3121244 3121319 3121482 "TRIMAT" 3121747 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1239 3119056 3119347 3119704 "TRIGMNIP" 3120993 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1238 3118540 3118689 3118719 "TRIGCAT" 3118932 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1237 3118185 3118288 3118429 "TRIGCAT-" 3118434 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1236 3114910 3117043 3117324 "TREE" 3117939 NIL TREE (NIL T) -8 NIL NIL NIL) (-1235 3114016 3114712 3114742 "TRANFUN" 3114777 T TRANFUN (NIL) -9 NIL 3114843 NIL) (-1234 3113235 3113486 3113766 "TRANFUN-" 3113771 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1233 3113033 3113071 3113132 "TOPSP" 3113196 T TOPSP (NIL) -7 NIL NIL NIL) (-1232 3112363 3112496 3112650 "TOOLSIGN" 3112914 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1231 3110877 3111540 3111779 "TEXTFILE" 3112146 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1230 3110652 3110689 3110761 "TEX1" 3110840 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1229 3108456 3109105 3109534 "TEX" 3110245 T TEX (NIL) -8 NIL NIL NIL) (-1228 3108092 3108167 3108257 "TEMUTL" 3108388 T TEMUTL (NIL) -7 NIL NIL NIL) (-1227 3106186 3106526 3106851 "TBCMPPK" 3107815 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1226 3097620 3104272 3104328 "TBAGG" 3104728 NIL TBAGG (NIL T T) -9 NIL 3104939 NIL) (-1225 3092504 3094178 3095932 "TBAGG-" 3095937 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1224 3091870 3091995 3092140 "TANEXP" 3092393 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1223 3091321 3091645 3091735 "TALGOP" 3091815 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1222 3090715 3090832 3090970 "TABLEAU" 3091218 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1221 3083843 3090572 3090665 "TABLE" 3090670 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1220 3078373 3079671 3080919 "TABLBUMP" 3082629 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1219 3077583 3077742 3077923 "SYSTEM" 3078214 T SYSTEM (NIL) -8 NIL NIL NIL) (-1218 3073988 3074741 3075524 "SYSSOLP" 3076834 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1217 3073750 3073943 3073974 "SYSPTR" 3073979 T SYSPTR (NIL) -8 NIL NIL NIL) (-1216 3072589 3073281 3073407 "SYSNNI" 3073593 NIL SYSNNI (NIL NIL) -8 NIL NIL 3073685) (-1215 3071796 3072351 3072430 "SYSINT" 3072490 NIL SYSINT (NIL NIL) -8 NIL NIL 3072535) (-1214 3067894 3069074 3069784 "SYNTAX" 3071108 T SYNTAX (NIL) -8 NIL NIL NIL) (-1213 3064974 3065654 3066286 "SYMTAB" 3067284 T SYMTAB (NIL) -8 NIL NIL NIL) (-1212 3060073 3061125 3062108 "SYMS" 3064013 T SYMS (NIL) -8 NIL NIL NIL) (-1211 3056979 3059524 3059757 "SYMPOLY" 3059875 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1210 3056484 3056571 3056694 "SYMFUNC" 3056891 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1209 3052282 3053796 3054609 "SYMBOL" 3055693 T SYMBOL (NIL) -8 NIL NIL NIL) (-1208 3045755 3047510 3049230 "SWITCH" 3050584 T SWITCH (NIL) -8 NIL NIL NIL) (-1207 3038516 3044711 3045005 "SUTS" 3045519 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1206 3030008 3037898 3038162 "SUPXS" 3038310 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3029155 3029294 3029511 "SUPFRACF" 3029876 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1204 3028770 3028835 3028948 "SUP2" 3029090 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1203 3019314 3028388 3028514 "SUP" 3028679 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3017738 3018036 3018392 "SUMRF" 3019013 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1201 3017061 3017139 3017331 "SUMFS" 3017659 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1200 2998927 3016373 3016615 "SULS" 3016877 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1199 2998475 2998749 2998819 "SUCHTAST" 2998879 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1198 2997716 2998000 2998140 "SUCH" 2998383 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1197 2991355 2992622 2993581 "SUBSPACE" 2996804 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1196 2990775 2990875 2991039 "SUBRESP" 2991243 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1195 2984786 2986068 2987215 "STTFNC" 2989675 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1194 2977980 2979451 2980762 "STTF" 2983522 NIL STTF (NIL T) -7 NIL NIL NIL) (-1193 2969096 2971162 2972956 "STTAYLOR" 2976221 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1192 2961964 2968960 2969043 "STRTBL" 2969048 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1191 2956475 2961673 2961772 "STRING" 2961887 T STRING (NIL) -8 NIL NIL NIL) (-1190 2955979 2956062 2956206 "STREAM3" 2956392 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1189 2954943 2955144 2955379 "STREAM2" 2955792 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1188 2954625 2954683 2954776 "STREAM1" 2954885 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1187 2946739 2952244 2952855 "STREAM" 2954049 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2945731 2945936 2946167 "STINPROD" 2946555 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1185 2944846 2945220 2945368 "STEPAST" 2945605 T STEPAST (NIL) -8 NIL NIL NIL) (-1184 2944342 2944587 2944617 "STEP" 2944711 T STEP (NIL) -9 NIL 2944782 NIL) (-1183 2937512 2944241 2944318 "STBL" 2944323 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1182 2931693 2936306 2936349 "STAGG" 2936781 NIL STAGG (NIL T) -9 NIL 2936960 NIL) (-1181 2929245 2929997 2930869 "STAGG-" 2930874 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1180 2927331 2929015 2929107 "STACK" 2929188 NIL STACK (NIL T) -8 NIL NIL NIL) (-1179 2926648 2927161 2927191 "SRING" 2927196 T SRING (NIL) -9 NIL 2927216 NIL) (-1178 2918770 2924789 2925245 "SREGSET" 2926278 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1177 2911117 2912564 2914077 "SRDCMPK" 2917376 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1176 2903531 2908476 2908506 "SRAGG" 2909809 T SRAGG (NIL) -9 NIL 2910417 NIL) (-1175 2902482 2902803 2903182 "SRAGG-" 2903187 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1174 2896180 2901429 2901850 "SQMATRIX" 2902108 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1173 2889706 2892898 2893625 "SPLTREE" 2895525 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1172 2885531 2886362 2887008 "SPLNODE" 2889132 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1171 2884506 2884811 2884841 "SPFCAT" 2885285 T SPFCAT (NIL) -9 NIL NIL NIL) (-1170 2883201 2883453 2883717 "SPECOUT" 2884264 T SPECOUT (NIL) -7 NIL NIL NIL) (-1169 2873847 2876165 2876195 "SPADXPT" 2880873 T SPADXPT (NIL) -9 NIL 2883039 NIL) (-1168 2873602 2873648 2873717 "SPADPRSR" 2873800 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1167 2871205 2873557 2873588 "SPADAST" 2873593 T SPADAST (NIL) -8 NIL NIL NIL) (-1166 2862806 2864909 2864952 "SPACEC" 2869325 NIL SPACEC (NIL T) -9 NIL 2871141 NIL) (-1165 2860606 2862738 2862787 "SPACE3" 2862792 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1164 2859338 2859529 2859820 "SORTPAK" 2860411 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1163 2857400 2857733 2858145 "SOLVETRA" 2859002 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1162 2856438 2856672 2856933 "SOLVESER" 2857173 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1161 2851670 2852630 2853625 "SOLVERAD" 2855490 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1160 2847395 2848094 2848823 "SOLVEFOR" 2851037 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1159 2841113 2846743 2846840 "SNTSCAT" 2846845 NIL SNTSCAT (NIL T T T T) -9 NIL 2846915 NIL) (-1158 2834664 2839436 2839827 "SMTS" 2840803 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1157 2828386 2834552 2834629 "SMP" 2834634 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1156 2826515 2826846 2827244 "SMITH" 2828083 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1155 2818154 2823094 2823197 "SMATCAT" 2824548 NIL SMATCAT (NIL NIL T T T) -9 NIL 2825098 NIL) (-1154 2814926 2815917 2817095 "SMATCAT-" 2817100 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1153 2812506 2814134 2814177 "SKAGG" 2814438 NIL SKAGG (NIL T) -9 NIL 2814573 NIL) (-1152 2808026 2811989 2812166 "SINT" 2812318 T SINT (NIL) -8 NIL NIL 2812473) (-1151 2807792 2807836 2807902 "SIMPAN" 2807982 T SIMPAN (NIL) -7 NIL NIL NIL) (-1150 2806612 2806851 2807126 "SIGNRF" 2807551 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1149 2805427 2805596 2805880 "SIGNEF" 2806441 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1148 2804667 2805010 2805134 "SIGAST" 2805325 T SIGAST (NIL) -8 NIL NIL NIL) (-1147 2803892 2804202 2804342 "SIG" 2804549 T SIG (NIL) -8 NIL NIL NIL) (-1146 2801544 2802036 2802542 "SHP" 2803433 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1145 2794982 2801445 2801521 "SHDP" 2801526 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1144 2794493 2794733 2794763 "SGROUP" 2794856 T SGROUP (NIL) -9 NIL 2794918 NIL) (-1143 2794345 2794377 2794450 "SGROUP-" 2794455 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1142 2791064 2791834 2792557 "SGCF" 2793644 T SGCF (NIL) -7 NIL NIL NIL) (-1141 2784880 2790510 2790607 "SFRTCAT" 2790612 NIL SFRTCAT (NIL T T T T) -9 NIL 2790651 NIL) (-1140 2778199 2779319 2780455 "SFRGCD" 2783863 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1139 2771217 2772398 2773584 "SFQCMPK" 2777132 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2770819 2770926 2771037 "SFORT" 2771158 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1137 2769745 2770659 2770780 "SEXOF" 2770785 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1136 2765334 2766241 2766336 "SEXCAT" 2768958 NIL SEXCAT (NIL T T T T T) -9 NIL 2769518 NIL) (-1135 2764249 2765215 2765283 "SEX" 2765288 T SEX (NIL) -8 NIL NIL NIL) (-1134 2762371 2762962 2763267 "SETMN" 2763990 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1133 2761901 2762089 2762119 "SETCAT" 2762236 T SETCAT (NIL) -9 NIL 2762321 NIL) (-1132 2761669 2761733 2761832 "SETCAT-" 2761837 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1131 2757883 2760130 2760173 "SETAGG" 2761043 NIL SETAGG (NIL T) -9 NIL 2761383 NIL) (-1130 2757305 2757457 2757694 "SETAGG-" 2757699 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1129 2754228 2757239 2757287 "SET" 2757292 NIL SET (NIL T) -8 NIL NIL NIL) (-1128 2753611 2753924 2754025 "SEQAST" 2754149 T SEQAST (NIL) -8 NIL NIL NIL) (-1127 2752738 2753104 2753165 "SEGXCAT" 2753451 NIL SEGXCAT (NIL T T) -9 NIL 2753571 NIL) (-1126 2751663 2751931 2751974 "SEGCAT" 2752496 NIL SEGCAT (NIL T) -9 NIL 2752717 NIL) (-1125 2751278 2751343 2751456 "SEGBIND2" 2751598 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1124 2750168 2750641 2750849 "SEGBIND" 2751105 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1123 2749687 2749969 2750046 "SEGAST" 2750113 T SEGAST (NIL) -8 NIL NIL NIL) (-1122 2748896 2749032 2749236 "SEG2" 2749531 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1121 2747812 2748562 2748744 "SEG" 2748749 NIL SEG (NIL T) -8 NIL NIL NIL) (-1120 2747045 2747747 2747794 "SDVAR" 2747799 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1119 2738403 2746815 2746945 "SDPOL" 2746950 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1118 2736972 2737262 2737581 "SCPKG" 2738118 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1117 2736094 2736308 2736500 "SCOPE" 2736802 T SCOPE (NIL) -8 NIL NIL NIL) (-1116 2735290 2735448 2735627 "SCACHE" 2735949 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1115 2734874 2735108 2735138 "SASTCAT" 2735143 T SASTCAT (NIL) -9 NIL 2735156 NIL) (-1114 2734277 2734709 2734785 "SAOS" 2734820 T SAOS (NIL) -8 NIL NIL NIL) (-1113 2733836 2733877 2734050 "SAERFFC" 2734236 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1112 2733423 2733464 2733623 "SAEFACT" 2733795 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1111 2726471 2733320 2733400 "SAE" 2733405 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2724774 2725106 2725507 "RURPK" 2726137 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1109 2723351 2723717 2724022 "RULESET" 2724608 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1108 2722921 2723145 2723228 "RULECOLD" 2723303 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1107 2720036 2720674 2721132 "RULE" 2722602 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2719820 2719854 2719925 "RTVALUE" 2719987 T RTVALUE (NIL) -8 NIL NIL NIL) (-1105 2719231 2719537 2719631 "RSTRCAST" 2719748 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1104 2714001 2714874 2715794 "RSETGCD" 2718430 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1103 2702679 2708309 2708406 "RSETCAT" 2712525 NIL RSETCAT (NIL T T T T) -9 NIL 2713622 NIL) (-1102 2700498 2701145 2701969 "RSETCAT-" 2701974 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1101 2692806 2694260 2695780 "RSDCMPK" 2699097 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2690675 2691238 2691312 "RRCC" 2692398 NIL RRCC (NIL T T) -9 NIL 2692742 NIL) (-1099 2689996 2690200 2690479 "RRCC-" 2690484 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1098 2689379 2689692 2689793 "RPTAST" 2689917 T RPTAST (NIL) -8 NIL NIL NIL) (-1097 2661765 2672491 2672558 "RPOLCAT" 2683224 NIL RPOLCAT (NIL T T T) -9 NIL 2686384 NIL) (-1096 2652735 2655603 2658725 "RPOLCAT-" 2658730 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1095 2643302 2650946 2651428 "ROUTINE" 2652275 T ROUTINE (NIL) -8 NIL NIL NIL) (-1094 2639365 2642928 2643068 "ROMAN" 2643184 T ROMAN (NIL) -8 NIL NIL NIL) (-1093 2637477 2638225 2638485 "ROIRC" 2639170 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1092 2633250 2636019 2636049 "RNS" 2636318 T RNS (NIL) -9 NIL 2636574 NIL) (-1091 2631657 2632142 2632676 "RNS-" 2632751 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1090 2630618 2631022 2631224 "RNGBIND" 2631508 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1089 2629911 2630415 2630445 "RNG" 2630450 T RNG (NIL) -9 NIL 2630471 NIL) (-1088 2629206 2629684 2629727 "RMODULE" 2629732 NIL RMODULE (NIL T) -9 NIL 2629759 NIL) (-1087 2628030 2628136 2628472 "RMCAT2" 2629107 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1086 2624646 2627376 2627673 "RMATRIX" 2627792 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1085 2617256 2619733 2619848 "RMATCAT" 2623207 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2624189 NIL) (-1084 2616595 2616778 2617085 "RMATCAT-" 2617090 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1083 2616168 2616382 2616425 "RLINSET" 2616487 NIL RLINSET (NIL T) -9 NIL 2616531 NIL) (-1082 2615729 2615810 2615938 "RINTERP" 2616087 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1081 2614653 2615327 2615357 "RING" 2615413 T RING (NIL) -9 NIL 2615505 NIL) (-1080 2614433 2614489 2614586 "RING-" 2614591 NIL RING- (NIL T) -8 NIL NIL NIL) (-1079 2613244 2613511 2613769 "RIDIST" 2614197 T RIDIST (NIL) -7 NIL NIL NIL) (-1078 2603983 2612712 2612918 "RGCHAIN" 2613092 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1077 2603241 2603725 2603766 "RGBCSPC" 2603824 NIL RGBCSPC (NIL T) -9 NIL 2603876 NIL) (-1076 2602307 2602766 2602807 "RGBCMDL" 2603039 NIL RGBCMDL (NIL T) -9 NIL 2603153 NIL) (-1075 2601947 2602016 2602119 "RFFACTOR" 2602238 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1074 2601666 2601707 2601804 "RFFACT" 2601906 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1073 2599717 2600147 2600529 "RFDIST" 2601306 T RFDIST (NIL) -7 NIL NIL NIL) (-1072 2596657 2597325 2597995 "RF" 2599081 NIL RF (NIL T) -7 NIL NIL NIL) (-1071 2596104 2596202 2596365 "RETSOL" 2596559 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1070 2595722 2595820 2595863 "RETRACT" 2595996 NIL RETRACT (NIL T) -9 NIL 2596083 NIL) (-1069 2595565 2595596 2595683 "RETRACT-" 2595688 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1068 2595113 2595387 2595457 "RETAST" 2595517 T RETAST (NIL) -8 NIL NIL NIL) (-1067 2587577 2594766 2594893 "RESULT" 2595008 T RESULT (NIL) -8 NIL NIL NIL) (-1066 2586012 2586846 2587045 "RESRING" 2587480 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1065 2585636 2585697 2585795 "RESLATC" 2585949 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1064 2585335 2585376 2585483 "REPSQ" 2585595 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1063 2585026 2585067 2585178 "REPDB" 2585294 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1062 2578858 2580315 2581538 "REP2" 2583838 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1061 2575161 2575916 2576724 "REP1" 2578085 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1060 2572541 2573163 2573765 "REP" 2574581 T REP (NIL) -7 NIL NIL NIL) (-1059 2564663 2570682 2571138 "REGSET" 2572171 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2563372 2563811 2564061 "REF" 2564448 NIL REF (NIL T) -8 NIL NIL NIL) (-1057 2562737 2562852 2563019 "REDORDER" 2563256 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1056 2558108 2561950 2562177 "RECLOS" 2562565 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1055 2557142 2557341 2557556 "REALSOLV" 2557915 T REALSOLV (NIL) -7 NIL NIL NIL) (-1054 2553589 2554427 2555311 "REAL0Q" 2556307 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1053 2549142 2550178 2551239 "REAL0" 2552570 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1052 2548976 2549029 2549059 "REAL" 2549064 T REAL (NIL) -9 NIL 2549099 NIL) (-1051 2548387 2548693 2548787 "RDUCEAST" 2548904 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1050 2547786 2547864 2548071 "RDIV" 2548309 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1049 2546836 2547028 2547241 "RDIST" 2547608 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1048 2545421 2545720 2546092 "RDETRS" 2546544 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1047 2543215 2543687 2544225 "RDETR" 2544963 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1046 2541834 2542118 2542515 "RDEEFS" 2542931 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1045 2540337 2540649 2541074 "RDEEF" 2541522 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1044 2533816 2537291 2537321 "RCFIELD" 2538616 T RCFIELD (NIL) -9 NIL 2539347 NIL) (-1043 2531772 2532384 2533080 "RCFIELD-" 2533155 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1042 2527935 2529845 2529888 "RCAGG" 2530972 NIL RCAGG (NIL T) -9 NIL 2531437 NIL) (-1041 2527545 2527657 2527820 "RCAGG-" 2527825 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1040 2526862 2526992 2527157 "RATRET" 2527429 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1039 2526403 2526482 2526603 "RATFACT" 2526790 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1038 2525681 2525831 2525983 "RANDSRC" 2526273 T RANDSRC (NIL) -7 NIL NIL NIL) (-1037 2525409 2525459 2525532 "RADUTIL" 2525630 T RADUTIL (NIL) -7 NIL NIL NIL) (-1036 2517554 2524240 2524551 "RADIX" 2525132 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1035 2507169 2517396 2517526 "RADFF" 2517531 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1034 2506798 2506891 2506921 "RADCAT" 2507081 T RADCAT (NIL) -9 NIL NIL NIL) (-1033 2506568 2506628 2506728 "RADCAT-" 2506733 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1032 2504593 2506338 2506430 "QUEUE" 2506511 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1031 2504218 2504267 2504398 "QUATCT2" 2504544 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1030 2496596 2500641 2500683 "QUATCAT" 2501474 NIL QUATCAT (NIL T) -9 NIL 2502240 NIL) (-1029 2492477 2493772 2495162 "QUATCAT-" 2495258 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1028 2488323 2492410 2492458 "QUAT" 2492463 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1027 2485690 2487371 2487414 "QUAGG" 2487795 NIL QUAGG (NIL T) -9 NIL 2487970 NIL) (-1026 2485238 2485512 2485582 "QQUTAST" 2485642 T QQUTAST (NIL) -8 NIL NIL NIL) (-1025 2484149 2484751 2484916 "QFORM" 2485119 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1024 2483774 2483823 2483954 "QFCAT2" 2484100 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1023 2473471 2479621 2479663 "QFCAT" 2480331 NIL QFCAT (NIL T) -9 NIL 2481332 NIL) (-1022 2468805 2470253 2471840 "QFCAT-" 2471936 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2468236 2468370 2468502 "QEQUAT" 2468695 T QEQUAT (NIL) -8 NIL NIL NIL) (-1020 2461254 2462435 2463621 "QCMPACK" 2467169 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2460483 2460665 2460901 "QALGSET2" 2461072 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1018 2457933 2458469 2458899 "QALGSET" 2460138 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2456600 2456842 2457161 "PWFFINTB" 2457706 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1016 2454745 2454943 2455299 "PUSHVAR" 2456414 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1015 2450472 2451688 2451731 "PTRANFN" 2453642 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1014 2448809 2449154 2449478 "PTPACK" 2450183 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1013 2448432 2448495 2448606 "PTFUNC2" 2448746 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1012 2442462 2447221 2447264 "PTCAT" 2447564 NIL PTCAT (NIL T) -9 NIL 2447717 NIL) (-1011 2442111 2442152 2442278 "PSQFR" 2442421 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1010 2440683 2440999 2441335 "PSEUDLIN" 2441809 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1009 2427203 2429778 2432104 "PSETPK" 2438443 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1008 2420022 2422939 2423037 "PSETCAT" 2426078 NIL PSETCAT (NIL T T T T) -9 NIL 2426892 NIL) (-1007 2417747 2418489 2419313 "PSETCAT-" 2419318 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1006 2417060 2417255 2417285 "PSCURVE" 2417557 T PSCURVE (NIL) -9 NIL 2417724 NIL) (-1005 2412783 2414550 2414617 "PSCAT" 2415469 NIL PSCAT (NIL T T T) -9 NIL 2415709 NIL) (-1004 2411777 2412059 2412462 "PSCAT-" 2412467 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1003 2409945 2410836 2411101 "PRTITION" 2411534 T PRTITION (NIL) -8 NIL NIL NIL) (-1002 2409356 2409662 2409756 "PRTDAST" 2409873 T PRTDAST (NIL) -8 NIL NIL NIL) (-1001 2398200 2400622 2402812 "PRS" 2407218 NIL PRS (NIL T T) -7 NIL NIL NIL) (-1000 2395926 2397517 2397559 "PRQAGG" 2397745 NIL PRQAGG (NIL T) -9 NIL 2397847 NIL) (-999 2395105 2395554 2395582 "PROPLOG" 2395721 T PROPLOG (NIL) -9 NIL 2395836 NIL) (-998 2394703 2394766 2394889 "PROPFUN2" 2395028 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-997 2394000 2394139 2394311 "PROPFUN1" 2394564 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-996 2391981 2392747 2393044 "PROPFRML" 2393736 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-995 2391426 2391557 2391685 "PROPERTY" 2391873 T PROPERTY (NIL) -8 NIL NIL NIL) (-994 2385239 2389592 2390412 "PRODUCT" 2390652 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-993 2385029 2385067 2385126 "PRINT" 2385200 T PRINT (NIL) -7 NIL NIL NIL) (-992 2384345 2384486 2384638 "PRIMES" 2384909 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-991 2382392 2382811 2383277 "PRIMELT" 2383924 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-990 2382109 2382170 2382198 "PRIMCAT" 2382322 T PRIMCAT (NIL) -9 NIL NIL NIL) (-989 2381098 2381294 2381522 "PRIMARR2" 2381927 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-988 2376934 2381036 2381081 "PRIMARR" 2381086 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-987 2376571 2376633 2376744 "PREASSOC" 2376872 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-986 2373536 2376029 2376263 "PR" 2376382 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2372987 2373144 2373172 "PPCURVE" 2373377 T PPCURVE (NIL) -9 NIL 2373513 NIL) (-984 2372534 2372782 2372865 "PORTNUM" 2372924 T PORTNUM (NIL) -8 NIL NIL NIL) (-983 2369871 2370292 2370884 "POLYROOT" 2372115 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-982 2369248 2369312 2369546 "POLYLIFT" 2369807 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-981 2365469 2365972 2366601 "POLYCATQ" 2368793 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-980 2351117 2357216 2357281 "POLYCAT" 2360795 NIL POLYCAT (NIL T T T) -9 NIL 2362673 NIL) (-979 2344257 2346442 2348819 "POLYCAT-" 2348824 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-978 2343838 2343912 2344032 "POLY2UP" 2344183 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-977 2343464 2343527 2343636 "POLY2" 2343775 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-976 2336679 2343068 2343228 "POLY" 2343337 NIL POLY (NIL T) -8 NIL NIL NIL) (-975 2335340 2335603 2335879 "POLUTIL" 2336453 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-974 2333659 2333972 2334303 "POLTOPOL" 2335062 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-973 2328769 2333593 2333640 "POINT" 2333645 NIL POINT (NIL T) -8 NIL NIL NIL) (-972 2326902 2327313 2327688 "PNTHEORY" 2328414 T PNTHEORY (NIL) -7 NIL NIL NIL) (-971 2325348 2325657 2326056 "PMTOOLS" 2326600 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-970 2324935 2325019 2325136 "PMSYM" 2325264 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-969 2324437 2324512 2324687 "PMQFCAT" 2324860 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-968 2323818 2323916 2324078 "PMPREDFS" 2324338 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-967 2323161 2323283 2323439 "PMPRED" 2323695 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2321815 2322033 2322411 "PMPLCAT" 2322923 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-965 2321341 2321426 2321578 "PMLSAGG" 2321730 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-964 2320808 2320890 2321072 "PMKERNEL" 2321259 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-963 2320419 2320500 2320613 "PMINS" 2320727 NIL PMINS (NIL T) -7 NIL NIL NIL) (-962 2319855 2319930 2320139 "PMFS" 2320344 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-961 2319071 2319201 2319406 "PMDOWN" 2319732 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-960 2318320 2318454 2318617 "PMASSFS" 2318958 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-959 2317463 2317645 2317826 "PMASS" 2318159 T PMASS (NIL) -7 NIL NIL NIL) (-958 2317112 2317186 2317280 "PLOTTOOL" 2317389 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-957 2312764 2313958 2314880 "PLOT3D" 2316210 T PLOT3D (NIL) -8 NIL NIL NIL) (-956 2311652 2311853 2312088 "PLOT1" 2312568 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-955 2306073 2307463 2308611 "PLOT" 2310524 T PLOT (NIL) -8 NIL NIL NIL) (-954 2281248 2286139 2290990 "PLEQN" 2301339 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-953 2280935 2280988 2281091 "PINTERPA" 2281195 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-952 2280241 2280375 2280555 "PINTERP" 2280800 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2278325 2279491 2279519 "PID" 2279716 T PID (NIL) -9 NIL 2279843 NIL) (-950 2278070 2278113 2278188 "PICOERCE" 2278282 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-949 2277166 2277834 2277921 "PI" 2277961 T PI (NIL) -8 NIL NIL 2278028) (-948 2276474 2276625 2276801 "PGROEB" 2277022 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-947 2271913 2272872 2273778 "PGE" 2275588 T PGE (NIL) -7 NIL NIL NIL) (-946 2269994 2270283 2270649 "PGCD" 2271630 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-945 2269320 2269435 2269596 "PFRPAC" 2269878 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-944 2265578 2267868 2268221 "PFR" 2268999 NIL PFR (NIL T) -8 NIL NIL NIL) (-943 2263931 2264211 2264536 "PFOTOOLS" 2265325 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-942 2262446 2262703 2263054 "PFOQ" 2263688 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-941 2260929 2261159 2261515 "PFO" 2262230 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-940 2258013 2259519 2259547 "PFECAT" 2260140 T PFECAT (NIL) -9 NIL 2260517 NIL) (-939 2257461 2257626 2257833 "PFECAT-" 2257838 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-938 2256034 2256316 2256617 "PFBRU" 2257210 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-937 2253863 2254252 2254684 "PFBR" 2255685 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-936 2249809 2253752 2253821 "PF" 2253826 NIL PF (NIL NIL) -8 NIL NIL NIL) (-935 2244863 2246016 2246886 "PERMGRP" 2248972 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-934 2242775 2243887 2243928 "PERMCAT" 2244328 NIL PERMCAT (NIL T) -9 NIL 2244626 NIL) (-933 2242422 2242469 2242593 "PERMAN" 2242728 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-932 2238224 2239931 2240579 "PERM" 2241807 NIL PERM (NIL T) -8 NIL NIL NIL) (-931 2235579 2237889 2238011 "PENDTREE" 2238135 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-930 2234460 2234723 2234764 "PDSPC" 2235297 NIL PDSPC (NIL T) -9 NIL 2235542 NIL) (-929 2233515 2233781 2234143 "PDSPC-" 2234148 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-928 2232229 2233165 2233206 "PDRING" 2233211 NIL PDRING (NIL T) -9 NIL 2233239 NIL) (-927 2230972 2231734 2231788 "PDMOD" 2231793 NIL PDMOD (NIL T T) -9 NIL 2231897 NIL) (-926 2228139 2228965 2229633 "PDEPROB" 2230324 T PDEPROB (NIL) -8 NIL NIL NIL) (-925 2225648 2226188 2226743 "PDEPACK" 2227604 T PDEPACK (NIL) -7 NIL NIL NIL) (-924 2224536 2224750 2225001 "PDECOMP" 2225447 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-923 2222053 2222944 2222972 "PDECAT" 2223759 T PDECAT (NIL) -9 NIL 2224472 NIL) (-922 2221670 2221737 2221791 "PDDOM" 2221956 NIL PDDOM (NIL T T) -9 NIL 2222036 NIL) (-921 2221483 2221519 2221626 "PDDOM-" 2221631 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-920 2221228 2221267 2221357 "PCOMP" 2221444 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-919 2219268 2220029 2220326 "PBWLB" 2220957 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-918 2218894 2218957 2219066 "PATTERN2" 2219205 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-917 2216603 2217039 2217496 "PATTERN1" 2218483 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-916 2208782 2210676 2212014 "PATTERN" 2215286 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2208340 2208413 2208545 "PATRES2" 2208709 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-914 2205606 2206289 2206770 "PATRES" 2207905 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2203459 2203894 2204301 "PATMATCH" 2205273 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-912 2202913 2203164 2203205 "PATMAB" 2203312 NIL PATMAB (NIL T) -9 NIL 2203395 NIL) (-911 2201359 2201767 2202025 "PATLRES" 2202718 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-910 2200897 2201028 2201069 "PATAB" 2201074 NIL PATAB (NIL T) -9 NIL 2201246 NIL) (-909 2199037 2199474 2199897 "PARTPERM" 2200494 T PARTPERM (NIL) -7 NIL NIL NIL) (-908 2198646 2198721 2198823 "PARSURF" 2198968 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-907 2198272 2198335 2198444 "PARSU2" 2198583 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-906 2198030 2198076 2198143 "PARSER" 2198225 T PARSER (NIL) -7 NIL NIL NIL) (-905 2197639 2197714 2197816 "PARSCURV" 2197961 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-904 2197265 2197328 2197437 "PARSC2" 2197576 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-903 2196892 2196962 2197059 "PARPCURV" 2197201 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-902 2196518 2196581 2196690 "PARPC2" 2196829 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-901 2195507 2195891 2196073 "PARAMAST" 2196356 T PARAMAST (NIL) -8 NIL NIL NIL) (-900 2195015 2195113 2195232 "PAN2EXPR" 2195408 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-899 2193708 2194136 2194364 "PALETTE" 2194807 T PALETTE (NIL) -8 NIL NIL NIL) (-898 2192053 2192713 2193073 "PAIR" 2193394 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-897 2184986 2191310 2191505 "PADICRC" 2191907 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-896 2177243 2184330 2184515 "PADICRAT" 2184833 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-895 2174040 2175903 2175943 "PADICCT" 2176524 NIL PADICCT (NIL NIL) -9 NIL 2176806 NIL) (-894 2172056 2173977 2174022 "PADIC" 2174027 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2171001 2171213 2171481 "PADEPAC" 2171843 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-892 2170201 2170346 2170552 "PADE" 2170863 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-891 2168434 2169409 2169689 "OWP" 2170005 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-890 2167879 2168140 2168237 "OVERSET" 2168357 T OVERSET (NIL) -8 NIL NIL NIL) (-889 2166799 2167484 2167656 "OVAR" 2167747 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-888 2155035 2157908 2160108 "OUTFORM" 2164619 T OUTFORM (NIL) -8 NIL NIL NIL) (-887 2154317 2154632 2154759 "OUTBFILE" 2154928 T OUTBFILE (NIL) -8 NIL NIL NIL) (-886 2153594 2153789 2153817 "OUTBCON" 2154135 T OUTBCON (NIL) -9 NIL 2154301 NIL) (-885 2153177 2153307 2153464 "OUTBCON-" 2153469 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-884 2152417 2152562 2152723 "OUT" 2153036 T OUT (NIL) -7 NIL NIL NIL) (-883 2151713 2152146 2152235 "OSI" 2152348 T OSI (NIL) -8 NIL NIL NIL) (-882 2151132 2151554 2151582 "OSGROUP" 2151587 T OSGROUP (NIL) -9 NIL 2151609 NIL) (-881 2149843 2150104 2150389 "ORTHPOL" 2150879 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-880 2147094 2149678 2149799 "OREUP" 2149804 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-879 2144197 2146785 2146912 "ORESUP" 2147036 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-878 2141697 2142225 2142786 "OREPCTO" 2143686 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-877 2135075 2137570 2137611 "OREPCAT" 2139959 NIL OREPCAT (NIL T) -9 NIL 2141063 NIL) (-876 2132048 2133004 2134062 "OREPCAT-" 2134067 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-875 2131240 2131518 2131546 "ORDTYPE" 2131855 T ORDTYPE (NIL) -9 NIL 2132018 NIL) (-874 2130541 2130757 2131012 "ORDTYPE-" 2131017 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-873 2129897 2130280 2130438 "ORDSTRCT" 2130443 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-872 2129395 2129765 2129793 "ORDSET" 2129798 T ORDSET (NIL) -9 NIL 2129820 NIL) (-871 2128046 2129017 2129045 "ORDRING" 2129050 T ORDRING (NIL) -9 NIL 2129079 NIL) (-870 2127297 2127862 2127890 "ORDMON" 2127895 T ORDMON (NIL) -9 NIL 2127916 NIL) (-869 2126441 2126606 2126801 "ORDFUNS" 2127146 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-868 2125656 2126171 2126199 "ORDFIN" 2126264 T ORDFIN (NIL) -9 NIL 2126338 NIL) (-867 2124910 2125049 2125235 "ORDCOMP2" 2125516 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-866 2121257 2123496 2123905 "ORDCOMP" 2124534 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-865 2117778 2118748 2119562 "OPTPROB" 2120463 T OPTPROB (NIL) -8 NIL NIL NIL) (-864 2114520 2115219 2115923 "OPTPACK" 2117094 T OPTPACK (NIL) -7 NIL NIL NIL) (-863 2112133 2112959 2112987 "OPTCAT" 2113806 T OPTCAT (NIL) -9 NIL 2114456 NIL) (-862 2111451 2111810 2111915 "OPSIG" 2112048 T OPSIG (NIL) -8 NIL NIL NIL) (-861 2111213 2111258 2111324 "OPQUERY" 2111405 T OPQUERY (NIL) -7 NIL NIL NIL) (-860 2110519 2110799 2110840 "OPERCAT" 2111052 NIL OPERCAT (NIL T) -9 NIL 2111149 NIL) (-859 2110262 2110330 2110447 "OPERCAT-" 2110452 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-858 2107178 2108573 2109077 "OP" 2109791 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2106471 2106598 2106772 "ONECOMP2" 2107050 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-856 2103084 2105268 2105637 "ONECOMP" 2106135 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-855 2102485 2102609 2102739 "OMSERVER" 2102974 T OMSERVER (NIL) -7 NIL NIL NIL) (-854 2099108 2101923 2101963 "OMSAGG" 2102024 NIL OMSAGG (NIL T) -9 NIL 2102089 NIL) (-853 2097683 2097994 2098276 "OMPKG" 2098846 T OMPKG (NIL) -7 NIL NIL NIL) (-852 2096030 2097232 2097401 "OMLO" 2097564 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-851 2094966 2095137 2095357 "OMEXPR" 2095856 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-850 2094051 2094387 2094547 "OMERRK" 2094826 T OMERRK (NIL) -8 NIL NIL NIL) (-849 2093288 2093597 2093733 "OMERR" 2093935 T OMERR (NIL) -8 NIL NIL NIL) (-848 2092679 2092965 2093073 "OMENC" 2093200 T OMENC (NIL) -8 NIL NIL NIL) (-847 2086316 2087759 2088930 "OMDEV" 2091528 T OMDEV (NIL) -8 NIL NIL NIL) (-846 2085349 2085556 2085750 "OMCONN" 2086142 T OMCONN (NIL) -8 NIL NIL NIL) (-845 2084755 2084882 2084910 "OM" 2085209 T OM (NIL) -9 NIL NIL NIL) (-844 2083033 2084225 2084253 "OINTDOM" 2084258 T OINTDOM (NIL) -9 NIL 2084279 NIL) (-843 2080108 2081721 2082058 "OFMONOID" 2082728 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-842 2079342 2080045 2080090 "ODVAR" 2080095 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-841 2076486 2079087 2079242 "ODR" 2079247 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-840 2067898 2076262 2076388 "ODPOL" 2076393 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-839 2061306 2067770 2067875 "ODP" 2067880 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-838 2060048 2060287 2060562 "ODETOOLS" 2061080 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-837 2056991 2057673 2058389 "ODESYS" 2059381 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-836 2051821 2052781 2053806 "ODERTRIC" 2056066 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-835 2051241 2051329 2051523 "ODERED" 2051733 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-834 2048093 2048677 2049354 "ODERAT" 2050664 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-833 2045009 2045517 2046114 "ODEPRRIC" 2047622 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-832 2042904 2043548 2044034 "ODEPROB" 2044543 T ODEPROB (NIL) -8 NIL NIL NIL) (-831 2039370 2039909 2040556 "ODEPRIM" 2042383 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-830 2038613 2038721 2038981 "ODEPAL" 2039262 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-829 2034715 2035566 2036430 "ODEPACK" 2037769 T ODEPACK (NIL) -7 NIL NIL NIL) (-828 2033758 2033883 2034105 "ODEINT" 2034604 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-827 2027823 2029284 2030731 "ODEIFTBL" 2032331 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-826 2023173 2024007 2024959 "ODEEF" 2026982 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-825 2022516 2022611 2022834 "ODECONST" 2023078 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-824 2020579 2021288 2021316 "ODECAT" 2021921 T ODECAT (NIL) -9 NIL 2022452 NIL) (-823 2020211 2020260 2020387 "OCTCT2" 2020530 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-822 2016711 2019916 2020038 "OCT" 2020121 NIL OCT (NIL T) -8 NIL NIL NIL) (-821 2015904 2016504 2016532 "OCAMON" 2016537 T OCAMON (NIL) -9 NIL 2016558 NIL) (-820 2010175 2012947 2012987 "OC" 2014084 NIL OC (NIL T) -9 NIL 2014942 NIL) (-819 2007210 2008150 2009140 "OC-" 2009234 NIL OC- (NIL T T) -8 NIL NIL NIL) (-818 2006630 2007055 2007083 "OASGP" 2007088 T OASGP (NIL) -9 NIL 2007108 NIL) (-817 2005726 2006353 2006381 "OAMONS" 2006421 T OAMONS (NIL) -9 NIL 2006464 NIL) (-816 2004902 2005461 2005489 "OAMON" 2005547 T OAMON (NIL) -9 NIL 2005599 NIL) (-815 2004760 2004793 2004861 "OAMON-" 2004866 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-814 2003541 2004294 2004322 "OAGROUP" 2004469 T OAGROUP (NIL) -9 NIL 2004562 NIL) (-813 2003244 2003332 2003450 "OAGROUP-" 2003455 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-812 2002926 2002982 2003071 "NUMTUBE" 2003188 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 1996445 1998017 1999553 "NUMQUAD" 2001410 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 1992125 1993159 1994194 "NUMODE" 1995430 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1989406 1990346 1990374 "NUMINT" 1991297 T NUMINT (NIL) -9 NIL 1992061 NIL) (-808 1988318 1988551 1988769 "NUMFMT" 1989208 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1974501 1977622 1980154 "NUMERIC" 1985825 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1968319 1973949 1974044 "NTSCAT" 1974049 NIL NTSCAT (NIL T T T T) -9 NIL 1974088 NIL) (-805 1967499 1967678 1967871 "NTPOLFN" 1968158 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1967125 1967188 1967297 "NSUP2" 1967436 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1953907 1963950 1964762 "NSUP" 1966346 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1942750 1953681 1953814 "NSMP" 1953819 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1941158 1941483 1941840 "NREP" 1942438 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1939737 1940001 1940359 "NPCOEF" 1940901 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1938785 1938918 1939134 "NORMRETR" 1939618 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1936796 1937116 1937525 "NORMPK" 1938493 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1936475 1936509 1936633 "NORMMA" 1936762 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1936258 1936293 1936362 "NONE1" 1936439 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1936022 1936215 1936244 "NONE" 1936249 T NONE (NIL) -8 NIL NIL NIL) (-794 1935513 1935581 1935760 "NODE1" 1935954 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1933574 1934636 1934891 "NNI" 1935238 T NNI (NIL) -8 NIL NIL 1935473) (-792 1931970 1932307 1932671 "NLINSOL" 1933242 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1928151 1929206 1930105 "NIPROB" 1931091 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1926890 1927142 1927444 "NFINTBAS" 1927913 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1925974 1926540 1926581 "NETCLT" 1926753 NIL NETCLT (NIL T) -9 NIL 1926835 NIL) (-788 1924646 1924913 1925194 "NCODIV" 1925742 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1924402 1924445 1924520 "NCNTFRAC" 1924603 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1922558 1922946 1923366 "NCEP" 1924027 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1921221 1922168 1922196 "NASRING" 1922306 T NASRING (NIL) -9 NIL 1922386 NIL) (-784 1921004 1921060 1921154 "NASRING-" 1921159 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1919971 1920622 1920650 "NARNG" 1920767 T NARNG (NIL) -9 NIL 1920858 NIL) (-782 1919645 1919730 1919864 "NARNG-" 1919869 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1918482 1918731 1918966 "NAGSP" 1919430 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1909526 1911438 1913111 "NAGS" 1916829 T NAGS (NIL) -7 NIL NIL NIL) (-779 1908050 1908382 1908713 "NAGF07" 1909215 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1902522 1903879 1905186 "NAGF04" 1906763 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1895394 1897104 1898737 "NAGF02" 1900909 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1890558 1891718 1892835 "NAGF01" 1894297 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1884138 1885752 1887337 "NAGE04" 1888993 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1875199 1877428 1879558 "NAGE02" 1882028 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1871092 1872099 1873063 "NAGE01" 1874255 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1868869 1869421 1869979 "NAGD03" 1870554 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1860565 1862547 1864501 "NAGD02" 1866935 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1854304 1855801 1857241 "NAGD01" 1859145 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1850441 1851335 1852172 "NAGC06" 1853487 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1848888 1849238 1849594 "NAGC05" 1850105 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1848252 1848383 1848527 "NAGC02" 1848764 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1847053 1847780 1847820 "NAALG" 1847899 NIL NAALG (NIL T) -9 NIL 1847960 NIL) (-765 1846882 1846917 1847007 "NAALG-" 1847012 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1840754 1841940 1843127 "MULTSQFR" 1845778 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1840061 1840148 1840332 "MULTFACT" 1840666 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1832206 1836644 1836697 "MTSCAT" 1837767 NIL MTSCAT (NIL T T) -9 NIL 1838283 NIL) (-761 1831912 1831972 1832064 "MTHING" 1832146 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1831698 1831737 1831797 "MSYSCMD" 1831872 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1828554 1831259 1831300 "MSETAGG" 1831305 NIL MSETAGG (NIL T) -9 NIL 1831339 NIL) (-758 1824382 1827309 1827629 "MSET" 1828267 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1819984 1821761 1822506 "MRING" 1823682 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1819544 1819617 1819748 "MRF2" 1819911 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1819156 1819197 1819341 "MRATFAC" 1819503 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1816726 1817063 1817494 "MPRFF" 1818861 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1810060 1816580 1816677 "MPOLY" 1816682 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1809544 1809585 1809793 "MPCPF" 1810019 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1809052 1809101 1809285 "MPC3" 1809495 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1808235 1808328 1808549 "MPC2" 1808967 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1806512 1806873 1807263 "MONOTOOL" 1807895 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1805657 1806040 1806068 "MONOID" 1806287 T MONOID (NIL) -9 NIL 1806434 NIL) (-747 1805173 1805322 1805503 "MONOID-" 1805508 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1794146 1800993 1801052 "MONOGEN" 1801726 NIL MONOGEN (NIL T T) -9 NIL 1802182 NIL) (-745 1791196 1792099 1793099 "MONOGEN-" 1793218 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1789913 1790461 1790489 "MONADWU" 1790881 T MONADWU (NIL) -9 NIL 1791119 NIL) (-743 1789243 1789444 1789692 "MONADWU-" 1789697 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1788528 1788832 1788860 "MONAD" 1789067 T MONAD (NIL) -9 NIL 1789179 NIL) (-741 1788195 1788291 1788423 "MONAD-" 1788428 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1786334 1787108 1787387 "MOEBIUS" 1787948 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1785502 1786002 1786042 "MODULE" 1786047 NIL MODULE (NIL T) -9 NIL 1786086 NIL) (-738 1785040 1785166 1785356 "MODULE-" 1785361 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1782570 1783404 1783731 "MODRING" 1784864 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1779299 1780675 1781196 "MODOP" 1782099 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1777785 1778366 1778643 "MODMONOM" 1779162 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1766545 1776076 1776490 "MODMON" 1777422 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1763378 1765389 1765665 "MODFIELD" 1766420 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1762289 1762659 1762849 "MMLFORM" 1763208 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1761809 1761858 1762037 "MMAP" 1762240 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1759702 1760641 1760682 "MLO" 1761105 NIL MLO (NIL T) -9 NIL 1761347 NIL) (-729 1757050 1757584 1758186 "MLIFT" 1759183 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1756429 1756525 1756679 "MKUCFUNC" 1756961 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1756022 1756098 1756221 "MKRECORD" 1756352 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1755045 1755231 1755459 "MKFUNC" 1755833 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1754421 1754537 1754693 "MKFLCFN" 1754928 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1753686 1753800 1753985 "MKBCFUNC" 1754314 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1749683 1753240 1753376 "MINT" 1753570 T MINT (NIL) -8 NIL NIL NIL) (-722 1748465 1748738 1749015 "MHROWRED" 1749438 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1743216 1747000 1747405 "MFLOAT" 1748080 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1742561 1742649 1742820 "MFINFACT" 1743128 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1738840 1739724 1740608 "MESH" 1741697 T MESH (NIL) -7 NIL NIL NIL) (-718 1737194 1737542 1737895 "MDDFACT" 1738527 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1733841 1736325 1736366 "MDAGG" 1736621 NIL MDAGG (NIL T) -9 NIL 1736764 NIL) (-716 1721564 1733134 1733341 "MCMPLX" 1733654 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1720683 1720847 1721048 "MCDEN" 1721413 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1718531 1718843 1719223 "MCALCFN" 1720413 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1717408 1717696 1717929 "MAYBE" 1718337 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1714966 1715543 1716105 "MATSTOR" 1716879 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1710502 1714338 1714586 "MATRIX" 1714751 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1706202 1706975 1707711 "MATLIN" 1709859 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1704778 1704949 1705282 "MATCAT2" 1706037 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1694231 1697835 1697912 "MATCAT" 1702944 NIL MATCAT (NIL T T T) -9 NIL 1704416 NIL) (-707 1690184 1691494 1692907 "MATCAT-" 1692912 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1688260 1688620 1689004 "MAPPKG3" 1689859 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1687217 1687414 1687636 "MAPPKG2" 1688084 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1685674 1686000 1686327 "MAPPKG1" 1686923 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1684675 1685080 1685257 "MAPPAST" 1685517 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1684280 1684344 1684467 "MAPHACK3" 1684611 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1683860 1683933 1684047 "MAPHACK2" 1684212 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1683286 1683401 1683543 "MAPHACK1" 1683751 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1681209 1681986 1682290 "MAGMA" 1683014 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1680628 1680933 1681024 "MACROAST" 1681138 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1676985 1678867 1679328 "M3D" 1680200 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1670457 1675296 1675337 "LZSTAGG" 1676119 NIL LZSTAGG (NIL T) -9 NIL 1676414 NIL) (-695 1666139 1667588 1669045 "LZSTAGG-" 1669050 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1663052 1664030 1664517 "LWORD" 1665684 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1662574 1662856 1662931 "LSTAST" 1662997 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1654616 1662345 1662479 "LSQM" 1662484 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1653834 1653979 1654207 "LSPP" 1654471 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1650571 1651287 1652017 "LSMP1" 1653136 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1648353 1648684 1649140 "LSMP" 1650260 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1641481 1647443 1647484 "LSAGG" 1647546 NIL LSAGG (NIL T) -9 NIL 1647624 NIL) (-687 1637990 1639100 1640313 "LSAGG-" 1640318 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1635285 1637134 1637383 "LPOLY" 1637785 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1634861 1634952 1635075 "LPEFRAC" 1635194 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1634544 1634623 1634651 "LOGIC" 1634762 T LOGIC (NIL) -9 NIL 1634844 NIL) (-683 1634400 1634429 1634500 "LOGIC-" 1634505 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1633575 1633733 1633926 "LODOOPS" 1634256 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1632099 1632348 1632701 "LODOF" 1633322 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1627975 1630734 1630775 "LODOCAT" 1631213 NIL LODOCAT (NIL T) -9 NIL 1631424 NIL) (-679 1627690 1627766 1627893 "LODOCAT-" 1627898 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1624676 1627531 1627649 "LODO2" 1627654 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1621783 1624613 1624658 "LODO1" 1624663 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1618878 1621699 1621765 "LODO" 1621770 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1617747 1617924 1618229 "LODEEF" 1618701 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1615733 1616841 1617094 "LO" 1617579 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1610816 1613899 1613940 "LNAGG" 1614802 NIL LNAGG (NIL T) -9 NIL 1615237 NIL) (-672 1609909 1610177 1610519 "LNAGG-" 1610524 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1605889 1606834 1607473 "LMOPS" 1609324 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1605188 1605666 1605707 "LMODULE" 1605712 NIL LMODULE (NIL T) -9 NIL 1605738 NIL) (-669 1602257 1604833 1604956 "LMDICT" 1605098 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1601833 1602047 1602088 "LLINSET" 1602149 NIL LLINSET (NIL T) -9 NIL 1602193 NIL) (-667 1601478 1601741 1601801 "LITERAL" 1601806 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1600997 1601077 1601216 "LIST3" 1601398 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1599095 1599443 1599842 "LIST2MAP" 1600644 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1598084 1598280 1598508 "LIST2" 1598913 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1590538 1597018 1597322 "LIST" 1597813 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1590121 1590357 1590398 "LINSET" 1590403 NIL LINSET (NIL T) -9 NIL 1590437 NIL) (-661 1588935 1589629 1589796 "LINFORM" 1590006 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1587234 1587962 1588003 "LINEXP" 1588493 NIL LINEXP (NIL T) -9 NIL 1588766 NIL) (-659 1585810 1586714 1586895 "LINELT" 1587105 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1584367 1584647 1584958 "LINDEP" 1585562 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1583503 1584099 1584209 "LINBASIS" 1584297 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1580240 1580989 1581766 "LIMITRF" 1582758 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1578525 1578839 1579248 "LIMITPS" 1579935 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1577353 1577928 1577968 "LIECAT" 1578108 NIL LIECAT (NIL T) -9 NIL 1578259 NIL) (-653 1577188 1577221 1577309 "LIECAT-" 1577314 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1571208 1576699 1576927 "LIE" 1577009 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1563507 1570748 1570904 "LIB" 1571072 T LIB (NIL) -8 NIL NIL NIL) (-650 1559076 1560025 1560960 "LGROBP" 1562624 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1557700 1558608 1558636 "LFCAT" 1558843 T LFCAT (NIL) -9 NIL 1558982 NIL) (-648 1555638 1555972 1556322 "LF" 1557421 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1552498 1553170 1553858 "LEXTRIPK" 1555002 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1549086 1550068 1550571 "LEXP" 1552078 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1548502 1548807 1548899 "LETAST" 1549014 T LETAST (NIL) -8 NIL NIL NIL) (-644 1546888 1547213 1547614 "LEADCDET" 1548184 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1546066 1546152 1546381 "LAZM3PK" 1546809 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1540591 1544143 1544681 "LAUPOL" 1545578 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1540164 1540214 1540375 "LAPLACE" 1540541 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1539012 1539728 1539769 "LALG" 1539831 NIL LALG (NIL T) -9 NIL 1539890 NIL) (-639 1538708 1538785 1538921 "LALG-" 1538926 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1536445 1537809 1538060 "LA" 1538541 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1536274 1536304 1536345 "KVTFROM" 1536407 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1535031 1535641 1535826 "KTVLOGIC" 1536109 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1534860 1534890 1534931 "KRCFROM" 1534993 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1533752 1533951 1534250 "KOVACIC" 1534660 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1533581 1533611 1533652 "KONVERT" 1533714 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1533410 1533440 1533481 "KOERCE" 1533543 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1532894 1532987 1533119 "KERNEL2" 1533324 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1530581 1531487 1531864 "KERNEL" 1532550 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1524163 1529058 1529112 "KDAGG" 1529489 NIL KDAGG (NIL T T) -9 NIL 1529695 NIL) (-628 1523674 1523816 1524021 "KDAGG-" 1524026 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1516488 1523335 1523490 "KAFILE" 1523552 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1516092 1516377 1516440 "JVMOP" 1516445 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1514828 1515332 1515581 "JVMMDACC" 1515863 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1513764 1514218 1514423 "JVMFDACC" 1514643 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1512345 1512840 1513140 "JVMCSTTG" 1513484 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1511481 1511885 1512046 "JVMCFACC" 1512204 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1511159 1511398 1511447 "JVMBCODE" 1511452 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1505178 1510670 1510898 "JORDAN" 1510980 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1504491 1504827 1504948 "JOINAST" 1505077 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1500637 1502668 1502722 "IXAGG" 1503651 NIL IXAGG (NIL T T) -9 NIL 1504110 NIL) (-617 1499490 1499862 1500281 "IXAGG-" 1500286 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1494693 1499412 1499471 "IVECTOR" 1499476 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1493418 1493696 1493962 "ITUPLE" 1494460 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1491890 1492097 1492392 "ITRIGMNP" 1493240 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1490617 1490839 1491122 "ITFUN3" 1491666 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1490215 1490278 1490401 "ITFUN2" 1490540 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1489320 1489695 1489869 "ITFORM" 1490061 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1487089 1488340 1488618 "ITAYLOR" 1489075 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1475493 1481226 1482389 "ISUPS" 1485959 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1474585 1474737 1474973 "ISUMP" 1475340 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1469549 1474530 1474571 "ISTRING" 1474576 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1468965 1469270 1469362 "ISAST" 1469477 T ISAST (NIL) -8 NIL NIL NIL) (-605 1468163 1468256 1468472 "IRURPK" 1468879 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1467075 1467300 1467540 "IRSN" 1467943 T IRSN (NIL) -7 NIL NIL NIL) (-603 1465120 1465501 1465930 "IRRF2F" 1466713 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1464861 1464905 1464981 "IRREDFFX" 1465076 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1463434 1463735 1464034 "IROOT" 1464594 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1462573 1462927 1463078 "IRFORM" 1463303 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1461655 1461786 1462000 "IR2F" 1462456 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1459244 1459763 1460329 "IR2" 1461133 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1455684 1456928 1457620 "IR" 1458584 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1455469 1455509 1455569 "IPRNTPK" 1455644 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1451443 1455358 1455427 "IPF" 1455432 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1449471 1451368 1451425 "IPADIC" 1451430 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1448729 1449031 1449161 "IP4ADDR" 1449361 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1448067 1448358 1448490 "IOMODE" 1448617 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1447038 1447664 1447791 "IOBFILE" 1447960 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1446448 1446942 1446970 "IOBCON" 1446975 T IOBCON (NIL) -9 NIL 1446996 NIL) (-589 1445953 1446017 1446200 "INVLAPLA" 1446384 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1435523 1437955 1440341 "INTTR" 1443617 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1431816 1432600 1433465 "INTTOOLS" 1434708 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1431396 1431493 1431610 "INTSLPE" 1431719 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1428863 1431319 1431378 "INTRVL" 1431383 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1426441 1426977 1427552 "INTRF" 1428348 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1425834 1425949 1426091 "INTRET" 1426339 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1423807 1424220 1424690 "INTRAT" 1425442 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1421052 1421653 1422272 "INTPM" 1423292 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1417769 1418396 1419134 "INTPAF" 1420438 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1412870 1413910 1414961 "INTPACK" 1416738 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1412116 1412274 1412482 "INTHERTR" 1412712 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1411549 1411635 1411823 "INTHERAL" 1412030 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1409317 1409838 1410295 "INTHEORY" 1411112 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1400649 1402344 1404116 "INTG0" 1407669 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1381174 1386012 1390822 "INTFTBL" 1395859 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1380399 1380561 1380734 "INTFACT" 1381033 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1377796 1378272 1378829 "INTEF" 1379953 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1375993 1376888 1376916 "INTDOM" 1377217 T INTDOM (NIL) -9 NIL 1377424 NIL) (-570 1375332 1375536 1375778 "INTDOM-" 1375783 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1371200 1373621 1373675 "INTCAT" 1374474 NIL INTCAT (NIL T) -9 NIL 1374795 NIL) (-568 1370654 1370775 1370903 "INTBIT" 1371092 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1369335 1369507 1369814 "INTALG" 1370499 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1368812 1368908 1369065 "INTAF" 1369239 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1361893 1368622 1368762 "INTABL" 1368767 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1361134 1361696 1361761 "INT8" 1361795 T INT8 (NIL) -8 NIL NIL 1361840) (-563 1360374 1360936 1361001 "INT64" 1361035 T INT64 (NIL) -8 NIL NIL 1361080) (-562 1359614 1360176 1360241 "INT32" 1360275 T INT32 (NIL) -8 NIL NIL 1360320) (-561 1358854 1359416 1359481 "INT16" 1359515 T INT16 (NIL) -8 NIL NIL 1359560) (-560 1355058 1358651 1358760 "INT" 1358765 T INT (NIL) -8 NIL NIL NIL) (-559 1349167 1352606 1352634 "INS" 1353568 T INS (NIL) -9 NIL 1354233 NIL) (-558 1346324 1347244 1348185 "INS-" 1348258 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1345081 1345326 1345624 "INPSIGN" 1346077 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1344175 1344316 1344513 "INPRODPF" 1344961 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1343045 1343186 1343423 "INPRODFF" 1344055 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1342033 1342197 1342457 "INNMFACT" 1342881 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1341212 1341327 1341515 "INMODGCD" 1341932 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1339696 1339965 1340289 "INFSP" 1340957 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1338856 1338997 1339180 "INFPROD0" 1339576 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1338454 1338526 1338624 "INFORM1" 1338791 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1335021 1336519 1337034 "INFORM" 1337947 T INFORM (NIL) -8 NIL NIL NIL) (-548 1334526 1334633 1334747 "INFINITY" 1334927 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1333600 1334246 1334347 "INETCLTS" 1334445 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1332198 1332466 1332787 "INEP" 1333348 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1331228 1332095 1332160 "INDE" 1332165 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1330780 1330860 1330977 "INCRMAPS" 1331155 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1329502 1330049 1330255 "INBFILE" 1330594 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1324682 1325738 1326682 "INBFF" 1328590 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1323536 1323859 1323887 "INBCON" 1324400 T INBCON (NIL) -9 NIL 1324666 NIL) (-540 1322746 1323011 1323287 "INBCON-" 1323292 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1322165 1322470 1322561 "INAST" 1322675 T INAST (NIL) -8 NIL NIL NIL) (-538 1321532 1321844 1321950 "IMPTAST" 1322079 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1317567 1321376 1321480 "IMATRIX" 1321485 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1316259 1316398 1316714 "IMATQF" 1317423 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1314439 1314706 1315043 "IMATLIN" 1316015 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1308354 1314363 1314421 "ILIST" 1314426 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1306134 1308214 1308327 "IIARRAY2" 1308332 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1300955 1306045 1306109 "IFF" 1306114 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1300236 1300572 1300688 "IFAST" 1300859 T IFAST (NIL) -8 NIL NIL NIL) (-530 1294862 1299528 1299716 "IFARRAY" 1300093 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1293900 1294766 1294839 "IFAMON" 1294844 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1293472 1293549 1293603 "IEVALAB" 1293810 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1293135 1293215 1293375 "IEVALAB-" 1293380 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1292168 1293024 1293099 "IDPOAMS" 1293104 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1291270 1292057 1292132 "IDPOAM" 1292137 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1290651 1291185 1291247 "IDPO" 1291252 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1289131 1289658 1289710 "IDPC" 1290222 NIL IDPC (NIL T T) -9 NIL 1290503 NIL) (-522 1288463 1289023 1289096 "IDPAM" 1289101 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1287678 1288355 1288428 "IDPAG" 1288433 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1287222 1287484 1287574 "IDENT" 1287608 T IDENT (NIL) -8 NIL NIL NIL) (-519 1283441 1284325 1285220 "IDECOMP" 1286379 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1276076 1277364 1278411 "IDEAL" 1282477 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1275218 1275348 1275548 "ICDEN" 1275960 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1274193 1274698 1274845 "ICARD" 1275091 T ICARD (NIL) -8 NIL NIL NIL) (-515 1272223 1272566 1272971 "IBPTOOLS" 1273870 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1267452 1271843 1271956 "IBITS" 1272142 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1264127 1264751 1265446 "IBATOOL" 1266869 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1261888 1262368 1262901 "IBACHIN" 1263662 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1259592 1261734 1261837 "IARRAY2" 1261842 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1255419 1259518 1259575 "IARRAY1" 1259580 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1248436 1253831 1254312 "IAN" 1254958 T IAN (NIL) -8 NIL NIL NIL) (-508 1247941 1248004 1248177 "IALGFACT" 1248373 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1247433 1247582 1247610 "HYPCAT" 1247817 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1246935 1247088 1247274 "HYPCAT-" 1247279 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1246482 1246730 1246813 "HOSTNAME" 1246872 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1246315 1246364 1246405 "HOMOTOP" 1246410 NIL HOMOTOP (NIL T) -9 NIL 1246443 NIL) (-503 1242859 1244247 1244288 "HOAGG" 1245269 NIL HOAGG (NIL T) -9 NIL 1245998 NIL) (-502 1241375 1241852 1242378 "HOAGG-" 1242383 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1234432 1240968 1241118 "HEXADEC" 1241245 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1233144 1233402 1233665 "HEUGCD" 1234209 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1232076 1232981 1233111 "HELLFDIV" 1233116 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1230198 1231851 1231940 "HEAP" 1232019 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1229395 1229750 1229884 "HEADAST" 1230084 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1222847 1229310 1229372 "HDP" 1229377 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1215866 1222482 1222634 "HDMP" 1222748 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1215172 1215330 1215494 "HB" 1215722 T HB (NIL) -7 NIL NIL NIL) (-493 1208296 1215018 1215122 "HASHTBL" 1215127 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1207712 1208017 1208109 "HASAST" 1208224 T HASAST (NIL) -8 NIL NIL NIL) (-491 1205125 1207334 1207516 "HACKPI" 1207550 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1200411 1204978 1205091 "GTSET" 1205096 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1193564 1200289 1200387 "GSTBL" 1200392 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1185327 1192729 1192985 "GSERIES" 1193364 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1184358 1184871 1184899 "GROUP" 1185102 T GROUP (NIL) -9 NIL 1185236 NIL) (-486 1183682 1183883 1184134 "GROUP-" 1184139 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1182031 1182370 1182757 "GROEBSOL" 1183359 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1180859 1181219 1181270 "GRMOD" 1181799 NIL GRMOD (NIL T T) -9 NIL 1181967 NIL) (-483 1180615 1180663 1180791 "GRMOD-" 1180796 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1175755 1176969 1177969 "GRIMAGE" 1179635 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1174149 1174482 1174806 "GRDEF" 1175451 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1173581 1173709 1173850 "GRAY" 1174028 T GRAY (NIL) -7 NIL NIL NIL) (-479 1172658 1173160 1173211 "GRALG" 1173364 NIL GRALG (NIL T T) -9 NIL 1173457 NIL) (-478 1172295 1172392 1172555 "GRALG-" 1172560 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1168890 1171878 1172057 "GPOLSET" 1172201 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1168238 1168301 1168559 "GOSPER" 1168827 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1163808 1164676 1165202 "GMODPOL" 1167937 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1162795 1162997 1163235 "GHENSEL" 1163620 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1156867 1157794 1158814 "GENUPS" 1161879 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1156558 1156615 1156704 "GENUFACT" 1156810 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1155958 1156047 1156212 "GENPGCD" 1156476 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1155426 1155467 1155680 "GENMFACT" 1155917 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1153963 1154249 1154556 "GENEEZ" 1155169 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1147141 1153574 1153736 "GDMP" 1153886 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1135879 1140912 1142018 "GCNAALG" 1146124 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1134006 1135054 1135082 "GCDDOM" 1135337 T GCDDOM (NIL) -9 NIL 1135494 NIL) (-465 1133446 1133603 1133818 "GCDDOM-" 1133823 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1121918 1124392 1126784 "GBINTERN" 1131137 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1119719 1120047 1120468 "GBF" 1121593 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1118476 1118665 1118932 "GBEUCLID" 1119535 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1117126 1117333 1117637 "GB" 1118255 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1116457 1116600 1116749 "GAUSSFAC" 1116997 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1114778 1115126 1115440 "GALUTIL" 1116176 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1113038 1113360 1113684 "GALPOLYU" 1114505 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1110337 1110693 1111100 "GALFACTU" 1112735 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1101951 1103642 1105250 "GALFACT" 1108769 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1099237 1099997 1100025 "FVFUN" 1101181 T FVFUN (NIL) -9 NIL 1101901 NIL) (-454 1098467 1098685 1098713 "FVC" 1099004 T FVC (NIL) -9 NIL 1099187 NIL) (-453 1098068 1098292 1098360 "FUNDESC" 1098419 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1097641 1097865 1097946 "FUNCTION" 1098020 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1096318 1096942 1097145 "FTEM" 1097458 T FTEM (NIL) -8 NIL NIL NIL) (-450 1093948 1094640 1095106 "FT" 1095872 T FT (NIL) -8 NIL NIL NIL) (-449 1092217 1092528 1092925 "FSUPFACT" 1093639 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1090536 1090903 1091235 "FST" 1091905 T FST (NIL) -8 NIL NIL NIL) (-447 1089717 1089841 1090029 "FSRED" 1090418 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1088406 1088672 1089019 "FSPRMELT" 1089432 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1085616 1086150 1086636 "FSPECF" 1087969 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1085138 1085198 1085368 "FSINT" 1085557 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1083274 1084131 1084434 "FSERIES" 1084917 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1082298 1082432 1082656 "FSCINT" 1083154 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1081322 1081483 1081710 "FSAGG2" 1082151 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1077297 1080266 1080307 "FSAGG" 1080677 NIL FSAGG (NIL T) -9 NIL 1080936 NIL) (-439 1074897 1075660 1076456 "FSAGG-" 1076551 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1072557 1072855 1073403 "FS2UPS" 1074615 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1071423 1071606 1071908 "FS2EXPXP" 1072382 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1071051 1071100 1071229 "FS2" 1071374 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1051289 1060825 1060866 "FS" 1064750 NIL FS (NIL T) -9 NIL 1067039 NIL) (-434 1039350 1042925 1046982 "FS-" 1047282 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1038764 1038891 1039043 "FRUTIL" 1039230 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1033275 1036453 1036493 "FRNAALG" 1037813 NIL FRNAALG (NIL T) -9 NIL 1038411 NIL) (-431 1028756 1030024 1031299 "FRNAALG-" 1032049 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1028388 1028437 1028564 "FRNAAF2" 1028707 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1026675 1027237 1027533 "FRMOD" 1028200 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1025860 1025953 1026244 "FRIDEAL2" 1026582 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1023465 1024235 1024553 "FRIDEAL" 1025651 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1022556 1023012 1023053 "FRETRCT" 1023058 NIL FRETRCT (NIL T) -9 NIL 1023234 NIL) (-425 1021614 1021899 1022250 "FRETRCT-" 1022255 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1018435 1019898 1019957 "FRAMALG" 1020839 NIL FRAMALG (NIL T T) -9 NIL 1021131 NIL) (-423 1016473 1017024 1017654 "FRAMALG-" 1017877 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1016103 1016166 1016273 "FRAC2" 1016410 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1009096 1015576 1015853 "FRAC" 1015858 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1008726 1008789 1008896 "FR2" 1009033 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 999643 1004221 1005579 "FR" 1007400 NIL FR (NIL T) -8 NIL NIL NIL) (-418 993562 997022 997050 "FPS" 998169 T FPS (NIL) -9 NIL 998726 NIL) (-417 992987 993120 993284 "FPS-" 993430 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 989953 991944 991972 "FPC" 992197 T FPC (NIL) -9 NIL 992339 NIL) (-415 989734 989786 989883 "FPC-" 989888 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 988492 989222 989263 "FPATMAB" 989268 NIL FPATMAB (NIL T) -9 NIL 989420 NIL) (-413 986635 987234 987581 "FPARFRAC" 988208 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 981927 982527 983209 "FORTRAN" 986067 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 979501 980165 980193 "FORTFN" 981253 T FORTFN (NIL) -9 NIL 981877 NIL) (-410 979253 979315 979343 "FORTCAT" 979402 T FORTCAT (NIL) -9 NIL 979464 NIL) (-409 976939 977469 978008 "FORT" 978734 T FORT (NIL) -7 NIL NIL NIL) (-408 976721 976757 976826 "FORMULA1" 976903 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 974725 975337 975727 "FORMULA" 976351 T FORMULA (NIL) -8 NIL NIL NIL) (-406 974242 974300 974473 "FORDER" 974667 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 973302 973502 973695 "FOP" 974069 T FOP (NIL) -7 NIL NIL NIL) (-404 971715 972582 972756 "FNLA" 973184 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 970334 970845 970873 "FNCAT" 971333 T FNCAT (NIL) -9 NIL 971593 NIL) (-402 969777 970293 970321 "FNAME" 970326 T FNAME (NIL) -8 NIL NIL NIL) (-401 968103 969276 969304 "FMTC" 969309 T FMTC (NIL) -9 NIL 969345 NIL) (-400 966652 968039 968085 "FMONOID" 968090 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 963241 964607 964648 "FMONCAT" 965865 NIL FMONCAT (NIL T) -9 NIL 966470 NIL) (-398 960563 961311 961339 "FMFUN" 962483 T FMFUN (NIL) -9 NIL 963191 NIL) (-397 957436 958488 958542 "FMCAT" 959737 NIL FMCAT (NIL T T) -9 NIL 960232 NIL) (-396 956669 956886 956914 "FMC" 957204 T FMC (NIL) -9 NIL 957386 NIL) (-395 955337 956435 956535 "FM1" 956614 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 954355 955079 955228 "FM" 955233 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 952093 952545 953039 "FLOATRP" 953906 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 949495 950031 950609 "FLOATCP" 951560 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 942158 947224 947845 "FLOAT" 948894 T FLOAT (NIL) -8 NIL NIL NIL) (-390 940676 941750 941791 "FLINEXP" 941796 NIL FLINEXP (NIL T) -9 NIL 941889 NIL) (-389 939806 940065 940393 "FLINEXP-" 940398 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 938864 939026 939250 "FLASORT" 939658 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 935782 936834 936886 "FLALG" 938113 NIL FLALG (NIL T T) -9 NIL 938580 NIL) (-386 934806 934967 935194 "FLAGG2" 935635 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 928175 932215 932256 "FLAGG" 933518 NIL FLAGG (NIL T) -9 NIL 934170 NIL) (-384 926829 927240 927730 "FLAGG-" 927735 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 923467 924674 924733 "FINRALG" 925861 NIL FINRALG (NIL T T) -9 NIL 926369 NIL) (-382 922591 922856 923195 "FINRALG-" 923200 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 921897 922196 922224 "FINITE" 922420 T FINITE (NIL) -9 NIL 922527 NIL) (-380 913848 916427 916467 "FINAALG" 920134 NIL FINAALG (NIL T) -9 NIL 921587 NIL) (-379 908964 910230 911374 "FINAALG-" 912753 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 907524 907946 908000 "FILECAT" 908684 NIL FILECAT (NIL T T) -9 NIL 908900 NIL) (-377 906802 907279 907382 "FILE" 907454 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 904205 906032 906060 "FIELD" 906100 T FIELD (NIL) -9 NIL 906180 NIL) (-375 902747 903210 903721 "FIELD-" 903726 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 900430 901382 901729 "FGROUP" 902433 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 899502 899684 899904 "FGLMICPK" 900262 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 894757 899427 899484 "FFX" 899489 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 894352 894419 894554 "FFSLPE" 894690 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 893850 893892 894101 "FFPOLY2" 894310 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 889726 890622 891418 "FFPOLY" 893086 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 884995 889645 889708 "FFP" 889713 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 879526 884338 884528 "FFNBX" 884849 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 873859 878661 878919 "FFNBP" 879380 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 867897 873143 873354 "FFNB" 873692 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 866717 866927 867242 "FFINTBAS" 867694 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 862310 864964 864992 "FFIELDC" 865612 T FFIELDC (NIL) -9 NIL 865988 NIL) (-362 860930 861371 861854 "FFIELDC-" 861859 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 860487 860545 860669 "FFHOM" 860872 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 858146 858669 859186 "FFF" 860002 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 853181 857888 857989 "FFCGX" 858089 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 848220 852913 853020 "FFCGP" 853124 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 842820 847947 848055 "FFCG" 848156 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 842225 842274 842509 "FFCAT2" 842771 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 820907 831957 832043 "FFCAT" 837208 NIL FFCAT (NIL T T T) -9 NIL 838659 NIL) (-354 815918 817152 818466 "FFCAT-" 819696 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 810739 815829 815893 "FF" 815898 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 799392 803711 804931 "FEXPR" 809591 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 798320 798789 798830 "FEVALAB" 798914 NIL FEVALAB (NIL T) -9 NIL 799175 NIL) (-350 797437 797689 798027 "FEVALAB-" 798032 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 794299 795184 795299 "FDIVCAT" 796867 NIL FDIVCAT (NIL T T T T) -9 NIL 797304 NIL) (-348 794055 794088 794258 "FDIVCAT-" 794263 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 793269 793362 793639 "FDIV2" 793962 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 791679 792652 792855 "FDIV" 793168 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 790587 790974 791176 "FCTRDATA" 791497 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 789243 789532 789821 "FCPAK1" 790318 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 788246 788743 788884 "FCOMP" 789134 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 771560 775396 778934 "FC" 784728 T FC (NIL) -8 NIL NIL NIL) (-341 763269 767881 767921 "FAXF" 769723 NIL FAXF (NIL T) -9 NIL 770415 NIL) (-340 760410 761217 762035 "FAXF-" 762500 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 755093 759786 759962 "FARRAY" 760267 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 749658 752040 752093 "FAMR" 753116 NIL FAMR (NIL T T) -9 NIL 753576 NIL) (-337 748482 748850 749285 "FAMR-" 749290 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 747509 748404 748457 "FAMONOID" 748462 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 745139 745991 746044 "FAMONC" 746985 NIL FAMONC (NIL T T) -9 NIL 747371 NIL) (-334 743613 744893 745030 "FAGROUP" 745035 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 741366 741727 742130 "FACUTIL" 743294 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 740453 740650 740872 "FACTFUNC" 741176 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 732194 739756 739955 "EXPUPXS" 740309 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 729647 730217 730803 "EXPRTUBE" 731628 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 725858 726510 727240 "EXPRODE" 728986 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 720292 720999 721805 "EXPR2UPS" 725156 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 719918 719981 720090 "EXPR2" 720229 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 704226 718567 718996 "EXPR" 719522 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 694564 703377 703668 "EXPEXPAN" 704062 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 693984 694288 694379 "EXITAST" 694493 T EXITAST (NIL) -8 NIL NIL NIL) (-323 693748 693941 693970 "EXIT" 693975 T EXIT (NIL) -8 NIL NIL NIL) (-322 693369 693437 693550 "EVALCYC" 693680 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 692886 693028 693069 "EVALAB" 693239 NIL EVALAB (NIL T) -9 NIL 693343 NIL) (-320 692343 692489 692710 "EVALAB-" 692715 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 689458 690999 691027 "EUCDOM" 691582 T EUCDOM (NIL) -9 NIL 691932 NIL) (-318 687818 688319 688902 "EUCDOM-" 688907 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 687444 687507 687616 "ESTOOLS2" 687755 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 687189 687237 687317 "ESTOOLS1" 687396 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 674506 677487 680237 "ESTOOLS" 684459 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 674245 674283 674365 "ESCONT1" 674468 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 670553 671380 672160 "ESCONT" 673485 T ESCONT (NIL) -7 NIL NIL NIL) (-312 670222 670278 670378 "ES2" 670497 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 669846 669910 670019 "ES1" 670158 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 663547 665477 665505 "ES" 668273 T ES (NIL) -9 NIL 669683 NIL) (-309 658224 659781 661598 "ES-" 661762 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 657416 657569 657745 "ERROR" 658068 T ERROR (NIL) -7 NIL NIL NIL) (-307 650546 657275 657366 "EQTBL" 657371 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 650172 650235 650344 "EQ2" 650483 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 642431 645486 646935 "EQ" 648756 NIL -3350 (NIL T) -8 NIL NIL NIL) (-304 637673 638769 639862 "EP" 641370 NIL EP (NIL T) -7 NIL NIL NIL) (-303 636213 636564 636870 "ENV" 637387 T ENV (NIL) -8 NIL NIL NIL) (-302 635173 635847 635875 "ENTIRER" 635880 T ENTIRER (NIL) -9 NIL 635926 NIL) (-301 631592 633355 633716 "EMR" 634981 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 630696 630907 630961 "ELTAGG" 631341 NIL ELTAGG (NIL T T) -9 NIL 631552 NIL) (-299 630403 630477 630618 "ELTAGG-" 630623 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 630161 630196 630250 "ELTAB" 630334 NIL ELTAB (NIL T T) -9 NIL 630386 NIL) (-297 629263 629433 629632 "ELFUTS" 630012 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 628987 629061 629089 "ELEMFUN" 629194 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 628851 628878 628946 "ELEMFUN-" 628951 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 623376 626893 626934 "ELAGG" 627874 NIL ELAGG (NIL T) -9 NIL 628337 NIL) (-293 621553 622095 622758 "ELAGG-" 622763 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 620835 621002 621158 "ELABOR" 621417 T ELABOR (NIL) -8 NIL NIL NIL) (-291 619441 619775 620069 "ELABEXPR" 620561 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 611953 614078 614907 "EFUPXS" 618716 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 605079 607202 608013 "EFULS" 611228 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 602516 602922 603394 "EFSTRUC" 604711 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 591954 593873 595421 "EF" 601031 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 590932 591439 591588 "EAB" 591825 T EAB (NIL) -8 NIL NIL NIL) (-285 590054 590891 590919 "E04UCFA" 590924 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 589176 590013 590041 "E04NAFA" 590046 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 588298 589135 589163 "E04MBFA" 589168 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 587420 588257 588285 "E04JAFA" 588290 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 586544 587379 587407 "E04GCFA" 587412 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 585668 586503 586531 "E04FDFA" 586536 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 584790 585627 585655 "E04DGFA" 585660 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 578867 580315 581679 "E04AGNT" 583446 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 577487 578168 578208 "DVARCAT" 578549 NIL DVARCAT (NIL T) -9 NIL 578712 NIL) (-276 576637 576903 577217 "DVARCAT-" 577222 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 568605 576436 576565 "DSMP" 576570 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 566956 567747 567788 "DSEXT" 568151 NIL DSEXT (NIL T) -9 NIL 568445 NIL) (-273 565145 565669 566335 "DSEXT-" 566340 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 564804 564869 564967 "DROPT1" 565080 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 559823 561045 562182 "DROPT0" 563687 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 554406 555768 556836 "DROPT" 558775 T DROPT (NIL) -8 NIL NIL NIL) (-269 552715 553076 553462 "DRAWPT" 554040 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 552342 552401 552519 "DRAWHACK" 552656 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 551043 551342 551633 "DRAWCX" 552071 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 550552 550627 550778 "DRAWCURV" 550969 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 540870 542982 545097 "DRAWCFUN" 548457 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 535361 536380 537459 "DRAW" 539844 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 531943 534026 534067 "DQAGG" 534696 NIL DQAGG (NIL T) -9 NIL 534970 NIL) (-262 518526 526154 526237 "DPOLCAT" 528089 NIL DPOLCAT (NIL T T T T) -9 NIL 528634 NIL) (-261 513045 514711 516669 "DPOLCAT-" 516674 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 505967 512906 513004 "DPMO" 513009 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 498786 505747 505914 "DPMM" 505919 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 498308 498570 498659 "DOMTMPLT" 498717 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 497657 498110 498190 "DOMCTOR" 498248 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 496809 497137 497288 "DOMAIN" 497526 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 489828 496444 496596 "DMP" 496710 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 487605 488895 488936 "DMEXT" 488941 NIL DMEXT (NIL T) -9 NIL 489117 NIL) (-253 487199 487261 487405 "DLP" 487543 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 480322 486526 486716 "DLIST" 487041 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 476971 479147 479188 "DLAGG" 479738 NIL DLAGG (NIL T) -9 NIL 479968 NIL) (-250 475483 476297 476325 "DIVRING" 476417 T DIVRING (NIL) -9 NIL 476500 NIL) (-249 474666 474910 475210 "DIVRING-" 475215 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 472708 473125 473531 "DISPLAY" 474280 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 471538 471759 472024 "DIRPROD2" 472501 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 465010 471452 471515 "DIRPROD" 471520 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 453287 459721 459774 "DIRPCAT" 460032 NIL DIRPCAT (NIL NIL T) -9 NIL 460907 NIL) (-244 450487 451255 452136 "DIRPCAT-" 452473 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 449768 449934 450120 "DIOSP" 450321 T DIOSP (NIL) -7 NIL NIL NIL) (-242 446293 448652 448693 "DIOPS" 449127 NIL DIOPS (NIL T) -9 NIL 449356 NIL) (-241 445812 445956 446147 "DIOPS-" 446152 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 444719 445491 445519 "DIFRING" 445524 T DIFRING (NIL) -9 NIL 445546 NIL) (-239 444367 444465 444493 "DIFFSPC" 444612 T DIFFSPC (NIL) -9 NIL 444687 NIL) (-238 443988 444090 444242 "DIFFSPC-" 444247 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 442924 443522 443563 "DIFFMOD" 443568 NIL DIFFMOD (NIL T) -9 NIL 443666 NIL) (-236 442620 442677 442718 "DIFFDOM" 442839 NIL DIFFDOM (NIL T) -9 NIL 442907 NIL) (-235 442467 442497 442581 "DIFFDOM-" 442586 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 440207 441671 441712 "DIFEXT" 441717 NIL DIFEXT (NIL T) -9 NIL 441870 NIL) (-233 437352 439711 439752 "DIAGG" 439757 NIL DIAGG (NIL T) -9 NIL 439777 NIL) (-232 436700 436893 437145 "DIAGG-" 437150 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 431664 435659 435936 "DHMATRIX" 436469 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 427132 428185 429195 "DFSFUN" 430674 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 421373 426063 426375 "DFLOAT" 426840 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 419612 419917 420306 "DFINTTLS" 421081 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 416431 417633 418033 "DERHAM" 419278 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 414081 416206 416295 "DEQUEUE" 416375 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 413323 413468 413651 "DEGRED" 413943 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 409729 410498 411344 "DEFINTRF" 412551 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 407266 407753 408345 "DEFINTEF" 409248 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 406550 406886 407001 "DEFAST" 407171 T DEFAST (NIL) -8 NIL NIL NIL) (-221 399607 406143 406293 "DECIMAL" 406420 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 397065 397577 398083 "DDFACT" 399151 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 396655 396704 396855 "DBLRESP" 397016 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 395856 396425 396516 "DBASIS" 396604 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 393640 394086 394447 "DBASE" 395622 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 392828 393120 393266 "DATAARY" 393539 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 391886 392787 392815 "D03FAFA" 392820 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 390945 391845 391873 "D03EEFA" 391878 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 388871 389361 389850 "D03AGNT" 390476 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 388112 388830 388858 "D02EJFA" 388863 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 387353 388071 388099 "D02CJFA" 388104 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 386594 387312 387340 "D02BHFA" 387345 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 385835 386553 386581 "D02BBFA" 386586 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 378966 380621 382227 "D02AGNT" 384249 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 376716 377257 377803 "D01WGTS" 378440 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 375723 376675 376703 "D01TRNS" 376708 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 374731 375682 375710 "D01GBFA" 375715 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 373739 374690 374718 "D01FCFA" 374723 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 372747 373698 373726 "D01ASFA" 373731 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 371755 372706 372734 "D01AQFA" 372739 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 370763 371714 371742 "D01APFA" 371747 T D01APFA (NIL) -8 NIL NIL NIL) (-200 369771 370722 370750 "D01ANFA" 370755 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 368779 369730 369758 "D01AMFA" 369763 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 367787 368738 368766 "D01ALFA" 368771 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 366795 367746 367774 "D01AKFA" 367779 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 365803 366754 366782 "D01AJFA" 366787 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 359026 360651 362212 "D01AGNT" 364262 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 358345 358491 358643 "CYCLOTOM" 358894 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 355000 355793 356520 "CYCLES" 357638 T CYCLES (NIL) -7 NIL NIL NIL) (-192 354300 354446 354617 "CVMP" 354861 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 352087 352399 352768 "CTRIGMNP" 354028 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 351560 351818 351919 "CTORKIND" 352006 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 350765 351153 351181 "CTORCAT" 351363 T CTORCAT (NIL) -9 NIL 351476 NIL) (-188 350339 350474 350633 "CTORCAT-" 350638 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 349753 350013 350121 "CTORCALL" 350263 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 349111 349547 349620 "CTOR" 349700 T CTOR (NIL) -8 NIL NIL NIL) (-185 348467 348584 348737 "CSTTOOLS" 349008 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 344164 344923 345681 "CRFP" 347779 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 343579 343885 343977 "CRCEAST" 344092 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 342602 342811 343039 "CRAPACK" 343383 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 341982 342087 342291 "CPMATCH" 342478 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 341701 341735 341841 "CPIMA" 341948 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 337959 338721 339440 "COORDSYS" 341036 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 337347 337492 337634 "CONTOUR" 337837 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 332818 335350 335842 "CONTFRAC" 336887 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 332692 332719 332747 "CONDUIT" 332784 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 331646 332320 332348 "COMRING" 332353 T COMRING (NIL) -9 NIL 332405 NIL) (-174 330628 331004 331188 "COMPPROP" 331482 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 330283 330324 330452 "COMPLPAT" 330587 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 329913 329976 330083 "COMPLEX2" 330220 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 318317 329722 329831 "COMPLEX" 329836 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 317638 317777 317937 "COMPILER" 318177 T COMPILER (NIL) -8 NIL NIL NIL) (-169 317350 317391 317489 "COMPFACT" 317597 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 298744 311054 311094 "COMPCAT" 312098 NIL COMPCAT (NIL T) -9 NIL 313446 NIL) (-167 287632 291183 294810 "COMPCAT-" 295166 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 287355 287389 287492 "COMMUPC" 287598 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 287143 287183 287242 "COMMONOP" 287316 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 286665 286947 287022 "COMMAAST" 287088 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 286172 286416 286503 "COMM" 286598 T COMM (NIL) -8 NIL NIL NIL) (-162 285367 285615 285643 "COMBOPC" 285981 T COMBOPC (NIL) -9 NIL 286156 NIL) (-161 284221 284473 284715 "COMBINAT" 285157 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 280564 281252 281879 "COMBF" 283643 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 279226 279680 279915 "COLOR" 280349 T COLOR (NIL) -8 NIL NIL NIL) (-158 278642 278947 279039 "COLONAST" 279154 T COLONAST (NIL) -8 NIL NIL NIL) (-157 278276 278329 278454 "CMPLXRT" 278589 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 277664 277976 278075 "CLLCTAST" 278197 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 273124 274194 275274 "CLIP" 276604 T CLIP (NIL) -7 NIL NIL NIL) (-154 271297 272225 272465 "CLIF" 272951 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 267390 269415 269456 "CLAGG" 270385 NIL CLAGG (NIL T) -9 NIL 270921 NIL) (-152 265734 266269 266852 "CLAGG-" 266857 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 265272 265363 265503 "CINTSLPE" 265643 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 262737 263244 263792 "CHVAR" 264800 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 261777 262451 262479 "CHARZ" 262484 T CHARZ (NIL) -9 NIL 262499 NIL) (-148 261525 261571 261649 "CHARPOL" 261731 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 260443 261149 261177 "CHARNZ" 261238 T CHARNZ (NIL) -9 NIL 261287 NIL) (-146 257387 258497 259026 "CHAR" 259934 T CHAR (NIL) -8 NIL NIL NIL) (-145 257095 257174 257202 "CFCAT" 257313 T CFCAT (NIL) -9 NIL NIL NIL) (-144 256318 256447 256630 "CDEN" 256979 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 252029 255471 255751 "CCLASS" 256058 T CCLASS (NIL) -8 NIL NIL NIL) (-142 251250 251437 251614 "CATEGORY" 251872 T -10 (NIL) -8 NIL NIL NIL) (-141 250745 251169 251217 "CATCTOR" 251222 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 250136 250448 250546 "CATAST" 250667 T CATAST (NIL) -8 NIL NIL NIL) (-139 249552 249857 249949 "CASEAST" 250064 T CASEAST (NIL) -8 NIL NIL NIL) (-138 248648 248808 249029 "CARTEN2" 249399 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 243545 244805 245549 "CARTEN" 247960 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 241675 242695 242952 "CARD" 243308 T CARD (NIL) -8 NIL NIL NIL) (-135 241197 241479 241554 "CAPSLAST" 241620 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 240639 240895 240923 "CACHSET" 241055 T CACHSET (NIL) -9 NIL 241133 NIL) (-133 240029 240417 240445 "CABMON" 240495 T CABMON (NIL) -9 NIL 240551 NIL) (-132 239466 239733 239843 "BYTEORD" 239939 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 234507 238971 239143 "BYTEBUF" 239314 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 233338 234050 234185 "BYTE" 234348 T BYTE (NIL) -8 NIL NIL 234463) (-129 230714 233030 233137 "BTREE" 233264 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 228030 230362 230484 "BTOURN" 230624 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 225248 227472 227513 "BTCAT" 227581 NIL BTCAT (NIL T) -9 NIL 227658 NIL) (-126 224897 224995 225144 "BTCAT-" 225149 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 219900 224143 224171 "BTAGG" 224285 T BTAGG (NIL) -9 NIL 224395 NIL) (-124 219354 219515 219721 "BTAGG-" 219726 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 216204 218632 218847 "BSTREE" 219171 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 215312 215468 215652 "BRILL" 216060 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 211818 214010 214051 "BRAGG" 214700 NIL BRAGG (NIL T) -9 NIL 214958 NIL) (-120 210251 210753 211308 "BRAGG-" 211313 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 202508 209595 209780 "BPADICRT" 210098 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 200524 202445 202490 "BPADIC" 202495 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 200216 200252 200366 "BOUNDZRO" 200488 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 197943 198401 198876 "BOP1" 199774 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 192973 194403 195301 "BOP" 197065 T BOP (NIL) -8 NIL NIL NIL) (-114 191638 192561 192703 "BOOLEAN" 192851 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 191231 191388 191416 "BOOLE" 191527 T BOOLE (NIL) -9 NIL 191608 NIL) (-112 191099 191126 191192 "BOOLE-" 191197 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 190268 190768 190822 "BMODULE" 190827 NIL BMODULE (NIL T T) -9 NIL 190892 NIL) (-110 185703 190066 190139 "BITS" 190215 T BITS (NIL) -8 NIL NIL NIL) (-109 185100 185243 185383 "BINDING" 185583 T BINDING (NIL) -8 NIL NIL NIL) (-108 178160 184695 184844 "BINARY" 184971 T BINARY (NIL) -8 NIL NIL NIL) (-107 175878 177387 177428 "BGAGG" 177688 NIL BGAGG (NIL T) -9 NIL 177825 NIL) (-106 175703 175741 175832 "BGAGG-" 175837 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 174726 175087 175292 "BFUNCT" 175518 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 173396 173594 173882 "BEZOUT" 174550 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 169708 172248 172578 "BBTREE" 173099 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 169291 169387 169415 "BASTYPE" 169592 T BASTYPE (NIL) -9 NIL 169691 NIL) (-101 168949 169048 169183 "BASTYPE-" 169188 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 168371 168459 168611 "BALFACT" 168860 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 167107 167786 167972 "AUTOMOR" 168216 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 166833 166838 166864 "ATTREG" 166869 T ATTREG (NIL) -9 NIL NIL NIL) (-97 164995 165530 165882 "ATTRBUT" 166499 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 164549 164823 164889 "ATTRAST" 164947 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 164049 164198 164224 "ATRIG" 164425 T ATRIG (NIL) -9 NIL NIL NIL) (-94 163846 163899 163986 "ATRIG-" 163991 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 163429 163663 163689 "ASTCAT" 163694 T ASTCAT (NIL) -9 NIL 163724 NIL) (-92 163138 163215 163334 "ASTCAT-" 163339 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 161226 162914 163002 "ASTACK" 163081 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 159715 160028 160393 "ASSOCEQ" 160908 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 158639 159374 159498 "ASP9" 159622 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 157399 158244 158386 "ASP80" 158528 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 157127 157347 157386 "ASP8" 157391 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 155973 156804 156922 "ASP78" 157040 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 154834 155653 155770 "ASP77" 155887 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 153638 154472 154603 "ASP74" 154734 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 152430 153273 153405 "ASP73" 153537 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 151220 152065 152197 "ASP7" 152329 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 150216 151046 151146 "ASP6" 151151 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 149055 149893 150011 "ASP55" 150129 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 147896 148729 148848 "ASP50" 148967 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 146876 147597 147707 "ASP49" 147817 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 145552 146415 146583 "ASP42" 146765 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 144221 145085 145255 "ASP41" 145439 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 143201 143922 144032 "ASP4" 144142 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 142043 142878 142996 "ASP35" 143114 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 141772 141991 142030 "ASP34" 142035 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 141491 141576 141652 "ASP33" 141727 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 140277 141126 141258 "ASP31" 141390 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 140006 140225 140264 "ASP30" 140269 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 139723 139810 139886 "ASP29" 139961 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 139452 139671 139710 "ASP28" 139715 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 139181 139400 139439 "ASP27" 139444 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 138157 138879 138990 "ASP24" 139101 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 137126 137959 138071 "ASP20" 138076 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 135961 136800 136919 "ASP19" 137038 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 135680 135765 135841 "ASP12" 135916 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 134424 135279 135423 "ASP10" 135567 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 133404 134125 134235 "ASP1" 134345 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 131130 133248 133339 "ARRAY2" 133344 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 130144 130335 130556 "ARRAY12" 130953 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 125618 129792 129906 "ARRAY1" 130061 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 119774 121820 121895 "ARR2CAT" 124525 NIL ARR2CAT (NIL T T T) -9 NIL 125283 NIL) (-56 117373 118150 119005 "ARR2CAT-" 119010 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 116624 117000 117125 "ARITY" 117266 T ARITY (NIL) -8 NIL NIL NIL) (-54 115382 115552 115851 "APPRULE" 116460 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115027 115081 115200 "APPLYORE" 115328 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 114281 114428 114585 "ANY1" 114901 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 113581 113874 113994 "ANY" 114179 T ANY (NIL) -8 NIL NIL NIL) (-50 110907 112018 112345 "ANTISYM" 113305 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 110351 110614 110710 "ANON" 110829 T ANON (NIL) -8 NIL NIL NIL) (-48 103514 108890 109344 "AN" 109915 T AN (NIL) -8 NIL NIL NIL) (-47 99177 100786 100837 "AMR" 101585 NIL AMR (NIL T T) -9 NIL 102185 NIL) (-46 98229 98510 98873 "AMR-" 98878 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 81698 98146 98207 "ALIST" 98212 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 77995 81292 81461 "ALGSC" 81616 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 74445 75105 75712 "ALGPKG" 77435 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 73710 73823 74007 "ALGMFACT" 74331 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 69693 70324 70918 "ALGMANIP" 73294 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59053 69319 69469 "ALGFF" 69626 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 58225 58380 58559 "ALGFACT" 58911 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57014 57752 57790 "ALGEBRA" 57795 NIL ALGEBRA (NIL T) -9 NIL 57836 NIL) (-37 56714 56791 56923 "ALGEBRA-" 56928 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 37668 54551 54603 "ALAGG" 54739 NIL ALAGG (NIL T T) -9 NIL 54900 NIL) (-35 37168 37317 37343 "AHYP" 37544 T AHYP (NIL) -9 NIL NIL NIL) (-34 36470 36653 36679 "AGG" 36962 T AGG (NIL) -9 NIL 37151 NIL) (-33 36177 36264 36379 "AGG-" 36384 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 33937 34406 34811 "AF" 35819 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33357 33662 33752 "ADDAST" 33865 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32589 32884 33040 "ACPLOT" 33219 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20153 29521 29559 "ACFS" 30166 NIL ACFS (NIL T) -9 NIL 30405 NIL) (-28 18060 18670 19432 "ACFS-" 19437 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13768 16093 16119 "ACF" 16998 T ACF (NIL) -9 NIL 17411 NIL) (-26 12400 12806 13299 "ACF-" 13304 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11910 12153 12179 "ABELSG" 12271 T ABELSG (NIL) -9 NIL 12336 NIL) (-24 11771 11802 11868 "ABELSG-" 11873 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11040 11387 11413 "ABELMON" 11583 T ABELMON (NIL) -9 NIL 11695 NIL) (-22 10680 10788 10926 "ABELMON-" 10931 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9930 10386 10412 "ABELGRP" 10484 T ABELGRP (NIL) -9 NIL 10559 NIL) (-20 9357 9522 9738 "ABELGRP-" 9743 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8619 8658 "A1AGG" 8663 NIL A1AGG (NIL T) -9 NIL 8703 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3450289 3450294 3450299 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3450274 3450279 3450284 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3450259 3450264 3450269 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3450244 3450249 3450254 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1329 3449237 3450119 3450196 "ZMOD" 3450201 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1328 3448273 3448455 3448678 "ZLINDEP" 3449069 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1327 3437435 3439341 3441313 "ZDSOLVE" 3446403 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1326 3436669 3436822 3437011 "YSTREAM" 3437281 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1325 3436029 3436338 3436453 "YDIAGRAM" 3436576 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1324 3433477 3435330 3435534 "XRPOLY" 3435872 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1323 3429744 3431348 3431923 "XPR" 3432949 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1322 3427075 3428751 3428806 "XPOLYC" 3429094 NIL XPOLYC (NIL T T) -9 NIL 3429207 NIL) (-1321 3424479 3426415 3426619 "XPOLY" 3426915 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1320 3420427 3422996 3423384 "XPBWPOLY" 3424137 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1319 3415319 3416898 3416953 "XFALG" 3419125 NIL XFALG (NIL T T) -9 NIL 3419914 NIL) (-1318 3410597 3413295 3413337 "XF" 3413958 NIL XF (NIL T) -9 NIL 3414358 NIL) (-1317 3410194 3410306 3410475 "XF-" 3410480 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1316 3409309 3409431 3409636 "XEXPPKG" 3410086 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1315 3407050 3409159 3409255 "XDPOLY" 3409260 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1314 3405705 3406443 3406486 "XALG" 3406491 NIL XALG (NIL T) -9 NIL 3406602 NIL) (-1313 3398756 3403682 3404176 "WUTSET" 3405297 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1312 3396858 3397808 3398131 "WP" 3398567 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1311 3396406 3396680 3396750 "WHILEAST" 3396810 T WHILEAST (NIL) -8 NIL NIL NIL) (-1310 3395818 3396123 3396217 "WHEREAST" 3396334 T WHEREAST (NIL) -8 NIL NIL NIL) (-1309 3394692 3394902 3395197 "WFFINTBS" 3395615 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1308 3392560 3393023 3393485 "WEIER" 3394264 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1307 3391484 3392042 3392084 "VSPACE" 3392220 NIL VSPACE (NIL T) -9 NIL 3392294 NIL) (-1306 3391316 3391349 3391440 "VSPACE-" 3391445 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1305 3391113 3391167 3391235 "VOID" 3391270 T VOID (NIL) -8 NIL NIL NIL) (-1304 3387381 3388176 3388913 "VIEWDEF" 3390398 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1303 3376325 3378929 3381102 "VIEW3D" 3385230 T VIEW3D (NIL) -8 NIL NIL NIL) (-1302 3368342 3370236 3371815 "VIEW2D" 3374768 T VIEW2D (NIL) -8 NIL NIL NIL) (-1301 3366442 3366837 3367243 "VIEW" 3367958 T VIEW (NIL) -7 NIL NIL NIL) (-1300 3364995 3365278 3365596 "VECTOR2" 3366172 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1299 3360015 3364765 3364857 "VECTOR" 3364938 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1298 3353074 3357719 3357762 "VECTCAT" 3358757 NIL VECTCAT (NIL T) -9 NIL 3359344 NIL) (-1297 3352016 3352342 3352732 "VECTCAT-" 3352737 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1296 3351422 3351667 3351787 "VARIABLE" 3351931 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1295 3351355 3351360 3351390 "UTYPE" 3351395 T UTYPE (NIL) -9 NIL NIL NIL) (-1294 3350163 3350339 3350601 "UTSODETL" 3351181 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1293 3347555 3348063 3348587 "UTSODE" 3349704 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1292 3337565 3343488 3343531 "UTSCAT" 3344643 NIL UTSCAT (NIL T) -9 NIL 3345401 NIL) (-1291 3334691 3335635 3336624 "UTSCAT-" 3336629 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1290 3334312 3334361 3334494 "UTS2" 3334642 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1289 3325629 3332073 3332553 "UTS" 3333890 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1288 3319608 3322439 3322482 "URAGG" 3324552 NIL URAGG (NIL T) -9 NIL 3325275 NIL) (-1287 3316643 3317610 3318633 "URAGG-" 3318638 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1286 3312026 3315278 3315743 "UPXSSING" 3316307 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1285 3304457 3311930 3312002 "UPXSCONS" 3312007 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1284 3293217 3300659 3300721 "UPXSCCA" 3301295 NIL UPXSCCA (NIL T T) -9 NIL 3301528 NIL) (-1283 3292837 3292940 3293114 "UPXSCCA-" 3293119 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1282 3281497 3288664 3288707 "UPXSCAT" 3289355 NIL UPXSCAT (NIL T) -9 NIL 3289964 NIL) (-1281 3280921 3281006 3281185 "UPXS2" 3281412 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1280 3272417 3280303 3280567 "UPXS" 3280715 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1279 3271056 3271326 3271676 "UPSQFREE" 3272161 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1278 3263887 3267322 3267377 "UPSCAT" 3268457 NIL UPSCAT (NIL T T) -9 NIL 3269223 NIL) (-1277 3263043 3263298 3263625 "UPSCAT-" 3263630 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1276 3262664 3262713 3262846 "UPOLYC2" 3262994 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1275 3246840 3255791 3255834 "UPOLYC" 3257935 NIL UPOLYC (NIL T) -9 NIL 3259156 NIL) (-1274 3237745 3240632 3243760 "UPOLYC-" 3243765 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1273 3237066 3237191 3237355 "UPMP" 3237634 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1272 3236613 3236700 3236839 "UPDIVP" 3236979 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1271 3235151 3235430 3235746 "UPDECOMP" 3236362 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1270 3234364 3234494 3234680 "UPCDEN" 3235035 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1269 3233877 3233952 3234101 "UP2" 3234289 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1268 3224508 3233560 3233689 "UP" 3233796 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1267 3223713 3223850 3224055 "UNISEG2" 3224351 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1266 3222066 3222917 3223194 "UNISEG" 3223471 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1265 3221108 3221306 3221532 "UNIFACT" 3221882 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1264 3207855 3221012 3221084 "ULSCONS" 3221089 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1263 3187688 3200935 3200997 "ULSCCAT" 3201635 NIL ULSCCAT (NIL T T) -9 NIL 3201924 NIL) (-1262 3186720 3187007 3187383 "ULSCCAT-" 3187388 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3175177 3182266 3182309 "ULSCAT" 3183172 NIL ULSCAT (NIL T) -9 NIL 3183903 NIL) (-1260 3174601 3174686 3174865 "ULS2" 3175092 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1259 3156448 3173913 3174155 "ULS" 3174417 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1258 3155367 3156067 3156181 "UINT8" 3156292 T UINT8 (NIL) -8 NIL NIL 3156384) (-1257 3154285 3154985 3155099 "UINT64" 3155210 T UINT64 (NIL) -8 NIL NIL 3155302) (-1256 3153203 3153903 3154017 "UINT32" 3154128 T UINT32 (NIL) -8 NIL NIL 3154220) (-1255 3152121 3152821 3152935 "UINT16" 3153046 T UINT16 (NIL) -8 NIL NIL 3153138) (-1254 3150200 3151367 3151397 "UFD" 3151609 T UFD (NIL) -9 NIL 3151723 NIL) (-1253 3149982 3150040 3150135 "UFD-" 3150140 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1252 3149040 3149247 3149463 "UDVO" 3149788 T UDVO (NIL) -7 NIL NIL NIL) (-1251 3146806 3147265 3147736 "UDPO" 3148604 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1250 3146518 3146761 3146792 "TYPEAST" 3146797 T TYPEAST (NIL) -8 NIL NIL NIL) (-1249 3146451 3146456 3146486 "TYPE" 3146491 T TYPE (NIL) -9 NIL NIL NIL) (-1248 3145404 3145624 3145864 "TWOFACT" 3146245 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1247 3144379 3144813 3145048 "TUPLE" 3145204 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1246 3142016 3142589 3143128 "TUBETOOL" 3143862 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1245 3140822 3141063 3141305 "TUBE" 3141809 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1244 3129071 3133579 3133676 "TSETCAT" 3138945 NIL TSETCAT (NIL T T T T) -9 NIL 3140477 NIL) (-1243 3123539 3125403 3127294 "TSETCAT-" 3127299 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1242 3117725 3122511 3122794 "TS" 3123291 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3112198 3113211 3114140 "TRMANIP" 3116861 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1240 3111627 3111702 3111865 "TRIMAT" 3112130 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1239 3109439 3109730 3110087 "TRIGMNIP" 3111376 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1238 3108923 3109072 3109102 "TRIGCAT" 3109315 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1237 3108568 3108671 3108812 "TRIGCAT-" 3108817 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1236 3105294 3107426 3107707 "TREE" 3108322 NIL TREE (NIL T) -8 NIL NIL NIL) (-1235 3104400 3105096 3105126 "TRANFUN" 3105161 T TRANFUN (NIL) -9 NIL 3105227 NIL) (-1234 3103619 3103870 3104150 "TRANFUN-" 3104155 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1233 3103417 3103455 3103516 "TOPSP" 3103580 T TOPSP (NIL) -7 NIL NIL NIL) (-1232 3102747 3102880 3103034 "TOOLSIGN" 3103298 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1231 3101261 3101924 3102163 "TEXTFILE" 3102530 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1230 3101036 3101073 3101145 "TEX1" 3101224 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1229 3098840 3099489 3099918 "TEX" 3100629 T TEX (NIL) -8 NIL NIL NIL) (-1228 3098476 3098551 3098641 "TEMUTL" 3098772 T TEMUTL (NIL) -7 NIL NIL NIL) (-1227 3096570 3096910 3097235 "TBCMPPK" 3098199 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1226 3088006 3094656 3094712 "TBAGG" 3095112 NIL TBAGG (NIL T T) -9 NIL 3095323 NIL) (-1225 3082890 3084564 3086318 "TBAGG-" 3086323 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1224 3082256 3082381 3082526 "TANEXP" 3082779 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1223 3081707 3082031 3082121 "TALGOP" 3082201 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1222 3081101 3081218 3081356 "TABLEAU" 3081604 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1221 3074231 3080958 3081051 "TABLE" 3081056 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1220 3068761 3070059 3071307 "TABLBUMP" 3073017 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1219 3067971 3068130 3068311 "SYSTEM" 3068602 T SYSTEM (NIL) -8 NIL NIL NIL) (-1218 3064376 3065129 3065912 "SYSSOLP" 3067222 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1217 3064138 3064331 3064362 "SYSPTR" 3064367 T SYSPTR (NIL) -8 NIL NIL NIL) (-1216 3062977 3063669 3063795 "SYSNNI" 3063981 NIL SYSNNI (NIL NIL) -8 NIL NIL 3064073) (-1215 3062184 3062739 3062818 "SYSINT" 3062878 NIL SYSINT (NIL NIL) -8 NIL NIL 3062923) (-1214 3058294 3059462 3060172 "SYNTAX" 3061496 T SYNTAX (NIL) -8 NIL NIL NIL) (-1213 3055374 3056054 3056686 "SYMTAB" 3057684 T SYMTAB (NIL) -8 NIL NIL NIL) (-1212 3050497 3051543 3052520 "SYMS" 3054419 T SYMS (NIL) -8 NIL NIL NIL) (-1211 3047415 3049953 3050186 "SYMPOLY" 3050304 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1210 3046920 3047007 3047130 "SYMFUNC" 3047327 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1209 3042718 3044232 3045045 "SYMBOL" 3046129 T SYMBOL (NIL) -8 NIL NIL NIL) (-1208 3036191 3037946 3039666 "SWITCH" 3041020 T SWITCH (NIL) -8 NIL NIL NIL) (-1207 3028952 3035147 3035441 "SUTS" 3035955 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1206 3020448 3028334 3028598 "SUPXS" 3028746 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3019595 3019734 3019951 "SUPFRACF" 3020316 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1204 3019210 3019275 3019388 "SUP2" 3019530 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1203 3009789 3018828 3018954 "SUP" 3019119 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3008213 3008511 3008867 "SUMRF" 3009488 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1201 3007536 3007614 3007806 "SUMFS" 3008134 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1200 2989418 3006848 3007090 "SULS" 3007352 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1199 2988966 2989240 2989310 "SUCHTAST" 2989370 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1198 2988207 2988491 2988631 "SUCH" 2988874 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1197 2981846 2983113 2984072 "SUBSPACE" 2987295 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1196 2981266 2981366 2981530 "SUBRESP" 2981734 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1195 2975277 2976559 2977706 "STTFNC" 2980166 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1194 2968471 2969942 2971253 "STTF" 2974013 NIL STTF (NIL T) -7 NIL NIL NIL) (-1193 2959587 2961653 2963447 "STTAYLOR" 2966712 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1192 2952457 2959451 2959534 "STRTBL" 2959539 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1191 2946968 2952166 2952265 "STRING" 2952380 T STRING (NIL) -8 NIL NIL NIL) (-1190 2946472 2946555 2946699 "STREAM3" 2946885 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1189 2945436 2945637 2945872 "STREAM2" 2946285 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1188 2945118 2945176 2945269 "STREAM1" 2945378 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1187 2937234 2942737 2943348 "STREAM" 2944542 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2936226 2936431 2936662 "STINPROD" 2937050 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1185 2935341 2935715 2935863 "STEPAST" 2936100 T STEPAST (NIL) -8 NIL NIL NIL) (-1184 2934837 2935082 2935112 "STEP" 2935206 T STEP (NIL) -9 NIL 2935277 NIL) (-1183 2928009 2934736 2934813 "STBL" 2934818 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1182 2922192 2926803 2926846 "STAGG" 2927278 NIL STAGG (NIL T) -9 NIL 2927457 NIL) (-1181 2919750 2920500 2921370 "STAGG-" 2921375 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1180 2917836 2919520 2919612 "STACK" 2919693 NIL STACK (NIL T) -8 NIL NIL NIL) (-1179 2917153 2917666 2917696 "SRING" 2917701 T SRING (NIL) -9 NIL 2917721 NIL) (-1178 2909302 2915294 2915750 "SREGSET" 2916783 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1177 2901649 2903096 2904609 "SRDCMPK" 2907908 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1176 2894063 2899008 2899038 "SRAGG" 2900341 T SRAGG (NIL) -9 NIL 2900949 NIL) (-1175 2893014 2893335 2893714 "SRAGG-" 2893719 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1174 2886716 2891961 2892382 "SQMATRIX" 2892640 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1173 2880243 2883434 2884161 "SPLTREE" 2886061 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1172 2876068 2876899 2877545 "SPLNODE" 2879669 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1171 2875043 2875348 2875378 "SPFCAT" 2875822 T SPFCAT (NIL) -9 NIL NIL NIL) (-1170 2873738 2873990 2874254 "SPECOUT" 2874801 T SPECOUT (NIL) -7 NIL NIL NIL) (-1169 2864384 2866702 2866732 "SPADXPT" 2871410 T SPADXPT (NIL) -9 NIL 2873576 NIL) (-1168 2864139 2864185 2864254 "SPADPRSR" 2864337 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1167 2861742 2864094 2864125 "SPADAST" 2864130 T SPADAST (NIL) -8 NIL NIL NIL) (-1166 2853343 2855446 2855489 "SPACEC" 2859862 NIL SPACEC (NIL T) -9 NIL 2861678 NIL) (-1165 2851143 2853275 2853324 "SPACE3" 2853329 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1164 2849875 2850066 2850357 "SORTPAK" 2850948 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1163 2847937 2848270 2848682 "SOLVETRA" 2849539 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1162 2846975 2847209 2847470 "SOLVESER" 2847710 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1161 2842207 2843167 2844162 "SOLVERAD" 2846027 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1160 2837932 2838631 2839360 "SOLVEFOR" 2841574 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1159 2831677 2837280 2837377 "SNTSCAT" 2837382 NIL SNTSCAT (NIL T T T T) -9 NIL 2837452 NIL) (-1158 2825228 2830000 2830391 "SMTS" 2831367 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1157 2818976 2825116 2825193 "SMP" 2825198 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1156 2817105 2817436 2817834 "SMITH" 2818673 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1155 2808742 2813678 2813781 "SMATCAT" 2815135 NIL SMATCAT (NIL NIL T T T) -9 NIL 2815685 NIL) (-1154 2805535 2806519 2807690 "SMATCAT-" 2807695 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1153 2803115 2804743 2804786 "SKAGG" 2805047 NIL SKAGG (NIL T) -9 NIL 2805182 NIL) (-1152 2798637 2802598 2802775 "SINT" 2802927 T SINT (NIL) -8 NIL NIL 2803082) (-1151 2798403 2798447 2798513 "SIMPAN" 2798593 T SIMPAN (NIL) -7 NIL NIL NIL) (-1150 2797244 2797476 2797744 "SIGNRF" 2798169 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1149 2796080 2796242 2796519 "SIGNEF" 2797080 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1148 2795320 2795663 2795787 "SIGAST" 2795978 T SIGAST (NIL) -8 NIL NIL NIL) (-1147 2794545 2794855 2794995 "SIG" 2795202 T SIG (NIL) -8 NIL NIL NIL) (-1146 2792197 2792689 2793195 "SHP" 2794086 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1145 2785642 2792098 2792174 "SHDP" 2792179 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1144 2785153 2785393 2785423 "SGROUP" 2785516 T SGROUP (NIL) -9 NIL 2785578 NIL) (-1143 2785005 2785037 2785110 "SGROUP-" 2785115 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1142 2781724 2782494 2783217 "SGCF" 2784304 T SGCF (NIL) -7 NIL NIL NIL) (-1141 2775567 2781170 2781267 "SFRTCAT" 2781272 NIL SFRTCAT (NIL T T T T) -9 NIL 2781311 NIL) (-1140 2768886 2770006 2771142 "SFRGCD" 2774550 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1139 2761904 2763085 2764271 "SFQCMPK" 2767819 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2761506 2761613 2761724 "SFORT" 2761845 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1137 2760432 2761346 2761467 "SEXOF" 2761472 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1136 2756021 2756928 2757023 "SEXCAT" 2759645 NIL SEXCAT (NIL T T T T T) -9 NIL 2760205 NIL) (-1135 2754936 2755902 2755970 "SEX" 2755975 T SEX (NIL) -8 NIL NIL NIL) (-1134 2753064 2753653 2753956 "SETMN" 2754679 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1133 2752594 2752782 2752812 "SETCAT" 2752929 T SETCAT (NIL) -9 NIL 2753014 NIL) (-1132 2752362 2752426 2752525 "SETCAT-" 2752530 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1131 2748576 2750823 2750866 "SETAGG" 2751736 NIL SETAGG (NIL T) -9 NIL 2752076 NIL) (-1130 2747998 2748150 2748387 "SETAGG-" 2748392 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1129 2744921 2747932 2747980 "SET" 2747985 NIL SET (NIL T) -8 NIL NIL NIL) (-1128 2744304 2744617 2744718 "SEQAST" 2744842 T SEQAST (NIL) -8 NIL NIL NIL) (-1127 2743431 2743797 2743858 "SEGXCAT" 2744144 NIL SEGXCAT (NIL T T) -9 NIL 2744264 NIL) (-1126 2742356 2742624 2742667 "SEGCAT" 2743189 NIL SEGCAT (NIL T) -9 NIL 2743410 NIL) (-1125 2741971 2742036 2742149 "SEGBIND2" 2742291 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1124 2740861 2741334 2741542 "SEGBIND" 2741798 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1123 2740380 2740662 2740739 "SEGAST" 2740806 T SEGAST (NIL) -8 NIL NIL NIL) (-1122 2739589 2739725 2739929 "SEG2" 2740224 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1121 2738505 2739255 2739437 "SEG" 2739442 NIL SEG (NIL T) -8 NIL NIL NIL) (-1120 2737738 2738440 2738487 "SDVAR" 2738492 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1119 2729132 2737508 2737638 "SDPOL" 2737643 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1118 2727701 2727991 2728310 "SCPKG" 2728847 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1117 2726823 2727037 2727229 "SCOPE" 2727531 T SCOPE (NIL) -8 NIL NIL NIL) (-1116 2726019 2726177 2726356 "SCACHE" 2726678 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1115 2725603 2725837 2725867 "SASTCAT" 2725872 T SASTCAT (NIL) -9 NIL 2725885 NIL) (-1114 2725006 2725438 2725514 "SAOS" 2725549 T SAOS (NIL) -8 NIL NIL NIL) (-1113 2724565 2724606 2724779 "SAERFFC" 2724965 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1112 2724152 2724193 2724352 "SAEFACT" 2724524 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1111 2717209 2724049 2724129 "SAE" 2724134 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2715512 2715844 2716245 "RURPK" 2716875 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1109 2714089 2714455 2714760 "RULESET" 2715346 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1108 2713659 2713883 2713966 "RULECOLD" 2714041 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1107 2710774 2711412 2711870 "RULE" 2713340 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2710558 2710592 2710663 "RTVALUE" 2710725 T RTVALUE (NIL) -8 NIL NIL NIL) (-1105 2709969 2710275 2710369 "RSTRCAST" 2710486 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1104 2704739 2705612 2706532 "RSETGCD" 2709168 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1103 2693444 2699047 2699144 "RSETCAT" 2703263 NIL RSETCAT (NIL T T T T) -9 NIL 2704360 NIL) (-1102 2691263 2691910 2692734 "RSETCAT-" 2692739 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1101 2683571 2685025 2686545 "RSDCMPK" 2689862 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2681440 2682003 2682077 "RRCC" 2683163 NIL RRCC (NIL T T) -9 NIL 2683507 NIL) (-1099 2680761 2680965 2681244 "RRCC-" 2681249 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1098 2680144 2680457 2680558 "RPTAST" 2680682 T RPTAST (NIL) -8 NIL NIL NIL) (-1097 2652556 2663256 2663323 "RPOLCAT" 2673989 NIL RPOLCAT (NIL T T T) -9 NIL 2677149 NIL) (-1096 2643562 2646418 2649528 "RPOLCAT-" 2649533 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1095 2634131 2641773 2642255 "ROUTINE" 2643102 T ROUTINE (NIL) -8 NIL NIL NIL) (-1094 2630196 2633757 2633897 "ROMAN" 2634013 T ROMAN (NIL) -8 NIL NIL NIL) (-1093 2628310 2629056 2629316 "ROIRC" 2630001 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1092 2624087 2626852 2626882 "RNS" 2627151 T RNS (NIL) -9 NIL 2627407 NIL) (-1091 2622494 2622979 2623513 "RNS-" 2623588 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1090 2621455 2621859 2622061 "RNGBIND" 2622345 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1089 2620748 2621252 2621282 "RNG" 2621287 T RNG (NIL) -9 NIL 2621308 NIL) (-1088 2620043 2620521 2620564 "RMODULE" 2620569 NIL RMODULE (NIL T) -9 NIL 2620596 NIL) (-1087 2618867 2618973 2619309 "RMCAT2" 2619944 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1086 2615483 2618213 2618510 "RMATRIX" 2618629 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1085 2608093 2610570 2610685 "RMATCAT" 2614044 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2615026 NIL) (-1084 2607432 2607615 2607922 "RMATCAT-" 2607927 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1083 2607005 2607219 2607262 "RLINSET" 2607324 NIL RLINSET (NIL T) -9 NIL 2607368 NIL) (-1082 2606566 2606647 2606775 "RINTERP" 2606924 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1081 2605490 2606164 2606194 "RING" 2606250 T RING (NIL) -9 NIL 2606342 NIL) (-1080 2605270 2605326 2605423 "RING-" 2605428 NIL RING- (NIL T) -8 NIL NIL NIL) (-1079 2604081 2604348 2604606 "RIDIST" 2605034 T RIDIST (NIL) -7 NIL NIL NIL) (-1078 2594847 2603549 2603755 "RGCHAIN" 2603929 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1077 2594105 2594589 2594630 "RGBCSPC" 2594688 NIL RGBCSPC (NIL T) -9 NIL 2594740 NIL) (-1076 2593171 2593630 2593671 "RGBCMDL" 2593903 NIL RGBCMDL (NIL T) -9 NIL 2594017 NIL) (-1075 2592811 2592880 2592983 "RFFACTOR" 2593102 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1074 2592530 2592571 2592668 "RFFACT" 2592770 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1073 2590581 2591011 2591393 "RFDIST" 2592170 T RFDIST (NIL) -7 NIL NIL NIL) (-1072 2587521 2588189 2588859 "RF" 2589945 NIL RF (NIL T) -7 NIL NIL NIL) (-1071 2586968 2587066 2587229 "RETSOL" 2587423 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1070 2586586 2586684 2586727 "RETRACT" 2586860 NIL RETRACT (NIL T) -9 NIL 2586947 NIL) (-1069 2586429 2586460 2586547 "RETRACT-" 2586552 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1068 2585977 2586251 2586321 "RETAST" 2586381 T RETAST (NIL) -8 NIL NIL NIL) (-1067 2578443 2585630 2585757 "RESULT" 2585872 T RESULT (NIL) -8 NIL NIL NIL) (-1066 2576878 2577712 2577911 "RESRING" 2578346 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1065 2576502 2576563 2576661 "RESLATC" 2576815 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1064 2576201 2576242 2576349 "REPSQ" 2576461 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1063 2575892 2575933 2576044 "REPDB" 2576160 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1062 2569724 2571181 2572404 "REP2" 2574704 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1061 2566027 2566782 2567590 "REP1" 2568951 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1060 2563407 2564029 2564631 "REP" 2565447 T REP (NIL) -7 NIL NIL NIL) (-1059 2555556 2561548 2562004 "REGSET" 2563037 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2554265 2554704 2554954 "REF" 2555341 NIL REF (NIL T) -8 NIL NIL NIL) (-1057 2553630 2553745 2553912 "REDORDER" 2554149 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1056 2549032 2552843 2553070 "RECLOS" 2553458 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1055 2548066 2548265 2548480 "REALSOLV" 2548839 T REALSOLV (NIL) -7 NIL NIL NIL) (-1054 2544513 2545351 2546235 "REAL0Q" 2547231 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1053 2540066 2541102 2542163 "REAL0" 2543494 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1052 2539900 2539953 2539983 "REAL" 2539988 T REAL (NIL) -9 NIL 2540023 NIL) (-1051 2539311 2539617 2539711 "RDUCEAST" 2539828 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1050 2538710 2538788 2538995 "RDIV" 2539233 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1049 2537760 2537952 2538165 "RDIST" 2538532 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1048 2536345 2536644 2537016 "RDETRS" 2537468 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1047 2534139 2534611 2535149 "RDETR" 2535887 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1046 2532758 2533042 2533439 "RDEEFS" 2533855 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1045 2531261 2531573 2531998 "RDEEF" 2532446 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1044 2524749 2528215 2528245 "RCFIELD" 2529540 T RCFIELD (NIL) -9 NIL 2530271 NIL) (-1043 2522705 2523317 2524013 "RCFIELD-" 2524088 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1042 2518868 2520778 2520821 "RCAGG" 2521905 NIL RCAGG (NIL T) -9 NIL 2522370 NIL) (-1041 2518478 2518590 2518753 "RCAGG-" 2518758 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1040 2517795 2517925 2518090 "RATRET" 2518362 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1039 2517336 2517415 2517536 "RATFACT" 2517723 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1038 2516614 2516764 2516916 "RANDSRC" 2517206 T RANDSRC (NIL) -7 NIL NIL NIL) (-1037 2516342 2516392 2516465 "RADUTIL" 2516563 T RADUTIL (NIL) -7 NIL NIL NIL) (-1036 2508503 2515173 2515484 "RADIX" 2516065 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1035 2498129 2508345 2508475 "RADFF" 2508480 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1034 2497758 2497851 2497881 "RADCAT" 2498041 T RADCAT (NIL) -9 NIL NIL NIL) (-1033 2497528 2497588 2497688 "RADCAT-" 2497693 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1032 2495553 2497298 2497390 "QUEUE" 2497471 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1031 2495178 2495227 2495358 "QUATCT2" 2495504 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1030 2487563 2491601 2491643 "QUATCAT" 2492434 NIL QUATCAT (NIL T) -9 NIL 2493200 NIL) (-1029 2483465 2484753 2486136 "QUATCAT-" 2486232 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1028 2479318 2483398 2483446 "QUAT" 2483451 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1027 2476685 2478366 2478409 "QUAGG" 2478790 NIL QUAGG (NIL T) -9 NIL 2478965 NIL) (-1026 2476233 2476507 2476577 "QQUTAST" 2476637 T QQUTAST (NIL) -8 NIL NIL NIL) (-1025 2475144 2475746 2475911 "QFORM" 2476114 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1024 2474769 2474818 2474949 "QFCAT2" 2475095 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1023 2464482 2470616 2470658 "QFCAT" 2471326 NIL QFCAT (NIL T) -9 NIL 2472327 NIL) (-1022 2459852 2461288 2462863 "QFCAT-" 2462959 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2459283 2459417 2459549 "QEQUAT" 2459742 T QEQUAT (NIL) -8 NIL NIL NIL) (-1020 2452301 2453482 2454668 "QCMPACK" 2458216 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2451530 2451712 2451948 "QALGSET2" 2452119 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1018 2448986 2449520 2449948 "QALGSET" 2451187 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2447653 2447895 2448214 "PWFFINTB" 2448759 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1016 2445815 2446013 2446369 "PUSHVAR" 2447467 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1015 2441542 2442758 2442801 "PTRANFN" 2444712 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1014 2439879 2440224 2440548 "PTPACK" 2441253 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1013 2439502 2439565 2439676 "PTFUNC2" 2439816 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1012 2433532 2438291 2438334 "PTCAT" 2438634 NIL PTCAT (NIL T) -9 NIL 2438787 NIL) (-1011 2433181 2433222 2433348 "PSQFR" 2433491 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1010 2431753 2432069 2432405 "PSEUDLIN" 2432879 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1009 2418273 2420848 2423174 "PSETPK" 2429513 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1008 2411092 2414009 2414107 "PSETCAT" 2417148 NIL PSETCAT (NIL T T T T) -9 NIL 2417962 NIL) (-1007 2408817 2409559 2410383 "PSETCAT-" 2410388 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1006 2408130 2408325 2408355 "PSCURVE" 2408627 T PSCURVE (NIL) -9 NIL 2408794 NIL) (-1005 2403853 2405620 2405687 "PSCAT" 2406539 NIL PSCAT (NIL T T T) -9 NIL 2406779 NIL) (-1004 2402847 2403129 2403532 "PSCAT-" 2403537 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1003 2401015 2401906 2402171 "PRTITION" 2402604 T PRTITION (NIL) -8 NIL NIL NIL) (-1002 2400426 2400732 2400826 "PRTDAST" 2400943 T PRTDAST (NIL) -8 NIL NIL NIL) (-1001 2389270 2391692 2393882 "PRS" 2398288 NIL PRS (NIL T T) -7 NIL NIL NIL) (-1000 2386996 2388587 2388629 "PRQAGG" 2388815 NIL PRQAGG (NIL T) -9 NIL 2388917 NIL) (-999 2386175 2386624 2386652 "PROPLOG" 2386791 T PROPLOG (NIL) -9 NIL 2386906 NIL) (-998 2385773 2385836 2385959 "PROPFUN2" 2386098 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-997 2385070 2385209 2385381 "PROPFUN1" 2385634 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-996 2383051 2383817 2384114 "PROPFRML" 2384806 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-995 2382496 2382627 2382755 "PROPERTY" 2382943 T PROPERTY (NIL) -8 NIL NIL NIL) (-994 2376309 2380662 2381482 "PRODUCT" 2381722 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-993 2376099 2376137 2376196 "PRINT" 2376270 T PRINT (NIL) -7 NIL NIL NIL) (-992 2375415 2375556 2375708 "PRIMES" 2375979 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-991 2373462 2373881 2374347 "PRIMELT" 2374994 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-990 2373179 2373240 2373268 "PRIMCAT" 2373392 T PRIMCAT (NIL) -9 NIL NIL NIL) (-989 2372168 2372364 2372592 "PRIMARR2" 2372997 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-988 2368004 2372106 2372151 "PRIMARR" 2372156 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-987 2367641 2367703 2367814 "PREASSOC" 2367942 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-986 2364613 2367099 2367333 "PR" 2367452 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2364064 2364221 2364249 "PPCURVE" 2364454 T PPCURVE (NIL) -9 NIL 2364590 NIL) (-984 2363611 2363859 2363942 "PORTNUM" 2364001 T PORTNUM (NIL) -8 NIL NIL NIL) (-983 2360948 2361369 2361961 "POLYROOT" 2363192 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-982 2360325 2360389 2360623 "POLYLIFT" 2360884 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-981 2356546 2357049 2357678 "POLYCATQ" 2359870 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-980 2342208 2348293 2348358 "POLYCAT" 2351872 NIL POLYCAT (NIL T T T) -9 NIL 2353750 NIL) (-979 2335390 2337561 2339924 "POLYCAT-" 2339929 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-978 2334971 2335045 2335165 "POLY2UP" 2335316 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-977 2334597 2334660 2334769 "POLY2" 2334908 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-976 2327838 2334201 2334361 "POLY" 2334470 NIL POLY (NIL T) -8 NIL NIL NIL) (-975 2326499 2326762 2327038 "POLUTIL" 2327612 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-974 2324818 2325131 2325462 "POLTOPOL" 2326221 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-973 2319928 2324752 2324799 "POINT" 2324804 NIL POINT (NIL T) -8 NIL NIL NIL) (-972 2318061 2318472 2318847 "PNTHEORY" 2319573 T PNTHEORY (NIL) -7 NIL NIL NIL) (-971 2316507 2316816 2317215 "PMTOOLS" 2317759 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-970 2316094 2316178 2316295 "PMSYM" 2316423 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-969 2315596 2315671 2315846 "PMQFCAT" 2316019 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-968 2314977 2315075 2315237 "PMPREDFS" 2315497 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-967 2314320 2314442 2314598 "PMPRED" 2314854 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2312974 2313192 2313570 "PMPLCAT" 2314082 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-965 2312500 2312585 2312737 "PMLSAGG" 2312889 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-964 2311967 2312049 2312231 "PMKERNEL" 2312418 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-963 2311578 2311659 2311772 "PMINS" 2311886 NIL PMINS (NIL T) -7 NIL NIL NIL) (-962 2311014 2311089 2311298 "PMFS" 2311503 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-961 2310230 2310360 2310565 "PMDOWN" 2310891 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-960 2309479 2309613 2309776 "PMASSFS" 2310117 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-959 2308622 2308804 2308985 "PMASS" 2309318 T PMASS (NIL) -7 NIL NIL NIL) (-958 2308271 2308345 2308439 "PLOTTOOL" 2308548 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-957 2303923 2305117 2306039 "PLOT3D" 2307369 T PLOT3D (NIL) -8 NIL NIL NIL) (-956 2302811 2303012 2303247 "PLOT1" 2303727 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-955 2297232 2298622 2299770 "PLOT" 2301683 T PLOT (NIL) -8 NIL NIL NIL) (-954 2272407 2277298 2282149 "PLEQN" 2292498 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-953 2272094 2272147 2272250 "PINTERPA" 2272354 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-952 2271400 2271534 2271714 "PINTERP" 2271959 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2269484 2270650 2270678 "PID" 2270875 T PID (NIL) -9 NIL 2271002 NIL) (-950 2269229 2269272 2269347 "PICOERCE" 2269441 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-949 2268325 2268993 2269080 "PI" 2269120 T PI (NIL) -8 NIL NIL 2269187) (-948 2267633 2267784 2267960 "PGROEB" 2268181 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-947 2263072 2264031 2264937 "PGE" 2266747 T PGE (NIL) -7 NIL NIL NIL) (-946 2261153 2261442 2261808 "PGCD" 2262789 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-945 2260479 2260594 2260755 "PFRPAC" 2261037 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-944 2256739 2259027 2259380 "PFR" 2260158 NIL PFR (NIL T) -8 NIL NIL NIL) (-943 2255092 2255372 2255697 "PFOTOOLS" 2256486 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-942 2253607 2253864 2254215 "PFOQ" 2254849 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-941 2252090 2252320 2252676 "PFO" 2253391 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-940 2249174 2250680 2250708 "PFECAT" 2251301 T PFECAT (NIL) -9 NIL 2251678 NIL) (-939 2248622 2248787 2248994 "PFECAT-" 2248999 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-938 2247195 2247477 2247778 "PFBRU" 2248371 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-937 2245024 2245413 2245845 "PFBR" 2246846 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-936 2240972 2244913 2244982 "PF" 2244987 NIL PF (NIL NIL) -8 NIL NIL NIL) (-935 2236026 2237179 2238049 "PERMGRP" 2240135 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-934 2233938 2235050 2235091 "PERMCAT" 2235491 NIL PERMCAT (NIL T) -9 NIL 2235789 NIL) (-933 2233585 2233632 2233756 "PERMAN" 2233891 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-932 2229387 2231094 2231742 "PERM" 2232970 NIL PERM (NIL T) -8 NIL NIL NIL) (-931 2226744 2229052 2229174 "PENDTREE" 2229298 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-930 2225625 2225888 2225929 "PDSPC" 2226462 NIL PDSPC (NIL T) -9 NIL 2226707 NIL) (-929 2224680 2224946 2225308 "PDSPC-" 2225313 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-928 2223394 2224330 2224371 "PDRING" 2224376 NIL PDRING (NIL T) -9 NIL 2224404 NIL) (-927 2222137 2222899 2222953 "PDMOD" 2222958 NIL PDMOD (NIL T T) -9 NIL 2223062 NIL) (-926 2219304 2220130 2220798 "PDEPROB" 2221489 T PDEPROB (NIL) -8 NIL NIL NIL) (-925 2216813 2217353 2217908 "PDEPACK" 2218769 T PDEPACK (NIL) -7 NIL NIL NIL) (-924 2215701 2215915 2216166 "PDECOMP" 2216612 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-923 2213218 2214109 2214137 "PDECAT" 2214924 T PDECAT (NIL) -9 NIL 2215637 NIL) (-922 2212835 2212902 2212956 "PDDOM" 2213121 NIL PDDOM (NIL T T) -9 NIL 2213201 NIL) (-921 2212648 2212684 2212791 "PDDOM-" 2212796 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-920 2212393 2212432 2212522 "PCOMP" 2212609 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-919 2210433 2211194 2211491 "PBWLB" 2212122 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-918 2210059 2210122 2210231 "PATTERN2" 2210370 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-917 2207768 2208204 2208661 "PATTERN1" 2209648 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-916 2199949 2201841 2203179 "PATTERN" 2206451 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2199507 2199580 2199712 "PATRES2" 2199876 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-914 2196773 2197456 2197937 "PATRES" 2199072 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2194626 2195061 2195468 "PATMATCH" 2196440 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-912 2194080 2194331 2194372 "PATMAB" 2194479 NIL PATMAB (NIL T) -9 NIL 2194562 NIL) (-911 2192526 2192934 2193192 "PATLRES" 2193885 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-910 2192064 2192195 2192236 "PATAB" 2192241 NIL PATAB (NIL T) -9 NIL 2192413 NIL) (-909 2190204 2190641 2191064 "PARTPERM" 2191661 T PARTPERM (NIL) -7 NIL NIL NIL) (-908 2189813 2189888 2189990 "PARSURF" 2190135 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-907 2189439 2189502 2189611 "PARSU2" 2189750 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-906 2189197 2189243 2189310 "PARSER" 2189392 T PARSER (NIL) -7 NIL NIL NIL) (-905 2188806 2188881 2188983 "PARSCURV" 2189128 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-904 2188432 2188495 2188604 "PARSC2" 2188743 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-903 2188059 2188129 2188226 "PARPCURV" 2188368 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-902 2187685 2187748 2187857 "PARPC2" 2187996 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-901 2186674 2187058 2187240 "PARAMAST" 2187523 T PARAMAST (NIL) -8 NIL NIL NIL) (-900 2186182 2186280 2186399 "PAN2EXPR" 2186575 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-899 2184875 2185303 2185531 "PALETTE" 2185974 T PALETTE (NIL) -8 NIL NIL NIL) (-898 2183220 2183880 2184240 "PAIR" 2184561 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-897 2176169 2182477 2182672 "PADICRC" 2183074 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-896 2168442 2175513 2175698 "PADICRAT" 2176016 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-895 2165241 2167102 2167142 "PADICCT" 2167723 NIL PADICCT (NIL NIL) -9 NIL 2168005 NIL) (-894 2163259 2165178 2165223 "PADIC" 2165228 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2162204 2162416 2162684 "PADEPAC" 2163046 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-892 2161404 2161549 2161755 "PADE" 2162066 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-891 2159637 2160612 2160892 "OWP" 2161208 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-890 2159082 2159343 2159440 "OVERSET" 2159560 T OVERSET (NIL) -8 NIL NIL NIL) (-889 2158002 2158687 2158859 "OVAR" 2158950 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-888 2146238 2149111 2151311 "OUTFORM" 2155822 T OUTFORM (NIL) -8 NIL NIL NIL) (-887 2145520 2145835 2145962 "OUTBFILE" 2146131 T OUTBFILE (NIL) -8 NIL NIL NIL) (-886 2144797 2144992 2145020 "OUTBCON" 2145338 T OUTBCON (NIL) -9 NIL 2145504 NIL) (-885 2144380 2144510 2144667 "OUTBCON-" 2144672 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-884 2143620 2143765 2143926 "OUT" 2144239 T OUT (NIL) -7 NIL NIL NIL) (-883 2142916 2143349 2143438 "OSI" 2143551 T OSI (NIL) -8 NIL NIL NIL) (-882 2142335 2142757 2142785 "OSGROUP" 2142790 T OSGROUP (NIL) -9 NIL 2142812 NIL) (-881 2141046 2141307 2141592 "ORTHPOL" 2142082 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-880 2138311 2140881 2141002 "OREUP" 2141007 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-879 2135428 2138002 2138129 "ORESUP" 2138253 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-878 2132928 2133456 2134017 "OREPCTO" 2134917 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-877 2126313 2128801 2128842 "OREPCAT" 2131190 NIL OREPCAT (NIL T) -9 NIL 2132294 NIL) (-876 2123307 2124256 2125307 "OREPCAT-" 2125312 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-875 2122499 2122777 2122805 "ORDTYPE" 2123114 T ORDTYPE (NIL) -9 NIL 2123277 NIL) (-874 2121800 2122016 2122271 "ORDTYPE-" 2122276 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-873 2121156 2121539 2121697 "ORDSTRCT" 2121702 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-872 2120654 2121024 2121052 "ORDSET" 2121057 T ORDSET (NIL) -9 NIL 2121079 NIL) (-871 2119305 2120276 2120304 "ORDRING" 2120309 T ORDRING (NIL) -9 NIL 2120338 NIL) (-870 2118556 2119121 2119149 "ORDMON" 2119154 T ORDMON (NIL) -9 NIL 2119175 NIL) (-869 2117700 2117865 2118060 "ORDFUNS" 2118405 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-868 2116915 2117430 2117458 "ORDFIN" 2117523 T ORDFIN (NIL) -9 NIL 2117597 NIL) (-867 2116169 2116308 2116494 "ORDCOMP2" 2116775 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-866 2112523 2114755 2115164 "ORDCOMP" 2115793 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-865 2109044 2110014 2110828 "OPTPROB" 2111729 T OPTPROB (NIL) -8 NIL NIL NIL) (-864 2105786 2106485 2107189 "OPTPACK" 2108360 T OPTPACK (NIL) -7 NIL NIL NIL) (-863 2103399 2104225 2104253 "OPTCAT" 2105072 T OPTCAT (NIL) -9 NIL 2105722 NIL) (-862 2102717 2103076 2103181 "OPSIG" 2103314 T OPSIG (NIL) -8 NIL NIL NIL) (-861 2102479 2102524 2102590 "OPQUERY" 2102671 T OPQUERY (NIL) -7 NIL NIL NIL) (-860 2101785 2102065 2102106 "OPERCAT" 2102318 NIL OPERCAT (NIL T) -9 NIL 2102415 NIL) (-859 2101528 2101596 2101713 "OPERCAT-" 2101718 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-858 2098446 2099839 2100343 "OP" 2101057 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2097739 2097866 2098040 "ONECOMP2" 2098318 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-856 2094359 2096536 2096905 "ONECOMP" 2097403 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-855 2093760 2093884 2094014 "OMSERVER" 2094249 T OMSERVER (NIL) -7 NIL NIL NIL) (-854 2090383 2093198 2093238 "OMSAGG" 2093299 NIL OMSAGG (NIL T) -9 NIL 2093364 NIL) (-853 2088958 2089269 2089551 "OMPKG" 2090121 T OMPKG (NIL) -7 NIL NIL NIL) (-852 2087305 2088507 2088676 "OMLO" 2088839 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-851 2086241 2086412 2086632 "OMEXPR" 2087131 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-850 2085326 2085662 2085822 "OMERRK" 2086101 T OMERRK (NIL) -8 NIL NIL NIL) (-849 2084563 2084872 2085008 "OMERR" 2085210 T OMERR (NIL) -8 NIL NIL NIL) (-848 2083954 2084240 2084348 "OMENC" 2084475 T OMENC (NIL) -8 NIL NIL NIL) (-847 2077591 2079034 2080205 "OMDEV" 2082803 T OMDEV (NIL) -8 NIL NIL NIL) (-846 2076624 2076831 2077025 "OMCONN" 2077417 T OMCONN (NIL) -8 NIL NIL NIL) (-845 2076030 2076157 2076185 "OM" 2076484 T OM (NIL) -9 NIL NIL NIL) (-844 2074308 2075500 2075528 "OINTDOM" 2075533 T OINTDOM (NIL) -9 NIL 2075554 NIL) (-843 2071390 2072996 2073333 "OFMONOID" 2074003 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-842 2070624 2071327 2071372 "ODVAR" 2071377 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-841 2067770 2070369 2070524 "ODR" 2070529 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-840 2059218 2067546 2067672 "ODPOL" 2067677 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-839 2052633 2059090 2059195 "ODP" 2059200 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-838 2051375 2051614 2051889 "ODETOOLS" 2052407 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-837 2048318 2049000 2049716 "ODESYS" 2050708 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-836 2043148 2044108 2045133 "ODERTRIC" 2047393 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-835 2042568 2042656 2042850 "ODERED" 2043060 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-834 2039428 2040010 2040685 "ODERAT" 2041993 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-833 2036344 2036852 2037449 "ODEPRRIC" 2038957 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-832 2034239 2034883 2035369 "ODEPROB" 2035878 T ODEPROB (NIL) -8 NIL NIL NIL) (-831 2030705 2031244 2031891 "ODEPRIM" 2033718 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-830 2029948 2030056 2030316 "ODEPAL" 2030597 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-829 2026050 2026901 2027765 "ODEPACK" 2029104 T ODEPACK (NIL) -7 NIL NIL NIL) (-828 2025093 2025218 2025440 "ODEINT" 2025939 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-827 2019158 2020619 2022066 "ODEIFTBL" 2023666 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-826 2014522 2015352 2016300 "ODEEF" 2018321 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-825 2013865 2013960 2014183 "ODECONST" 2014427 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-824 2011928 2012637 2012665 "ODECAT" 2013270 T ODECAT (NIL) -9 NIL 2013801 NIL) (-823 2011560 2011609 2011736 "OCTCT2" 2011879 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-822 2008072 2011265 2011387 "OCT" 2011470 NIL OCT (NIL T) -8 NIL NIL NIL) (-821 2007265 2007865 2007893 "OCAMON" 2007898 T OCAMON (NIL) -9 NIL 2007919 NIL) (-820 2001543 2004308 2004348 "OC" 2005445 NIL OC (NIL T) -9 NIL 2006303 NIL) (-819 1998599 1999532 2000515 "OC-" 2000609 NIL OC- (NIL T T) -8 NIL NIL NIL) (-818 1998019 1998444 1998472 "OASGP" 1998477 T OASGP (NIL) -9 NIL 1998497 NIL) (-817 1997115 1997742 1997770 "OAMONS" 1997810 T OAMONS (NIL) -9 NIL 1997853 NIL) (-816 1996291 1996850 1996878 "OAMON" 1996936 T OAMON (NIL) -9 NIL 1996988 NIL) (-815 1996149 1996182 1996250 "OAMON-" 1996255 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-814 1994930 1995683 1995711 "OAGROUP" 1995858 T OAGROUP (NIL) -9 NIL 1995951 NIL) (-813 1994633 1994721 1994839 "OAGROUP-" 1994844 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-812 1994315 1994371 1994460 "NUMTUBE" 1994577 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 1987834 1989406 1990942 "NUMQUAD" 1992799 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 1983514 1984548 1985583 "NUMODE" 1986819 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1980795 1981735 1981763 "NUMINT" 1982686 T NUMINT (NIL) -9 NIL 1983450 NIL) (-808 1979707 1979940 1980158 "NUMFMT" 1980597 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1965890 1969011 1971543 "NUMERIC" 1977214 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1959735 1965338 1965433 "NTSCAT" 1965438 NIL NTSCAT (NIL T T T T) -9 NIL 1965477 NIL) (-805 1958915 1959094 1959287 "NTPOLFN" 1959574 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1958541 1958604 1958713 "NSUP2" 1958852 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1945363 1955366 1956178 "NSUP" 1957762 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1934249 1945137 1945270 "NSMP" 1945275 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1932657 1932982 1933339 "NREP" 1933937 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1931236 1931500 1931858 "NPCOEF" 1932400 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1930284 1930417 1930633 "NORMRETR" 1931117 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1928295 1928615 1929024 "NORMPK" 1929992 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1927974 1928008 1928132 "NORMMA" 1928261 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1927757 1927792 1927861 "NONE1" 1927938 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1927521 1927714 1927743 "NONE" 1927748 T NONE (NIL) -8 NIL NIL NIL) (-794 1927012 1927080 1927259 "NODE1" 1927453 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1925073 1926135 1926390 "NNI" 1926737 T NNI (NIL) -8 NIL NIL 1926972) (-792 1923469 1923806 1924170 "NLINSOL" 1924741 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1919650 1920705 1921604 "NIPROB" 1922590 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1918389 1918641 1918943 "NFINTBAS" 1919412 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1917473 1918039 1918080 "NETCLT" 1918252 NIL NETCLT (NIL T) -9 NIL 1918334 NIL) (-788 1916145 1916412 1916693 "NCODIV" 1917241 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1915901 1915944 1916019 "NCNTFRAC" 1916102 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1914057 1914445 1914865 "NCEP" 1915526 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1912727 1913667 1913695 "NASRING" 1913805 T NASRING (NIL) -9 NIL 1913885 NIL) (-784 1912510 1912566 1912660 "NASRING-" 1912665 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1911477 1912128 1912156 "NARNG" 1912273 T NARNG (NIL) -9 NIL 1912364 NIL) (-782 1911151 1911236 1911370 "NARNG-" 1911375 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1909988 1910237 1910472 "NAGSP" 1910936 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1901032 1902944 1904617 "NAGS" 1908335 T NAGS (NIL) -7 NIL NIL NIL) (-779 1899556 1899888 1900219 "NAGF07" 1900721 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1894028 1895385 1896692 "NAGF04" 1898269 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1886900 1888610 1890243 "NAGF02" 1892415 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1882064 1883224 1884341 "NAGF01" 1885803 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1875644 1877258 1878843 "NAGE04" 1880499 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1866705 1868934 1871064 "NAGE02" 1873534 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1862598 1863605 1864569 "NAGE01" 1865761 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1860375 1860927 1861485 "NAGD03" 1862060 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1852071 1854053 1856007 "NAGD02" 1858441 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1845810 1847307 1848747 "NAGD01" 1850651 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1841947 1842841 1843678 "NAGC06" 1844993 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1840394 1840744 1841100 "NAGC05" 1841611 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1839758 1839889 1840033 "NAGC02" 1840270 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1838559 1839286 1839326 "NAALG" 1839405 NIL NAALG (NIL T) -9 NIL 1839466 NIL) (-765 1838388 1838423 1838513 "NAALG-" 1838518 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1832260 1833446 1834633 "MULTSQFR" 1837284 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1831567 1831654 1831838 "MULTFACT" 1832172 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1823712 1828150 1828203 "MTSCAT" 1829273 NIL MTSCAT (NIL T T) -9 NIL 1829789 NIL) (-761 1823418 1823478 1823570 "MTHING" 1823652 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1823204 1823243 1823303 "MSYSCMD" 1823378 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1820060 1822765 1822806 "MSETAGG" 1822811 NIL MSETAGG (NIL T) -9 NIL 1822845 NIL) (-758 1815888 1818815 1819135 "MSET" 1819773 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1811492 1813267 1814012 "MRING" 1815188 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1811052 1811125 1811256 "MRF2" 1811419 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1810664 1810705 1810849 "MRATFAC" 1811011 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1808234 1808571 1809002 "MPRFF" 1810369 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1801594 1808088 1808185 "MPOLY" 1808190 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1801078 1801119 1801327 "MPCPF" 1801553 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1800586 1800635 1800819 "MPC3" 1801029 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1799769 1799862 1800083 "MPC2" 1800501 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1798046 1798407 1798797 "MONOTOOL" 1799429 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1797191 1797574 1797602 "MONOID" 1797821 T MONOID (NIL) -9 NIL 1797968 NIL) (-747 1796707 1796856 1797037 "MONOID-" 1797042 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1785689 1792527 1792586 "MONOGEN" 1793260 NIL MONOGEN (NIL T T) -9 NIL 1793716 NIL) (-745 1782760 1783656 1784649 "MONOGEN-" 1784768 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1781477 1782025 1782053 "MONADWU" 1782445 T MONADWU (NIL) -9 NIL 1782683 NIL) (-743 1780807 1781008 1781256 "MONADWU-" 1781261 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1780092 1780396 1780424 "MONAD" 1780631 T MONAD (NIL) -9 NIL 1780743 NIL) (-741 1779759 1779855 1779987 "MONAD-" 1779992 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1777898 1778672 1778951 "MOEBIUS" 1779512 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1777066 1777566 1777606 "MODULE" 1777611 NIL MODULE (NIL T) -9 NIL 1777650 NIL) (-738 1776604 1776730 1776920 "MODULE-" 1776925 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1774178 1775012 1775339 "MODRING" 1776428 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1770909 1772283 1772804 "MODOP" 1773707 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1769395 1769976 1770253 "MODMONOM" 1770772 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1758190 1767686 1768100 "MODMON" 1769032 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1755049 1757058 1757334 "MODFIELD" 1758065 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1753960 1754330 1754520 "MMLFORM" 1754879 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1753480 1753529 1753708 "MMAP" 1753911 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1751373 1752312 1752353 "MLO" 1752776 NIL MLO (NIL T) -9 NIL 1753018 NIL) (-729 1748721 1749255 1749857 "MLIFT" 1750854 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1748100 1748196 1748350 "MKUCFUNC" 1748632 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1747693 1747769 1747892 "MKRECORD" 1748023 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1746716 1746902 1747130 "MKFUNC" 1747504 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1746092 1746208 1746364 "MKFLCFN" 1746599 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1745357 1745471 1745656 "MKBCFUNC" 1745985 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1741356 1744911 1745047 "MINT" 1745241 T MINT (NIL) -8 NIL NIL NIL) (-722 1740138 1740411 1740688 "MHROWRED" 1741111 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1734898 1738673 1739078 "MFLOAT" 1739753 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1734243 1734331 1734502 "MFINFACT" 1734810 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1730542 1731421 1732300 "MESH" 1733384 T MESH (NIL) -7 NIL NIL NIL) (-718 1728896 1729244 1729597 "MDDFACT" 1730229 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1725543 1728027 1728068 "MDAGG" 1728323 NIL MDAGG (NIL T) -9 NIL 1728466 NIL) (-716 1713279 1724836 1725043 "MCMPLX" 1725356 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1712398 1712562 1712763 "MCDEN" 1713128 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1710246 1710558 1710938 "MCALCFN" 1712128 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1709123 1709411 1709644 "MAYBE" 1710052 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1706681 1707258 1707820 "MATSTOR" 1708594 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1702216 1706053 1706301 "MATRIX" 1706466 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1697916 1698689 1699425 "MATLIN" 1701573 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1696492 1696663 1696996 "MATCAT2" 1697751 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1685939 1689546 1689623 "MATCAT" 1694658 NIL MATCAT (NIL T T T) -9 NIL 1696130 NIL) (-707 1681892 1683202 1684615 "MATCAT-" 1684620 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1679968 1680328 1680712 "MAPPKG3" 1681567 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1678925 1679122 1679344 "MAPPKG2" 1679792 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1677382 1677708 1678035 "MAPPKG1" 1678631 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1676383 1676788 1676965 "MAPPAST" 1677225 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1675988 1676052 1676175 "MAPHACK3" 1676319 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1675568 1675641 1675755 "MAPHACK2" 1675920 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1674994 1675109 1675251 "MAPHACK1" 1675459 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1672917 1673694 1673998 "MAGMA" 1674722 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1672336 1672641 1672732 "MACROAST" 1672846 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1668693 1670575 1671036 "M3D" 1671908 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1662167 1667004 1667045 "LZSTAGG" 1667827 NIL LZSTAGG (NIL T) -9 NIL 1668122 NIL) (-695 1657849 1659298 1660755 "LZSTAGG-" 1660760 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1654762 1655740 1656227 "LWORD" 1657394 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1654284 1654566 1654641 "LSTAST" 1654707 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1646357 1654055 1654189 "LSQM" 1654194 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1645575 1645720 1645948 "LSPP" 1646212 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1642375 1643074 1643787 "LSMP1" 1644894 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1640180 1640504 1640953 "LSMP" 1642071 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1633310 1639270 1639311 "LSAGG" 1639373 NIL LSAGG (NIL T) -9 NIL 1639451 NIL) (-687 1629819 1630929 1632142 "LSAGG-" 1632147 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1627114 1628963 1629212 "LPOLY" 1629614 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1626690 1626781 1626904 "LPEFRAC" 1627023 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1626373 1626452 1626480 "LOGIC" 1626591 T LOGIC (NIL) -9 NIL 1626673 NIL) (-683 1626229 1626258 1626329 "LOGIC-" 1626334 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1625404 1625562 1625755 "LODOOPS" 1626085 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1623928 1624177 1624530 "LODOF" 1625151 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1619818 1622563 1622604 "LODOCAT" 1623042 NIL LODOCAT (NIL T) -9 NIL 1623253 NIL) (-679 1619533 1619609 1619736 "LODOCAT-" 1619741 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1616533 1619374 1619492 "LODO2" 1619497 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1613654 1616470 1616515 "LODO1" 1616520 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1610763 1613570 1613636 "LODO" 1613641 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1609632 1609809 1610114 "LODEEF" 1610586 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1607618 1608726 1608979 "LO" 1609464 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1602701 1605784 1605825 "LNAGG" 1606687 NIL LNAGG (NIL T) -9 NIL 1607122 NIL) (-672 1601794 1602062 1602404 "LNAGG-" 1602409 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1597774 1598719 1599358 "LMOPS" 1601209 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1597073 1597551 1597592 "LMODULE" 1597597 NIL LMODULE (NIL T) -9 NIL 1597623 NIL) (-669 1594142 1596718 1596841 "LMDICT" 1596983 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1593718 1593932 1593973 "LLINSET" 1594034 NIL LLINSET (NIL T) -9 NIL 1594078 NIL) (-667 1593363 1593626 1593686 "LITERAL" 1593691 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1592882 1592962 1593101 "LIST3" 1593283 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1590980 1591328 1591727 "LIST2MAP" 1592529 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1589969 1590165 1590393 "LIST2" 1590798 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1582425 1588903 1589207 "LIST" 1589698 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1582008 1582244 1582285 "LINSET" 1582290 NIL LINSET (NIL T) -9 NIL 1582324 NIL) (-661 1580822 1581516 1581683 "LINFORM" 1581893 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1579121 1579849 1579890 "LINEXP" 1580380 NIL LINEXP (NIL T) -9 NIL 1580653 NIL) (-659 1577697 1578601 1578782 "LINELT" 1578992 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1576254 1576534 1576845 "LINDEP" 1577449 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1575390 1575986 1576096 "LINBASIS" 1576184 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1572198 1572928 1573686 "LIMITRF" 1574664 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1570506 1570813 1571215 "LIMITPS" 1571900 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1569334 1569909 1569949 "LIECAT" 1570089 NIL LIECAT (NIL T) -9 NIL 1570240 NIL) (-653 1569169 1569202 1569290 "LIECAT-" 1569295 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1563221 1568680 1568908 "LIE" 1568990 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1555522 1562761 1562917 "LIB" 1563085 T LIB (NIL) -8 NIL NIL NIL) (-650 1551091 1552040 1552975 "LGROBP" 1554639 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1549715 1550623 1550651 "LFCAT" 1550858 T LFCAT (NIL) -9 NIL 1550997 NIL) (-648 1547653 1547987 1548337 "LF" 1549436 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1544513 1545185 1545873 "LEXTRIPK" 1547017 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1541101 1542083 1542586 "LEXP" 1544093 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1540517 1540822 1540914 "LETAST" 1541029 T LETAST (NIL) -8 NIL NIL NIL) (-644 1538903 1539228 1539629 "LEADCDET" 1540199 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1538081 1538167 1538396 "LAZM3PK" 1538824 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1532620 1536158 1536696 "LAUPOL" 1537593 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1532193 1532243 1532404 "LAPLACE" 1532570 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1531041 1531757 1531798 "LALG" 1531860 NIL LALG (NIL T) -9 NIL 1531919 NIL) (-639 1530737 1530814 1530950 "LALG-" 1530955 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1528474 1529838 1530089 "LA" 1530570 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1528303 1528333 1528374 "KVTFROM" 1528436 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1527060 1527670 1527855 "KTVLOGIC" 1528138 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1526889 1526919 1526960 "KRCFROM" 1527022 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1525781 1525980 1526279 "KOVACIC" 1526689 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1525610 1525640 1525681 "KONVERT" 1525743 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1525439 1525469 1525510 "KOERCE" 1525572 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1524923 1525016 1525148 "KERNEL2" 1525353 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1522610 1523516 1523893 "KERNEL" 1524579 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1516192 1521087 1521141 "KDAGG" 1521518 NIL KDAGG (NIL T T) -9 NIL 1521724 NIL) (-628 1515703 1515845 1516050 "KDAGG-" 1516055 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1508519 1515364 1515519 "KAFILE" 1515581 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1508123 1508408 1508471 "JVMOP" 1508476 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1506859 1507363 1507612 "JVMMDACC" 1507894 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1505795 1506249 1506454 "JVMFDACC" 1506674 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1504376 1504871 1505171 "JVMCSTTG" 1505515 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1503512 1503916 1504077 "JVMCFACC" 1504235 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1503190 1503429 1503478 "JVMBCODE" 1503483 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1497241 1502701 1502929 "JORDAN" 1503011 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1496554 1496890 1497011 "JOINAST" 1497140 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1492700 1494731 1494785 "IXAGG" 1495714 NIL IXAGG (NIL T T) -9 NIL 1496173 NIL) (-617 1491553 1491925 1492344 "IXAGG-" 1492349 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1486756 1491475 1491534 "IVECTOR" 1491539 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1485481 1485759 1486025 "ITUPLE" 1486523 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1483953 1484160 1484455 "ITRIGMNP" 1485303 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1482680 1482902 1483185 "ITFUN3" 1483729 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1482278 1482341 1482464 "ITFUN2" 1482603 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1481383 1481758 1481932 "ITFORM" 1482124 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1479152 1480403 1480681 "ITAYLOR" 1481138 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1467556 1473289 1474452 "ISUPS" 1478022 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1466648 1466800 1467036 "ISUMP" 1467403 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1461612 1466593 1466634 "ISTRING" 1466639 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1461028 1461333 1461425 "ISAST" 1461540 T ISAST (NIL) -8 NIL NIL NIL) (-605 1460226 1460319 1460535 "IRURPK" 1460942 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1459138 1459363 1459603 "IRSN" 1460006 T IRSN (NIL) -7 NIL NIL NIL) (-603 1457183 1457564 1457993 "IRRF2F" 1458776 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1456924 1456968 1457044 "IRREDFFX" 1457139 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1455497 1455798 1456097 "IROOT" 1456657 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1454636 1454990 1455141 "IRFORM" 1455366 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1453718 1453849 1454063 "IR2F" 1454519 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1451307 1451826 1452392 "IR2" 1453196 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1447747 1448991 1449683 "IR" 1450647 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1447532 1447572 1447632 "IPRNTPK" 1447707 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1443508 1447421 1447490 "IPF" 1447495 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1441538 1443433 1443490 "IPADIC" 1443495 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1440796 1441098 1441228 "IP4ADDR" 1441428 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1440134 1440425 1440557 "IOMODE" 1440684 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1439105 1439731 1439858 "IOBFILE" 1440027 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1438515 1439009 1439037 "IOBCON" 1439042 T IOBCON (NIL) -9 NIL 1439063 NIL) (-589 1438020 1438084 1438267 "INVLAPLA" 1438451 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1427638 1430058 1432432 "INTTR" 1435696 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1423931 1424715 1425580 "INTTOOLS" 1426823 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1423511 1423608 1423725 "INTSLPE" 1423834 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1420978 1423434 1423493 "INTRVL" 1423498 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1418556 1419092 1419667 "INTRF" 1420463 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1417949 1418064 1418206 "INTRET" 1418454 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1415922 1416335 1416805 "INTRAT" 1417557 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1413167 1413768 1414387 "INTPM" 1415407 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1409907 1410527 1411258 "INTPAF" 1412560 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1405008 1406048 1407099 "INTPACK" 1408876 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1404254 1404412 1404620 "INTHERTR" 1404850 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1403687 1403773 1403961 "INTHERAL" 1404168 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1401455 1401976 1402433 "INTHEORY" 1403250 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1392845 1394522 1396276 "INTG0" 1399825 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1379070 1382483 1385868 "INTFTBL" 1389480 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1378295 1378457 1378630 "INTFACT" 1378929 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1375698 1376172 1376727 "INTEF" 1377851 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1373895 1374790 1374818 "INTDOM" 1375119 T INTDOM (NIL) -9 NIL 1375326 NIL) (-570 1373234 1373438 1373680 "INTDOM-" 1373685 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1369102 1371523 1371577 "INTCAT" 1372376 NIL INTCAT (NIL T) -9 NIL 1372697 NIL) (-568 1368556 1368677 1368805 "INTBIT" 1368994 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1367237 1367409 1367716 "INTALG" 1368401 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1366714 1366810 1366967 "INTAF" 1367141 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1359797 1366524 1366664 "INTABL" 1366669 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1359038 1359600 1359665 "INT8" 1359699 T INT8 (NIL) -8 NIL NIL 1359744) (-563 1358278 1358840 1358905 "INT64" 1358939 T INT64 (NIL) -8 NIL NIL 1358984) (-562 1357518 1358080 1358145 "INT32" 1358179 T INT32 (NIL) -8 NIL NIL 1358224) (-561 1356758 1357320 1357385 "INT16" 1357419 T INT16 (NIL) -8 NIL NIL 1357464) (-560 1352964 1356555 1356664 "INT" 1356669 T INT (NIL) -8 NIL NIL NIL) (-559 1347075 1350512 1350540 "INS" 1351474 T INS (NIL) -9 NIL 1352139 NIL) (-558 1344232 1345152 1346093 "INS-" 1346166 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1343062 1343285 1343561 "INPSIGN" 1344007 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1342156 1342297 1342494 "INPRODPF" 1342942 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1341026 1341167 1341404 "INPRODFF" 1342036 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1340014 1340178 1340438 "INNMFACT" 1340862 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1339193 1339308 1339496 "INMODGCD" 1339913 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1337677 1337946 1338270 "INFSP" 1338938 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1336837 1336978 1337161 "INFPROD0" 1337557 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1336435 1336507 1336605 "INFORM1" 1336772 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1333002 1334500 1335015 "INFORM" 1335928 T INFORM (NIL) -8 NIL NIL NIL) (-548 1332507 1332614 1332728 "INFINITY" 1332908 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1331581 1332227 1332328 "INETCLTS" 1332426 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1330179 1330447 1330768 "INEP" 1331329 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1329209 1330076 1330141 "INDE" 1330146 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1328761 1328841 1328958 "INCRMAPS" 1329136 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1327483 1328030 1328236 "INBFILE" 1328575 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1322663 1323719 1324663 "INBFF" 1326571 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1321517 1321840 1321868 "INBCON" 1322381 T INBCON (NIL) -9 NIL 1322647 NIL) (-540 1320727 1320992 1321268 "INBCON-" 1321273 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1320146 1320451 1320542 "INAST" 1320656 T INAST (NIL) -8 NIL NIL NIL) (-538 1319513 1319825 1319931 "IMPTAST" 1320060 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1315547 1319357 1319461 "IMATRIX" 1319466 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1314239 1314378 1314694 "IMATQF" 1315403 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1312419 1312686 1313023 "IMATLIN" 1313995 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1306336 1312343 1312401 "ILIST" 1312406 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1304116 1306196 1306309 "IIARRAY2" 1306314 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1298939 1304027 1304091 "IFF" 1304096 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1298220 1298556 1298672 "IFAST" 1298843 T IFAST (NIL) -8 NIL NIL NIL) (-530 1292846 1297512 1297700 "IFARRAY" 1298077 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1291884 1292750 1292823 "IFAMON" 1292828 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1291456 1291533 1291587 "IEVALAB" 1291794 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1291119 1291199 1291359 "IEVALAB-" 1291364 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1290152 1291008 1291083 "IDPOAMS" 1291088 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1289254 1290041 1290116 "IDPOAM" 1290121 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1288635 1289169 1289231 "IDPO" 1289236 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1287115 1287642 1287694 "IDPC" 1288206 NIL IDPC (NIL T T) -9 NIL 1288487 NIL) (-522 1286447 1287007 1287080 "IDPAM" 1287085 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1285662 1286339 1286412 "IDPAG" 1286417 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1285206 1285468 1285558 "IDENT" 1285592 T IDENT (NIL) -8 NIL NIL NIL) (-519 1281425 1282309 1283204 "IDECOMP" 1284363 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1274060 1275348 1276395 "IDEAL" 1280461 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1273202 1273332 1273532 "ICDEN" 1273944 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1272177 1272682 1272829 "ICARD" 1273075 T ICARD (NIL) -8 NIL NIL NIL) (-515 1270207 1270550 1270955 "IBPTOOLS" 1271854 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1265436 1269827 1269940 "IBITS" 1270126 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1262111 1262735 1263430 "IBATOOL" 1264853 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1259872 1260352 1260885 "IBACHIN" 1261646 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1257576 1259718 1259821 "IARRAY2" 1259826 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1253403 1257502 1257559 "IARRAY1" 1257564 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1246429 1251815 1252296 "IAN" 1252942 T IAN (NIL) -8 NIL NIL NIL) (-508 1245934 1245997 1246170 "IALGFACT" 1246366 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1245426 1245575 1245603 "HYPCAT" 1245810 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1244928 1245081 1245267 "HYPCAT-" 1245272 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1244475 1244723 1244806 "HOSTNAME" 1244865 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1244308 1244357 1244398 "HOMOTOP" 1244403 NIL HOMOTOP (NIL T) -9 NIL 1244436 NIL) (-503 1240852 1242240 1242281 "HOAGG" 1243262 NIL HOAGG (NIL T) -9 NIL 1243991 NIL) (-502 1239368 1239845 1240371 "HOAGG-" 1240376 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1232441 1238961 1239111 "HEXADEC" 1239238 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1231153 1231411 1231674 "HEUGCD" 1232218 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1230085 1230990 1231120 "HELLFDIV" 1231125 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1228207 1229860 1229949 "HEAP" 1230028 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1227404 1227759 1227893 "HEADAST" 1228093 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1220863 1227319 1227381 "HDP" 1227386 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1213908 1220498 1220650 "HDMP" 1220764 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1213214 1213372 1213536 "HB" 1213764 T HB (NIL) -7 NIL NIL NIL) (-493 1206340 1213060 1213164 "HASHTBL" 1213169 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1205756 1206061 1206153 "HASAST" 1206268 T HASAST (NIL) -8 NIL NIL NIL) (-491 1203173 1205378 1205560 "HACKPI" 1205594 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1198486 1203026 1203139 "GTSET" 1203144 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1191641 1198364 1198462 "GSTBL" 1198467 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1183406 1190806 1191062 "GSERIES" 1191441 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1182437 1182950 1182978 "GROUP" 1183181 T GROUP (NIL) -9 NIL 1183315 NIL) (-486 1181761 1181962 1182213 "GROUP-" 1182218 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1180110 1180449 1180836 "GROEBSOL" 1181438 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1178938 1179298 1179349 "GRMOD" 1179878 NIL GRMOD (NIL T T) -9 NIL 1180046 NIL) (-483 1178694 1178742 1178870 "GRMOD-" 1178875 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1173834 1175048 1176048 "GRIMAGE" 1177714 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1172228 1172561 1172885 "GRDEF" 1173530 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1171660 1171788 1171929 "GRAY" 1172107 T GRAY (NIL) -7 NIL NIL NIL) (-479 1170737 1171239 1171290 "GRALG" 1171443 NIL GRALG (NIL T T) -9 NIL 1171536 NIL) (-478 1170374 1170471 1170634 "GRALG-" 1170639 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1166969 1169957 1170136 "GPOLSET" 1170280 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1166317 1166380 1166638 "GOSPER" 1166906 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1161887 1162755 1163281 "GMODPOL" 1166016 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1160874 1161076 1161314 "GHENSEL" 1161699 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1154946 1155873 1156893 "GENUPS" 1159958 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1154637 1154694 1154783 "GENUFACT" 1154889 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1154037 1154126 1154291 "GENPGCD" 1154555 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1153505 1153546 1153759 "GENMFACT" 1153996 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1152042 1152328 1152635 "GENEEZ" 1153248 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1145246 1151653 1151815 "GDMP" 1151965 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1134006 1139017 1140123 "GCNAALG" 1144229 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1132133 1133181 1133209 "GCDDOM" 1133464 T GCDDOM (NIL) -9 NIL 1133621 NIL) (-465 1131573 1131730 1131945 "GCDDOM-" 1131950 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1120045 1122519 1124911 "GBINTERN" 1129264 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1117846 1118174 1118595 "GBF" 1119720 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1116603 1116792 1117059 "GBEUCLID" 1117662 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1115253 1115460 1115764 "GB" 1116382 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1114584 1114727 1114876 "GAUSSFAC" 1115124 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1112905 1113253 1113567 "GALUTIL" 1114303 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1111165 1111487 1111811 "GALPOLYU" 1112632 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1108464 1108820 1109227 "GALFACTU" 1110862 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1100078 1101769 1103377 "GALFACT" 1106896 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1097364 1098124 1098152 "FVFUN" 1099308 T FVFUN (NIL) -9 NIL 1100028 NIL) (-454 1096594 1096812 1096840 "FVC" 1097131 T FVC (NIL) -9 NIL 1097314 NIL) (-453 1096195 1096419 1096487 "FUNDESC" 1096546 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1095768 1095992 1096073 "FUNCTION" 1096147 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1094445 1095069 1095272 "FTEM" 1095585 T FTEM (NIL) -8 NIL NIL NIL) (-450 1092087 1092776 1093239 "FT" 1094002 T FT (NIL) -8 NIL NIL NIL) (-449 1090356 1090667 1091064 "FSUPFACT" 1091778 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1088675 1089042 1089374 "FST" 1090044 T FST (NIL) -8 NIL NIL NIL) (-447 1087856 1087980 1088168 "FSRED" 1088557 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1086545 1086811 1087158 "FSPRMELT" 1087571 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1083755 1084289 1084775 "FSPECF" 1086108 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1083277 1083337 1083507 "FSINT" 1083696 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1081413 1082270 1082573 "FSERIES" 1083056 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1080437 1080571 1080795 "FSCINT" 1081293 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1079461 1079622 1079849 "FSAGG2" 1080290 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1075436 1078405 1078446 "FSAGG" 1078816 NIL FSAGG (NIL T) -9 NIL 1079075 NIL) (-439 1073036 1073799 1074595 "FSAGG-" 1074690 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1070696 1070994 1071542 "FS2UPS" 1072754 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1069562 1069745 1070047 "FS2EXPXP" 1070521 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1069190 1069239 1069368 "FS2" 1069513 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1049457 1058964 1059005 "FS" 1062889 NIL FS (NIL T) -9 NIL 1065178 NIL) (-434 1037599 1041147 1045177 "FS-" 1045477 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1037013 1037140 1037292 "FRUTIL" 1037479 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1031556 1034702 1034742 "FRNAALG" 1036062 NIL FRNAALG (NIL T) -9 NIL 1036660 NIL) (-431 1027088 1028339 1029597 "FRNAALG-" 1030347 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1026720 1026769 1026896 "FRNAAF2" 1027039 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1025007 1025569 1025865 "FRMOD" 1026532 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1024192 1024285 1024576 "FRIDEAL2" 1024914 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1021797 1022567 1022885 "FRIDEAL" 1023983 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1020895 1021344 1021385 "FRETRCT" 1021390 NIL FRETRCT (NIL T) -9 NIL 1021566 NIL) (-425 1019974 1020252 1020596 "FRETRCT-" 1020601 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1016795 1018258 1018317 "FRAMALG" 1019199 NIL FRAMALG (NIL T T) -9 NIL 1019491 NIL) (-423 1014833 1015384 1016014 "FRAMALG-" 1016237 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1014463 1014526 1014633 "FRAC2" 1014770 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1007472 1013936 1014213 "FRAC" 1014218 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1007102 1007165 1007272 "FR2" 1007409 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 998134 1002678 1004009 "FR" 1005803 NIL FR (NIL T) -8 NIL NIL NIL) (-418 992057 995513 995541 "FPS" 996660 T FPS (NIL) -9 NIL 997217 NIL) (-417 991482 991615 991779 "FPS-" 991925 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 988450 990439 990467 "FPC" 990692 T FPC (NIL) -9 NIL 990834 NIL) (-415 988231 988283 988380 "FPC-" 988385 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 986989 987719 987760 "FPATMAB" 987765 NIL FPATMAB (NIL T) -9 NIL 987917 NIL) (-413 985132 985731 986078 "FPARFRAC" 986705 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 980463 981063 981745 "FORTRAN" 984564 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 978037 978701 978729 "FORTFN" 979789 T FORTFN (NIL) -9 NIL 980413 NIL) (-410 977789 977851 977879 "FORTCAT" 977938 T FORTCAT (NIL) -9 NIL 978000 NIL) (-409 975475 976005 976544 "FORT" 977270 T FORT (NIL) -7 NIL NIL NIL) (-408 975257 975293 975362 "FORMULA1" 975439 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 973261 973873 974263 "FORMULA" 974887 T FORMULA (NIL) -8 NIL NIL NIL) (-406 972778 972836 973009 "FORDER" 973203 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 971838 972038 972231 "FOP" 972605 T FOP (NIL) -7 NIL NIL NIL) (-404 970251 971118 971292 "FNLA" 971720 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 968870 969381 969409 "FNCAT" 969869 T FNCAT (NIL) -9 NIL 970129 NIL) (-402 968313 968829 968857 "FNAME" 968862 T FNAME (NIL) -8 NIL NIL NIL) (-401 966639 967812 967840 "FMTC" 967845 T FMTC (NIL) -9 NIL 967881 NIL) (-400 965195 966575 966621 "FMONOID" 966626 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 961784 963150 963191 "FMONCAT" 964408 NIL FMONCAT (NIL T) -9 NIL 965013 NIL) (-398 959106 959854 959882 "FMFUN" 961026 T FMFUN (NIL) -9 NIL 961734 NIL) (-397 955979 957031 957085 "FMCAT" 958280 NIL FMCAT (NIL T T) -9 NIL 958775 NIL) (-396 955212 955429 955457 "FMC" 955747 T FMC (NIL) -9 NIL 955929 NIL) (-395 953880 954978 955078 "FM1" 955157 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 952898 953622 953771 "FM" 953776 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 950636 951088 951582 "FLOATRP" 952449 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 948038 948574 949152 "FLOATCP" 950103 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 940705 945767 946388 "FLOAT" 947437 T FLOAT (NIL) -8 NIL NIL NIL) (-390 939223 940297 940338 "FLINEXP" 940343 NIL FLINEXP (NIL T) -9 NIL 940436 NIL) (-389 938353 938612 938940 "FLINEXP-" 938945 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 937411 937573 937797 "FLASORT" 938205 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 934329 935381 935433 "FLALG" 936660 NIL FLALG (NIL T T) -9 NIL 937127 NIL) (-386 933353 933514 933741 "FLAGG2" 934182 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 926722 930762 930803 "FLAGG" 932065 NIL FLAGG (NIL T) -9 NIL 932717 NIL) (-384 925376 925787 926277 "FLAGG-" 926282 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 922014 923221 923280 "FINRALG" 924408 NIL FINRALG (NIL T T) -9 NIL 924916 NIL) (-382 921138 921403 921742 "FINRALG-" 921747 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 920444 920743 920771 "FINITE" 920967 T FINITE (NIL) -9 NIL 921074 NIL) (-380 912395 914974 915014 "FINAALG" 918681 NIL FINAALG (NIL T) -9 NIL 920134 NIL) (-379 907511 908777 909921 "FINAALG-" 911300 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 906071 906493 906547 "FILECAT" 907231 NIL FILECAT (NIL T T) -9 NIL 907447 NIL) (-377 905349 905826 905929 "FILE" 906001 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 902754 904579 904607 "FIELD" 904647 T FIELD (NIL) -9 NIL 904727 NIL) (-375 901296 901759 902270 "FIELD-" 902275 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 898979 899931 900278 "FGROUP" 900982 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 898051 898233 898453 "FGLMICPK" 898811 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 893308 897976 898033 "FFX" 898038 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 892903 892970 893105 "FFSLPE" 893241 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 892401 892443 892652 "FFPOLY2" 892861 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 888277 889173 889969 "FFPOLY" 891637 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 883548 888196 888259 "FFP" 888264 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 878081 882891 883081 "FFNBX" 883402 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 872416 877216 877474 "FFNBP" 877935 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 866456 871700 871911 "FFNB" 872249 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 865276 865486 865801 "FFINTBAS" 866253 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 860871 863523 863551 "FFIELDC" 864171 T FFIELDC (NIL) -9 NIL 864547 NIL) (-362 859491 859932 860415 "FFIELDC-" 860420 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 859048 859106 859230 "FFHOM" 859433 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 856707 857230 857747 "FFF" 858563 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 851744 856449 856550 "FFCGX" 856650 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 846785 851476 851583 "FFCGP" 851687 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 841387 846512 846620 "FFCG" 846721 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 840792 840841 841076 "FFCAT2" 841338 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 819483 830524 830610 "FFCAT" 835775 NIL FFCAT (NIL T T T) -9 NIL 837226 NIL) (-354 814494 815728 817042 "FFCAT-" 818272 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 809317 814405 814469 "FF" 814474 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 797972 802289 803509 "FEXPR" 808169 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 796900 797369 797410 "FEVALAB" 797494 NIL FEVALAB (NIL T) -9 NIL 797755 NIL) (-350 796017 796269 796607 "FEVALAB-" 796612 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 792879 793764 793879 "FDIVCAT" 795447 NIL FDIVCAT (NIL T T T T) -9 NIL 795884 NIL) (-348 792635 792668 792838 "FDIVCAT-" 792843 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 791849 791942 792219 "FDIV2" 792542 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 790259 791232 791435 "FDIV" 791748 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 789167 789554 789756 "FCTRDATA" 790077 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 787823 788112 788401 "FCPAK1" 788898 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 786826 787323 787464 "FCOMP" 787714 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 770140 773976 777514 "FC" 783308 T FC (NIL) -8 NIL NIL NIL) (-341 761851 766461 766501 "FAXF" 768303 NIL FAXF (NIL T) -9 NIL 768995 NIL) (-340 758992 759799 760617 "FAXF-" 761082 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 753675 758368 758544 "FARRAY" 758849 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 748247 750622 750675 "FAMR" 751698 NIL FAMR (NIL T T) -9 NIL 752158 NIL) (-337 747071 747439 747874 "FAMR-" 747879 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 746098 746993 747046 "FAMONOID" 747051 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 743728 744580 744633 "FAMONC" 745574 NIL FAMONC (NIL T T) -9 NIL 745960 NIL) (-334 742202 743482 743619 "FAGROUP" 743624 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 739955 740316 740719 "FACUTIL" 741883 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 739042 739239 739461 "FACTFUNC" 739765 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 730785 738345 738544 "EXPUPXS" 738898 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 728238 728808 729394 "EXPRTUBE" 730219 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 724449 725101 725831 "EXPRODE" 727577 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 718883 719590 720396 "EXPR2UPS" 723747 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 718509 718572 718681 "EXPR2" 718820 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 702878 717158 717587 "EXPR" 718113 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 693237 702029 702320 "EXPEXPAN" 702714 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 692657 692961 693052 "EXITAST" 693166 T EXITAST (NIL) -8 NIL NIL NIL) (-323 692421 692614 692643 "EXIT" 692648 T EXIT (NIL) -8 NIL NIL NIL) (-322 692042 692110 692223 "EVALCYC" 692353 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 691559 691701 691742 "EVALAB" 691912 NIL EVALAB (NIL T) -9 NIL 692016 NIL) (-320 691016 691162 691383 "EVALAB-" 691388 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 688131 689672 689700 "EUCDOM" 690255 T EUCDOM (NIL) -9 NIL 690605 NIL) (-318 686491 686992 687575 "EUCDOM-" 687580 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 686117 686180 686289 "ESTOOLS2" 686428 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 685862 685910 685990 "ESTOOLS1" 686069 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 673179 676160 678910 "ESTOOLS" 683132 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 672918 672956 673038 "ESCONT1" 673141 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 669226 670053 670833 "ESCONT" 672158 T ESCONT (NIL) -7 NIL NIL NIL) (-312 668895 668951 669051 "ES2" 669170 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 668519 668583 668692 "ES1" 668831 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 662220 664150 664178 "ES" 666946 T ES (NIL) -9 NIL 668356 NIL) (-309 656897 658454 660271 "ES-" 660435 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 656089 656242 656418 "ERROR" 656741 T ERROR (NIL) -7 NIL NIL NIL) (-307 649221 655948 656039 "EQTBL" 656044 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 648847 648910 649019 "EQ2" 649158 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 641106 644161 645610 "EQ" 647431 NIL -4042 (NIL T) -8 NIL NIL NIL) (-304 636348 637444 638537 "EP" 640045 NIL EP (NIL T) -7 NIL NIL NIL) (-303 634888 635239 635545 "ENV" 636062 T ENV (NIL) -8 NIL NIL NIL) (-302 633848 634522 634550 "ENTIRER" 634555 T ENTIRER (NIL) -9 NIL 634601 NIL) (-301 630313 632074 632435 "EMR" 633656 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 629417 629628 629682 "ELTAGG" 630062 NIL ELTAGG (NIL T T) -9 NIL 630273 NIL) (-299 629124 629198 629339 "ELTAGG-" 629344 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 628882 628917 628971 "ELTAB" 629055 NIL ELTAB (NIL T T) -9 NIL 629107 NIL) (-297 627984 628154 628353 "ELFUTS" 628733 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 627708 627782 627810 "ELEMFUN" 627915 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 627572 627599 627667 "ELEMFUN-" 627672 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 622097 625614 625655 "ELAGG" 626595 NIL ELAGG (NIL T) -9 NIL 627058 NIL) (-293 620274 620816 621479 "ELAGG-" 621484 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 619556 619723 619879 "ELABOR" 620138 T ELABOR (NIL) -8 NIL NIL NIL) (-291 618162 618496 618790 "ELABEXPR" 619282 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 610801 612799 613628 "EFUPXS" 617437 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 604054 606050 606861 "EFULS" 610076 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 601491 601897 602369 "EFSTRUC" 603686 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 590929 592848 594396 "EF" 600006 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 589907 590414 590563 "EAB" 590800 T EAB (NIL) -8 NIL NIL NIL) (-285 589029 589866 589894 "E04UCFA" 589899 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 588151 588988 589016 "E04NAFA" 589021 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 587273 588110 588138 "E04MBFA" 588143 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 586395 587232 587260 "E04JAFA" 587265 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 585519 586354 586382 "E04GCFA" 586387 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 584643 585478 585506 "E04FDFA" 585511 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 583765 584602 584630 "E04DGFA" 584635 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 577842 579290 580654 "E04AGNT" 582421 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 576462 577143 577183 "DVARCAT" 577524 NIL DVARCAT (NIL T) -9 NIL 577687 NIL) (-276 575612 575878 576192 "DVARCAT-" 576197 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 567616 575411 575540 "DSMP" 575545 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 565967 566758 566799 "DSEXT" 567162 NIL DSEXT (NIL T) -9 NIL 567456 NIL) (-273 564156 564680 565346 "DSEXT-" 565351 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 563815 563880 563978 "DROPT1" 564091 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 558834 560056 561193 "DROPT0" 562698 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 553417 554779 555847 "DROPT" 557786 T DROPT (NIL) -8 NIL NIL NIL) (-269 551726 552087 552473 "DRAWPT" 553051 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 551353 551412 551530 "DRAWHACK" 551667 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 550054 550353 550644 "DRAWCX" 551082 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 549563 549638 549789 "DRAWCURV" 549980 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 539881 541993 544108 "DRAWCFUN" 547468 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 534372 535391 536470 "DRAW" 538855 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 530954 533037 533078 "DQAGG" 533707 NIL DQAGG (NIL T) -9 NIL 533981 NIL) (-262 517568 525165 525248 "DPOLCAT" 527100 NIL DPOLCAT (NIL T T T T) -9 NIL 527645 NIL) (-261 512138 513787 515728 "DPOLCAT-" 515733 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 505067 511999 512097 "DPMO" 512102 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 497893 504847 505014 "DPMM" 505019 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 497415 497677 497766 "DOMTMPLT" 497824 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 496764 497217 497297 "DOMCTOR" 497355 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 495916 496244 496395 "DOMAIN" 496633 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 488961 495551 495703 "DMP" 495817 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 486738 488028 488069 "DMEXT" 488074 NIL DMEXT (NIL T) -9 NIL 488250 NIL) (-253 486332 486394 486538 "DLP" 486676 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 479457 485659 485849 "DLIST" 486174 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 476107 478282 478323 "DLAGG" 478873 NIL DLAGG (NIL T) -9 NIL 479103 NIL) (-250 474619 475433 475461 "DIVRING" 475553 T DIVRING (NIL) -9 NIL 475636 NIL) (-249 473802 474046 474346 "DIVRING-" 474351 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 471844 472261 472667 "DISPLAY" 473416 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 470674 470895 471160 "DIRPROD2" 471637 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 464153 470588 470651 "DIRPROD" 470656 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 452437 458864 458917 "DIRPCAT" 459175 NIL DIRPCAT (NIL NIL T) -9 NIL 460050 NIL) (-244 449637 450405 451286 "DIRPCAT-" 451623 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 448918 449084 449270 "DIOSP" 449471 T DIOSP (NIL) -7 NIL NIL NIL) (-242 445443 447802 447843 "DIOPS" 448277 NIL DIOPS (NIL T) -9 NIL 448506 NIL) (-241 444962 445106 445297 "DIOPS-" 445302 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 443869 444641 444669 "DIFRING" 444674 T DIFRING (NIL) -9 NIL 444696 NIL) (-239 443517 443615 443643 "DIFFSPC" 443762 T DIFFSPC (NIL) -9 NIL 443837 NIL) (-238 443138 443240 443392 "DIFFSPC-" 443397 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 442074 442672 442713 "DIFFMOD" 442718 NIL DIFFMOD (NIL T) -9 NIL 442816 NIL) (-236 441770 441827 441868 "DIFFDOM" 441989 NIL DIFFDOM (NIL T) -9 NIL 442057 NIL) (-235 441617 441647 441731 "DIFFDOM-" 441736 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 439357 440821 440862 "DIFEXT" 440867 NIL DIFEXT (NIL T) -9 NIL 441020 NIL) (-233 436502 438861 438902 "DIAGG" 438907 NIL DIAGG (NIL T) -9 NIL 438927 NIL) (-232 435850 436043 436295 "DIAGG-" 436300 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 430813 434809 435086 "DHMATRIX" 435619 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 426281 427334 428344 "DFSFUN" 429823 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 420394 425111 425446 "DFLOAT" 425966 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 418633 418938 419327 "DFINTTLS" 420102 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 415452 416654 417054 "DERHAM" 418299 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 413102 415227 415316 "DEQUEUE" 415396 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 412344 412489 412672 "DEGRED" 412964 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 408930 409654 410455 "DEFINTRF" 411617 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 406579 407038 407602 "DEFINTEF" 408477 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 405863 406199 406314 "DEFAST" 406484 T DEFAST (NIL) -8 NIL NIL NIL) (-221 398936 405456 405606 "DECIMAL" 405733 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 396394 396906 397412 "DDFACT" 398480 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 395984 396033 396184 "DBLRESP" 396345 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 395185 395754 395845 "DBASIS" 395933 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 392969 393415 393776 "DBASE" 394951 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 392157 392449 392595 "DATAARY" 392868 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 391215 392116 392144 "D03FAFA" 392149 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 390274 391174 391202 "D03EEFA" 391207 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 388200 388690 389179 "D03AGNT" 389805 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 387441 388159 388187 "D02EJFA" 388192 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 386682 387400 387428 "D02CJFA" 387433 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 385923 386641 386669 "D02BHFA" 386674 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 385164 385882 385910 "D02BBFA" 385915 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 378295 379950 381556 "D02AGNT" 383578 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 376045 376586 377132 "D01WGTS" 377769 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 375052 376004 376032 "D01TRNS" 376037 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 374060 375011 375039 "D01GBFA" 375044 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 373068 374019 374047 "D01FCFA" 374052 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 372076 373027 373055 "D01ASFA" 373060 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 371084 372035 372063 "D01AQFA" 372068 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 370092 371043 371071 "D01APFA" 371076 T D01APFA (NIL) -8 NIL NIL NIL) (-200 369100 370051 370079 "D01ANFA" 370084 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 368108 369059 369087 "D01AMFA" 369092 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 367116 368067 368095 "D01ALFA" 368100 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 366124 367075 367103 "D01AKFA" 367108 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 365132 366083 366111 "D01AJFA" 366116 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 358355 359980 361541 "D01AGNT" 363591 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 357674 357820 357972 "CYCLOTOM" 358223 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 354329 355122 355849 "CYCLES" 356967 T CYCLES (NIL) -7 NIL NIL NIL) (-192 353629 353775 353946 "CVMP" 354190 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 351416 351728 352097 "CTRIGMNP" 353357 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 350889 351147 351248 "CTORKIND" 351335 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 350094 350482 350510 "CTORCAT" 350692 T CTORCAT (NIL) -9 NIL 350805 NIL) (-188 349668 349803 349962 "CTORCAT-" 349967 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 349082 349342 349450 "CTORCALL" 349592 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 348440 348876 348949 "CTOR" 349029 T CTOR (NIL) -8 NIL NIL NIL) (-185 347796 347913 348066 "CSTTOOLS" 348337 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 343493 344252 345010 "CRFP" 347108 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 342908 343214 343306 "CRCEAST" 343421 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 341931 342140 342368 "CRAPACK" 342712 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 341311 341416 341620 "CPMATCH" 341807 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 341030 341064 341170 "CPIMA" 341277 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 337288 338050 338769 "COORDSYS" 340365 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 336676 336821 336963 "CONTOUR" 337166 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 332149 334679 335171 "CONTFRAC" 336216 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 332023 332050 332078 "CONDUIT" 332115 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 330977 331651 331679 "COMRING" 331684 T COMRING (NIL) -9 NIL 331736 NIL) (-174 329959 330335 330519 "COMPPROP" 330813 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 329614 329655 329783 "COMPLPAT" 329918 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 329244 329307 329414 "COMPLEX2" 329551 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 317661 329053 329162 "COMPLEX" 329167 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 316982 317121 317281 "COMPILER" 317521 T COMPILER (NIL) -8 NIL NIL NIL) (-169 316694 316735 316833 "COMPFACT" 316941 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 298097 310398 310438 "COMPCAT" 311442 NIL COMPCAT (NIL T) -9 NIL 312790 NIL) (-167 287006 290550 294170 "COMPCAT-" 294526 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 286729 286763 286866 "COMMUPC" 286972 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 286517 286557 286616 "COMMONOP" 286690 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 286039 286321 286396 "COMMAAST" 286462 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 285546 285790 285877 "COMM" 285972 T COMM (NIL) -8 NIL NIL NIL) (-162 284741 284989 285017 "COMBOPC" 285355 T COMBOPC (NIL) -9 NIL 285530 NIL) (-161 283595 283847 284089 "COMBINAT" 284531 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 279938 280626 281253 "COMBF" 283017 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 278600 279054 279289 "COLOR" 279723 T COLOR (NIL) -8 NIL NIL NIL) (-158 278016 278321 278413 "COLONAST" 278528 T COLONAST (NIL) -8 NIL NIL NIL) (-157 277650 277703 277828 "CMPLXRT" 277963 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 277038 277350 277449 "CLLCTAST" 277571 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 272498 273568 274648 "CLIP" 275978 T CLIP (NIL) -7 NIL NIL NIL) (-154 270671 271599 271839 "CLIF" 272325 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 266764 268789 268830 "CLAGG" 269759 NIL CLAGG (NIL T) -9 NIL 270295 NIL) (-152 265108 265643 266226 "CLAGG-" 266231 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 264646 264737 264877 "CINTSLPE" 265017 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 262111 262618 263166 "CHVAR" 264174 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 261151 261825 261853 "CHARZ" 261858 T CHARZ (NIL) -9 NIL 261873 NIL) (-148 260899 260945 261023 "CHARPOL" 261105 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 259817 260523 260551 "CHARNZ" 260612 T CHARNZ (NIL) -9 NIL 260661 NIL) (-146 256761 257871 258400 "CHAR" 259308 T CHAR (NIL) -8 NIL NIL NIL) (-145 256469 256548 256576 "CFCAT" 256687 T CFCAT (NIL) -9 NIL NIL NIL) (-144 255692 255821 256004 "CDEN" 256353 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 251403 254845 255125 "CCLASS" 255432 T CCLASS (NIL) -8 NIL NIL NIL) (-142 250624 250811 250988 "CATEGORY" 251246 T -10 (NIL) -8 NIL NIL NIL) (-141 250119 250543 250591 "CATCTOR" 250596 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 249510 249822 249920 "CATAST" 250041 T CATAST (NIL) -8 NIL NIL NIL) (-139 248926 249231 249323 "CASEAST" 249438 T CASEAST (NIL) -8 NIL NIL NIL) (-138 248022 248182 248403 "CARTEN2" 248773 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 242919 244179 244923 "CARTEN" 247334 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 241049 242069 242326 "CARD" 242682 T CARD (NIL) -8 NIL NIL NIL) (-135 240571 240853 240928 "CAPSLAST" 240994 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 240013 240269 240297 "CACHSET" 240429 T CACHSET (NIL) -9 NIL 240507 NIL) (-133 239403 239791 239819 "CABMON" 239869 T CABMON (NIL) -9 NIL 239925 NIL) (-132 238840 239107 239217 "BYTEORD" 239313 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 233881 238345 238517 "BYTEBUF" 238688 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 232712 233424 233559 "BYTE" 233722 T BYTE (NIL) -8 NIL NIL 233837) (-129 230090 232404 232511 "BTREE" 232638 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 227408 229738 229860 "BTOURN" 230000 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 224628 226850 226891 "BTCAT" 226959 NIL BTCAT (NIL T) -9 NIL 227036 NIL) (-126 224277 224375 224524 "BTCAT-" 224529 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 219280 223523 223551 "BTAGG" 223665 T BTAGG (NIL) -9 NIL 223775 NIL) (-124 218734 218895 219101 "BTAGG-" 219106 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 215586 218012 218227 "BSTREE" 218551 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 214694 214850 215034 "BRILL" 215442 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 211201 213392 213433 "BRAGG" 214082 NIL BRAGG (NIL T) -9 NIL 214340 NIL) (-120 209637 210138 210692 "BRAGG-" 210697 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 201910 208981 209166 "BPADICRT" 209484 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 199928 201847 201892 "BPADIC" 201897 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 199620 199656 199770 "BOUNDZRO" 199892 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 197347 197805 198280 "BOP1" 199178 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 192377 193807 194705 "BOP" 196469 T BOP (NIL) -8 NIL NIL NIL) (-114 191042 191965 192107 "BOOLEAN" 192255 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 190635 190792 190820 "BOOLE" 190931 T BOOLE (NIL) -9 NIL 191012 NIL) (-112 190503 190530 190596 "BOOLE-" 190601 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 189672 190172 190226 "BMODULE" 190231 NIL BMODULE (NIL T T) -9 NIL 190296 NIL) (-110 185107 189470 189543 "BITS" 189619 T BITS (NIL) -8 NIL NIL NIL) (-109 184504 184647 184787 "BINDING" 184987 T BINDING (NIL) -8 NIL NIL NIL) (-108 177580 184099 184248 "BINARY" 184375 T BINARY (NIL) -8 NIL NIL NIL) (-107 175298 176807 176848 "BGAGG" 177108 NIL BGAGG (NIL T) -9 NIL 177245 NIL) (-106 175123 175161 175252 "BGAGG-" 175257 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 174146 174507 174712 "BFUNCT" 174938 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 172810 173011 173299 "BEZOUT" 173970 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 169124 171662 171992 "BBTREE" 172513 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 168707 168803 168831 "BASTYPE" 169008 T BASTYPE (NIL) -9 NIL 169107 NIL) (-101 168365 168464 168599 "BASTYPE-" 168604 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 167787 167875 168027 "BALFACT" 168276 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 166523 167202 167388 "AUTOMOR" 167632 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 166249 166254 166280 "ATTREG" 166285 T ATTREG (NIL) -9 NIL NIL NIL) (-97 164411 164946 165298 "ATTRBUT" 165915 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 163965 164239 164305 "ATTRAST" 164363 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 163465 163614 163640 "ATRIG" 163841 T ATRIG (NIL) -9 NIL NIL NIL) (-94 163262 163315 163402 "ATRIG-" 163407 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 162845 163079 163105 "ASTCAT" 163110 T ASTCAT (NIL) -9 NIL 163140 NIL) (-92 162554 162631 162750 "ASTCAT-" 162755 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 160642 162330 162418 "ASTACK" 162497 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 159131 159444 159809 "ASSOCEQ" 160324 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 158077 158790 158914 "ASP9" 159038 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 156859 157682 157824 "ASP80" 157966 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 156587 156807 156846 "ASP8" 156851 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 155455 156264 156382 "ASP78" 156500 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 154338 155135 155252 "ASP77" 155369 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 153164 153976 154107 "ASP74" 154238 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 151978 152799 152931 "ASP73" 153063 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 150790 151613 151745 "ASP7" 151877 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 149808 150616 150716 "ASP6" 150721 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 148669 149485 149603 "ASP55" 149721 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 147532 148343 148462 "ASP50" 148581 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 146534 147233 147343 "ASP49" 147453 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 145232 146073 146241 "ASP42" 146423 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 143923 144765 144935 "ASP41" 145119 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 142925 143624 143734 "ASP4" 143844 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 141789 142602 142720 "ASP35" 142838 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 141518 141737 141776 "ASP34" 141781 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 141237 141322 141398 "ASP33" 141473 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 140045 140872 141004 "ASP31" 141136 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 139774 139993 140032 "ASP30" 140037 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 139491 139578 139654 "ASP29" 139729 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 139220 139439 139478 "ASP28" 139483 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 138949 139168 139207 "ASP27" 139212 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 137947 138647 138758 "ASP24" 138869 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 136938 137749 137861 "ASP20" 137866 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 135795 136612 136731 "ASP19" 136850 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 135514 135599 135675 "ASP12" 135750 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 134280 135113 135257 "ASP10" 135401 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 133282 133981 134091 "ASP1" 134201 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 131008 133126 133217 "ARRAY2" 133222 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 130022 130213 130434 "ARRAY12" 130831 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 125496 129670 129784 "ARRAY1" 129939 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 119652 121698 121773 "ARR2CAT" 124403 NIL ARR2CAT (NIL T T T) -9 NIL 125161 NIL) (-56 117251 118028 118883 "ARR2CAT-" 118888 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 116502 116878 117003 "ARITY" 117144 T ARITY (NIL) -8 NIL NIL NIL) (-54 115260 115430 115729 "APPRULE" 116338 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 114905 114959 115078 "APPLYORE" 115206 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 114159 114306 114463 "ANY1" 114779 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 113459 113752 113872 "ANY" 114057 T ANY (NIL) -8 NIL NIL NIL) (-50 110785 111896 112223 "ANTISYM" 113183 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 110229 110492 110588 "ANON" 110707 T ANON (NIL) -8 NIL NIL NIL) (-48 103401 108768 109222 "AN" 109793 T AN (NIL) -8 NIL NIL NIL) (-47 99064 100673 100724 "AMR" 101472 NIL AMR (NIL T T) -9 NIL 102072 NIL) (-46 98116 98397 98760 "AMR-" 98765 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 81591 98033 98094 "ALIST" 98099 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 77920 81185 81354 "ALGSC" 81509 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 74370 75030 75637 "ALGPKG" 77360 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 73635 73748 73932 "ALGMFACT" 74256 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 69618 70249 70843 "ALGMANIP" 73219 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 58989 69244 69394 "ALGFF" 69551 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 58161 58316 58495 "ALGFACT" 58847 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 56950 57688 57726 "ALGEBRA" 57731 NIL ALGEBRA (NIL T) -9 NIL 57772 NIL) (-37 56650 56727 56859 "ALGEBRA-" 56864 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 37610 54487 54539 "ALAGG" 54675 NIL ALAGG (NIL T T) -9 NIL 54836 NIL) (-35 37110 37259 37285 "AHYP" 37486 T AHYP (NIL) -9 NIL NIL NIL) (-34 36412 36595 36621 "AGG" 36904 T AGG (NIL) -9 NIL 37093 NIL) (-33 36119 36206 36321 "AGG-" 36326 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 33879 34348 34753 "AF" 35761 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33299 33604 33694 "ADDAST" 33807 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32531 32826 32982 "ACPLOT" 33161 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20151 29463 29501 "ACFS" 30108 NIL ACFS (NIL T) -9 NIL 30347 NIL) (-28 18058 18668 19430 "ACFS-" 19435 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13768 16091 16117 "ACF" 16996 T ACF (NIL) -9 NIL 17409 NIL) (-26 12400 12806 13299 "ACF-" 13304 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11910 12153 12179 "ABELSG" 12271 T ABELSG (NIL) -9 NIL 12336 NIL) (-24 11771 11802 11868 "ABELSG-" 11873 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11040 11387 11413 "ABELMON" 11583 T ABELMON (NIL) -9 NIL 11695 NIL) (-22 10680 10788 10926 "ABELMON-" 10931 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9930 10386 10412 "ABELGRP" 10484 T ABELGRP (NIL) -9 NIL 10559 NIL) (-20 9357 9522 9738 "ABELGRP-" 9743 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8619 8658 "A1AGG" 8663 NIL A1AGG (NIL T) -9 NIL 8703 NIL) (-18 30 1497 3059 "A1AGG-" 3064 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 8467d8d5..6ba694d5 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,193 +1,853 @@ -(733460 . 3515605026) -(((*1 *2 *1 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1106)))) - ((*1 *2 *1 *1) - (-12 (-4 *1 (-1136 *3 *4 *5 *6 *7)) (-4 *3 (-1133)) (-4 *4 (-1133)) - (-4 *5 (-1133)) (-4 *6 (-1133)) (-4 *7 (-1133)) (-5 *2 (-114))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-376) (-871))) (-5 *1 (-184 *3 *2)) - (-4 *2 (-1275 (-171 *3)))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-571)) - (-5 *2 (-2 (|:| -3504 *4) (|:| -2105 *3) (|:| -3735 *3))) - (-5 *1 (-1001 *4 *3)) (-4 *3 (-1275 *4)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-1081)) (-4 *4 (-817)) (-4 *5 (-872)) - (-5 *2 (-2 (|:| -2105 *1) (|:| -3735 *1))) (-4 *1 (-1097 *3 *4 *5)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-571)) (-4 *3 (-1081)) - (-5 *2 (-2 (|:| -3504 *3) (|:| -2105 *1) (|:| -3735 *1))) - (-4 *1 (-1275 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(-1209)) + (-14 *4 (-3 (|:| |fst| (-448)) (|:| -4426 #1#))) (-14 *5 (-663 (-1209))) + (-14 *6 (-1213)))) ((*1 *1 *2) - (-12 (-5 *2 (-326 (-723))) (-5 *1 (-412 *3 *4 *5 *6)) - (-14 *3 (-1209)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -1617 "void"))) - (-14 *5 (-663 (-1209))) (-14 *6 (-1213)))) + (-12 (-5 *2 (-326 (-723))) (-5 *1 (-412 *3 *4 *5 *6)) (-14 *3 (-1209)) + (-14 *4 (-3 (|:| |fst| (-448)) (|:| -4426 #1#))) (-14 *5 (-663 (-1209))) + (-14 *6 (-1213)))) ((*1 *1 *2) - (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -3836 (-663 (-342))))) + (-12 (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -1825 (-663 (-342))))) (-5 *1 (-412 *3 *4 *5 *6)) (-14 *3 (-1209)) - (-14 *4 (-3 (|:| |fst| (-448)) (|:| -1617 "void"))) - (-14 *5 (-663 (-1209))) (-14 *6 (-1213)))) + (-14 *4 (-3 (|:| |fst| (-448)) (|:| -4426 #1#))) (-14 *5 (-663 (-1209))) + (-14 *6 (-1213)))) ((*1 *1 *2) - (-12 (-5 *2 (-663 (-342))) (-5 *1 (-412 *3 *4 *5 *6)) - (-14 *3 (-1209)) (-14 *4 (-3 (|:| |fst| (-448)) (|:| -1617 "void"))) - (-14 *5 (-663 (-1209))) (-14 *6 (-1213)))) + (-12 (-5 *2 (-663 (-342))) (-5 *1 (-412 *3 *4 *5 *6)) (-14 *3 (-1209)) + (-14 *4 (-3 (|:| |fst| (-448)) (|:| -4426 #1#))) (-14 *5 (-663 (-1209))) + (-14 *6 (-1213)))) ((*1 *1 *2) (-12 (-5 *2 (-342)) (-5 *1 (-412 *3 *4 *5 *6)) (-14 *3 (-1209)) - (-14 *4 (-3 (|:| |fst| (-448)) (|:| -1617 "void"))) - (-14 *5 (-663 (-1209))) (-14 *6 (-1213)))) + (-14 *4 (-3 (|:| |fst| (-448)) (|:| -4426 #1#))) (-14 *5 (-663 (-1209))) + (-14 *6 (-1213)))) ((*1 *1 *2) (-12 (-5 *2 (-421 (-976 (-421 *3)))) (-4 *3 (-571)) (-4 *3 (-1133)) (-4 *1 (-435 *3)))) @@ -318,14 +972,13 @@ (-12 (-5 *2 (-976 (-421 *3))) (-4 *3 (-571)) (-4 *3 (-1133)) (-4 *1 (-435 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-421 *3)) (-4 *3 (-571)) (-4 *3 (-1133)) - (-4 *1 (-435 *3)))) + (-12 (-5 *2 (-421 *3)) (-4 *3 (-571)) (-4 *3 (-1133)) (-4 *1 (-435 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-1157 *3 (-630 *1))) (-4 *3 (-1081)) (-4 *3 (-1133)) (-4 *1 (-435 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-343 *4)) (-4 *4 (-13 (-872) (-21))) - (-5 *1 (-443 *3 *4)) (-4 *3 (-13 (-175) (-38 (-421 (-560))))))) + (-12 (-5 *2 (-343 *4)) (-4 *4 (-13 (-872) (-21))) (-5 *1 (-443 *3 *4)) + (-4 *3 (-13 (-175) (-38 (-421 (-560))))))) ((*1 *1 *2) (-12 (-5 *1 (-443 *2 *3)) (-4 *2 (-13 (-175) (-38 (-421 (-560))))) (-4 *3 (-13 (-872) (-21))))) @@ -335,39 +988,36 @@ ((*1 *1 *2) (-12 (-5 *2 (-1191)) (-5 *1 (-448)))) ((*1 *1 *2) (-12 (-5 *2 (-448)) (-5 *1 (-450)))) ((*1 *1 *2) - (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -3836 (-663 (-342))))) + (-12 (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -1825 (-663 (-342))))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-663 (-342))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-1299 (-721))) (-4 *1 (-454)))) ((*1 *1 *2) - (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -3836 (-663 (-342))))) + (-12 (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -1825 (-663 (-342))))) (-4 *1 (-455)))) ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-455)))) ((*1 *1 *2) (-12 (-5 *2 (-663 (-342))) (-4 *1 (-455)))) ((*1 *1 *2) (-12 (-5 *2 (-1299 (-421 (-976 *3)))) (-4 *3 (-175)) - (-14 *6 (-1299 (-711 *3))) (-5 *1 (-467 *3 *4 *5 *6)) - (-14 *4 (-949)) (-14 *5 (-663 (-1209))))) + (-14 *6 (-1299 (-711 *3))) (-5 *1 (-467 *3 *4 *5 *6)) (-14 *4 (-949)) + (-14 *5 (-663 (-1209))))) ((*1 *1 *2) (-12 (-5 *2 (-663 (-663 (-973 (-229))))) (-5 *1 (-482)))) ((*1 *2 *1) (-12 (-5 *2 (-888)) (-5 *1 (-482)))) ((*1 *1 *2) - (-12 (-5 *2 (-1280 *3 *4 *5)) (-4 *3 (-1081)) (-14 *4 (-1209)) - (-14 *5 *3) (-5 *1 (-488 *3 *4 *5)))) + (-12 (-5 *2 (-1280 *3 *4 *5)) (-4 *3 (-1081)) (-14 *4 (-1209)) (-14 *5 *3) + (-5 *1 (-488 *3 *4 *5)))) ((*1 *1 *2) (-12 (-5 *2 (-1296 *4)) (-14 *4 (-1209)) (-5 *1 (-488 *3 *4 *5)) (-4 *3 (-1081)) (-14 *5 *3))) ((*1 *1 *2) (-12 (-5 *2 (-1157 (-560) (-630 (-509)))) (-5 *1 (-509)))) ((*1 *1 *2) (-12 (-5 *2 (-1191)) (-5 *1 (-516)))) ((*1 *1 *2) - (-12 (-5 *2 (-663 *6)) (-4 *6 (-980 *3 *4 *5)) (-4 *3 (-376)) - (-4 *4 (-817)) (-4 *5 (-872)) (-5 *1 (-518 *3 *4 *5 *6)))) + (-12 (-5 *2 (-663 *6)) (-4 *6 (-980 *3 *4 *5)) (-4 *3 (-376)) (-4 *4 (-817)) + (-4 *5 (-872)) (-5 *1 (-518 *3 *4 *5 *6)))) ((*1 *1 *2) (-12 (-5 *2 (-663 (-1250))) (-5 *1 (-538)))) ((*1 *1 *2) (-12 (-5 *2 (-663 (-1250))) (-5 *1 (-619)))) - ((*1 *1 *2) - (-12 (-4 *3 (-175)) (-5 *1 (-620 *3 *2)) (-4 *2 (-766 *3)))) + ((*1 *1 *2) (-12 (-4 *3 (-175)) (-5 *1 (-620 *3 *2)) (-4 *2 (-766 *3)))) ((*1 *2 *1) (-12 (-4 *1 (-632 *2)) (-4 *2 (-1249)))) ((*1 *1 *2) (-12 (-4 *1 (-635 *2)) (-4 *2 (-1249)))) ((*1 *1 *2) (-12 (-4 *1 (-640 *2)) (-4 *2 (-1081)))) @@ -377,16 +1027,13 @@ ((*1 *2 *1) (-12 (-5 *2 (-1315 *3 *4)) (-5 *1 (-646 *3 *4 *5)) (-4 *3 (-872)) (-4 *4 (-13 (-175) (-739 (-421 (-560))))) (-14 *5 (-949)))) - ((*1 *1 *2) - (-12 (-4 *3 (-175)) (-5 *1 (-652 *3 *2)) (-4 *2 (-766 *3)))) + ((*1 *1 *2) (-12 (-4 *3 (-175)) (-5 *1 (-652 *3 *2)) (-4 *2 (-766 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-699 *3)) (-5 *1 (-694 *3)) (-4 *3 (-872)))) ((*1 *2 *1) (-12 (-5 *2 (-843 *3)) (-5 *1 (-694 *3)) (-4 *3 (-872)))) ((*1 *2 *1) - (-12 (-5 *2 (-988 (-988 (-988 *3)))) (-5 *1 (-697 *3)) - (-4 *3 (-1133)))) + (-12 (-5 *2 (-988 (-988 (-988 *3)))) (-5 *1 (-697 *3)) (-4 *3 (-1133)))) ((*1 *1 *2) - (-12 (-5 *2 (-988 (-988 (-988 *3)))) (-4 *3 (-1133)) - (-5 *1 (-697 *3)))) + (-12 (-5 *2 (-988 (-988 (-988 *3)))) (-4 *3 (-1133)) (-5 *1 (-697 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-843 *3)) (-5 *1 (-699 *3)) (-4 *3 (-872)))) ((*1 *1 *2) (-12 (-5 *2 (-1147)) (-5 *1 (-703)))) ((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-704 *3)) (-4 *3 (-1133)))) @@ -400,8 +1047,7 @@ ((*1 *1 *2) (-12 (-5 *2 (-171 (-391))) (-5 *1 (-716)))) ((*1 *1 *2) (-12 (-5 *2 (-723)) (-5 *1 (-721)))) ((*1 *2 *1) (-12 (-5 *2 (-391)) (-5 *1 (-721)))) - ((*1 *2 *3) - (-12 (-5 *3 (-326 (-560))) (-5 *2 (-326 (-723))) (-5 *1 (-723)))) + ((*1 *2 *3) (-12 (-5 *3 (-326 (-560))) (-5 *2 (-326 (-723))) (-5 *1 (-723)))) ((*1 *2 *3) (-12 (-5 *3 (-888)) (-5 *2 (-1191)) (-5 *1 (-732)))) ((*1 *2 *1) (-12 (-4 *2 (-175)) (-5 *1 (-733 *2 *3 *4 *5 *6)) (-4 *3 (-23)) @@ -412,8 +1058,8 @@ (-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 (-663 (-2 (|:| -3504 *3) (|:| -3140 *4)))) - (-4 *3 (-1081)) (-4 *4 (-748)) (-5 *1 (-757 *3 *4)))) + (-12 (-5 *2 (-663 (-2 (|:| -4470 *3) (|:| -4454 *4)))) (-4 *3 (-1081)) + (-4 *4 (-748)) (-5 *1 (-757 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-560)) (-4 *1 (-785)))) ((*1 *1 *2) (-12 @@ -421,25 +1067,23 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -2683 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| |mdnia| - (-2 (|:| |fn| (-326 (-229))) - (|:| -2683 (-663 (-1121 (-866 (-229))))) + (-2 (|:| |fn| (-326 (-229))) (|:| -1650 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-326 (-229))) - (|:| -2683 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) - (|:| |relerr| (-229)))) + (-2 (|:| |fn| (-326 (-229))) (|:| -1650 (-663 (-1121 (-866 (-229))))) + (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -2683 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *2 *3) (-12 (-5 *2 (-795)) (-5 *1 (-796 *3)) (-4 *3 (-1249)))) @@ -457,33 +1101,27 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-229))) (|:| -4250 (-663 (-229))) - (|:| |lb| (-663 (-866 (-229)))) - (|:| |cf| (-663 (-326 (-229)))) + (-2 (|:| |fn| (-326 (-229))) (|:| -3952 (-663 (-229))) + (|:| |lb| (-663 (-866 (-229)))) (|:| |cf| (-663 (-326 (-229)))) (|:| |ub| (-663 (-866 (-229)))))) (|:| |lsa| - (-2 (|:| |lfn| (-663 (-326 (-229)))) - (|:| -4250 (-663 (-229))))))) + (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -3952 (-663 (-229))))))) (-5 *1 (-865)))) ((*1 *1 *2) - (-12 - (-5 *2 - (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -4250 (-663 (-229))))) + (-12 (-5 *2 (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -3952 (-663 (-229))))) (-5 *1 (-865)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-326 (-229))) (|:| -4250 (-663 (-229))) + (-2 (|:| |fn| (-326 (-229))) (|:| -3952 (-663 (-229))) (|:| |lb| (-663 (-866 (-229)))) (|:| |cf| (-663 (-326 (-229)))) (|:| |ub| (-663 (-866 (-229)))))) (-5 *1 (-865)))) ((*1 *1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-883)))) ((*1 *1 *2) (-12 (-5 *2 (-159)) (-5 *1 (-899)))) + ((*1 *2 *3) (-12 (-5 *3 (-976 (-48))) (-5 *2 (-326 (-560))) (-5 *1 (-900)))) ((*1 *2 *3) - (-12 (-5 *3 (-976 (-48))) (-5 *2 (-326 (-560))) (-5 *1 (-900)))) - ((*1 *2 *3) - (-12 (-5 *3 (-421 (-976 (-48)))) (-5 *2 (-326 (-560))) - (-5 *1 (-900)))) + (-12 (-5 *3 (-421 (-976 (-48)))) (-5 *2 (-326 (-560))) (-5 *1 (-900)))) ((*1 *1 *2) (-12 (-5 *1 (-919 *2)) (-4 *2 (-872)))) ((*1 *2 *1) (-12 (-5 *2 (-843 *3)) (-5 *1 (-919 *3)) (-4 *3 (-872)))) ((*1 *1 *2) @@ -492,33 +1130,26 @@ (-2 (|:| |pde| (-663 (-326 (-229)))) (|:| |constraints| (-663 - (-2 (|:| |start| (-229)) (|:| |finish| (-229)) - (|:| |grid| (-793)) (|:| |boundaryType| (-560)) - (|:| |dStart| (-711 (-229))) (|:| |dFinish| (-711 (-229)))))) + (-2 (|:| |start| (-229)) (|:| |finish| (-229)) (|:| |grid| (-793)) + (|:| |boundaryType| (-560)) (|:| |dStart| (-711 (-229))) + (|:| |dFinish| (-711 (-229)))))) (|:| |f| (-663 (-663 (-326 (-229))))) (|:| |st| (-1191)) (|:| |tol| (-229)))) (-5 *1 (-926)))) ((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1133)) (-5 *1 (-932 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-663 (-663 *3))) (-4 *3 (-1133)) (-5 *1 (-932 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-663 (-932 *3))) (-4 *3 (-1133)) (-5 *1 (-935 *3)))) - ((*1 *2 *1) - (-12 (-5 *2 (-663 (-932 *3))) (-5 *1 (-935 *3)) (-4 *3 (-1133)))) - ((*1 *1 *2) - (-12 (-5 *2 (-421 (-419 *3))) (-4 *3 (-319)) (-5 *1 (-944 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-663 (-663 *3))) (-4 *3 (-1133)) (-5 *1 (-932 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-663 (-932 *3))) (-4 *3 (-1133)) (-5 *1 (-935 *3)))) + ((*1 *2 *1) (-12 (-5 *2 (-663 (-932 *3))) (-5 *1 (-935 *3)) (-4 *3 (-1133)))) + ((*1 *1 *2) (-12 (-5 *2 (-421 (-419 *3))) (-4 *3 (-319)) (-5 *1 (-944 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-421 *3)) (-5 *1 (-944 *3)) (-4 *3 (-319)))) ((*1 *2 *3) - (-12 (-5 *3 (-491)) (-5 *2 (-326 *4)) (-5 *1 (-950 *4)) - (-4 *4 (-571)))) + (-12 (-5 *3 (-491)) (-5 *2 (-326 *4)) (-5 *1 (-950 *4)) (-4 *4 (-571)))) ((*1 *2 *3) (-12 (-5 *2 (-1305)) (-5 *1 (-1065 *3)) (-4 *3 (-1249)))) ((*1 *2 *3) (-12 (-5 *3 (-323)) (-5 *1 (-1065 *2)) (-4 *2 (-1249)))) ((*1 *1 *2) (-12 (-4 *3 (-376)) (-4 *4 (-817)) (-4 *5 (-872)) - (-5 *1 (-1066 *3 *4 *5 *2 *6)) (-4 *2 (-980 *3 *4 *5)) - (-14 *6 (-663 *2)))) - ((*1 *2 *3) - (-12 (-5 *2 (-421 (-976 *3))) (-5 *1 (-1072 *3)) (-4 *3 (-571)))) + (-5 *1 (-1066 *3 *4 *5 *2 *6)) (-4 *2 (-980 *3 *4 *5)) (-14 *6 (-663 *2)))) + ((*1 *2 *3) (-12 (-5 *2 (-421 (-976 *3))) (-5 *1 (-1072 *3)) (-4 *3 (-571)))) ((*1 *1 *2) (-12 (-4 *3 (-1081)) (-4 *4 (-872)) (-5 *1 (-1158 *3 *4 *2)) (-4 *2 (-980 *3 (-545 *4) *4)))) @@ -527,8 +1158,7 @@ (-4 *4 (-980 *3 (-545 *2) *2)))) ((*1 *2 *1) (-12 (-4 *1 (-1166 *3)) (-4 *3 (-1081)) (-5 *2 (-888)))) ((*1 *1 *2) (-12 (-5 *2 (-146)) (-4 *1 (-1176)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1187 *3)) (-5 *1 (-1193 *3)) (-4 *3 (-1081)))) + ((*1 *2 *3) (-12 (-5 *2 (-1187 *3)) (-5 *1 (-1193 *3)) (-4 *3 (-1081)))) ((*1 *1 *2) (-12 (-5 *2 (-1296 *4)) (-14 *4 (-1209)) (-5 *1 (-1200 *3 *4 *5)) (-4 *3 (-1081)) (-14 *5 *3))) @@ -536,8 +1166,8 @@ (-12 (-5 *2 (-1296 *4)) (-14 *4 (-1209)) (-5 *1 (-1207 *3 *4 *5)) (-4 *3 (-1081)) (-14 *5 *3))) ((*1 *1 *2) - (-12 (-5 *2 (-1268 *4 *3)) (-4 *3 (-1081)) (-14 *4 (-1209)) - (-14 *5 *3) (-5 *1 (-1207 *3 *4 *5)))) + (-12 (-5 *2 (-1268 *4 *3)) (-4 *3 (-1081)) (-14 *4 (-1209)) (-14 *5 *3) + (-5 *1 (-1207 *3 *4 *5)))) ((*1 *1 *2) (-12 (-5 *2 (-1209)) (-5 *1 (-1208)))) ((*1 *2 *1) (-12 (-5 *2 (-1221 (-1209) (-450))) (-5 *1 (-1213)))) ((*1 *2 *1) (-12 (-5 *2 (-1191)) (-5 *1 (-1214)))) @@ -546,25 +1176,22 @@ ((*1 *2 *1) (-12 (-5 *2 (-560)) (-5 *1 (-1214)))) ((*1 *2 *1) (-12 (-5 *2 (-888)) (-5 *1 (-1222 *3)) (-4 *3 (-1133)))) ((*1 *2 *3) (-12 (-5 *2 (-1229)) (-5 *1 (-1230 *3)) (-4 *3 (-1133)))) - ((*1 *1 *2) - (-12 (-5 *2 (-976 *3)) (-4 *3 (-1081)) (-5 *1 (-1242 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-976 *3)) (-4 *3 (-1081)) (-5 *1 (-1242 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-1209)) (-5 *1 (-1242 *3)) (-4 *3 (-1081)))) ((*1 *1 *2) (-12 (-5 *2 (-1296 *4)) (-14 *4 (-1209)) (-5 *1 (-1259 *3 *4 *5)) (-4 *3 (-1081)) (-14 *5 *3))) - ((*1 *1 *2) - (-12 (-5 *2 (-1121 *3)) (-4 *3 (-1249)) (-5 *1 (-1266 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-1121 *3)) (-4 *3 (-1249)) (-5 *1 (-1266 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-1296 *4)) (-14 *4 (-1209)) (-5 *1 (-1289 *3 *4 *5)) (-4 *3 (-1081)) (-14 *5 *3))) ((*1 *1 *2) - (-12 (-5 *2 (-1268 *4 *3)) (-4 *3 (-1081)) (-14 *4 (-1209)) - (-14 *5 *3) (-5 *1 (-1289 *3 *4 *5)))) + (-12 (-5 *2 (-1268 *4 *3)) (-4 *3 (-1081)) (-14 *4 (-1209)) (-14 *5 *3) + (-5 *1 (-1289 *3 *4 *5)))) ((*1 *2 *1) (-12 (-5 *2 (-1209)) (-5 *1 (-1296 *3)) (-14 *3 *2))) ((*1 *2 *3) (-12 (-5 *3 (-482)) (-5 *2 (-1302)) (-5 *1 (-1301)))) ((*1 *2 *1) (-12 (-5 *2 (-888)) (-5 *1 (-1302)))) - ((*1 *1 *2) - (-12 (-4 *1 (-1319 *2 *3)) (-4 *2 (-872)) (-4 *3 (-1081)))) + ((*1 *1 *2) (-12 (-4 *1 (-1319 *2 *3)) (-4 *2 (-872)) (-4 *3 (-1081)))) ((*1 *2 *1) (-12 (-5 *2 (-1324 *3 *4)) (-5 *1 (-1320 *3 *4)) (-4 *3 (-872)) (-4 *4 (-175)))) @@ -574,2109 +1201,513 @@ ((*1 *1 *2) (-12 (-5 *2 (-686 *3 *4)) (-4 *3 (-872)) (-4 *4 (-175)) (-5 *1 (-1320 *3 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-780))))) (((*1 *1 *2) - (-12 (-5 *2 (-1315 (-1209) *3)) (-4 *3 (-1081)) (-5 *1 (-1321 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1315 *3 *4)) (-4 *3 (-872)) (-4 *4 (-1081)) - (-5 *1 (-1324 *3 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-419 *3)) (-5 *1 (-944 *3)) (-4 *3 (-319))))) -(((*1 *1) (-5 *1 (-1212)))) -(((*1 *2 *3 *3 *3 *4) - (-12 (-5 *3 (-229)) (-5 *4 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|bothSingular| "There are singularities at both end points") + (|:| |notEvaluated| "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1187 (-229))) + (|:| |notEvaluated| "Internal singularities not yet evaluated"))) + (|:| -1650 + (-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 (-574))))) (((*1 *2 *3) - (-12 + (|partial| -12 (-5 *3 - (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-793)) (|:| |poli| *2) - (|:| |polj| *2))) - (-4 *5 (-817)) (-4 *2 (-980 *4 *5 *6)) (-5 *1 (-464 *4 *5 *6 *2)) - (-4 *4 (-466)) (-4 *6 (-872))))) -(((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4511)) (-4 *1 (-251 *2)) (-4 *2 (-1249))))) -(((*1 *2 *1 *1) + (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) + (|:| -1650 (-1121 (-866 (-229)))) (|:| |abserr| 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93312) (-4333 . 92814) (-4334 . 89989) (-4335 . 89839) + (-4336 . 89675) (-4337 . 89511) (-4338 . 89415) (-4339 . 89297) + (-4340 . 89173) (-4341 . 89030) (-4342 . 88859) (-4343 . 88732) + (-4344 . 88587) (-4345 . 88434) (-4346 . 88274) (-4347 . 87758) + (-4348 . 87667) (-4349 . 86997) (-4350 . 86802) (-4351 . 86706) + (-4352 . 86396) (-4353 . 85220) (-4354 . 85013) (-4355 . 83836) + (-4356 . 83761) (-4357 . 82580) (-4358 . 78987) (-4359 . 78623) + (-4360 . 78346) (-4361 . 78254) (-4362 . 78161) (-4363 . 77884) + (-4364 . 77791) (-4365 . 77698) (-4366 . 77605) (-4367 . 77221) + (-4368 . 77150) (-4369 . 77058) (-4370 . 76900) (-4371 . 76546) + (-4372 . 76388) (-4373 . 76280) (-4374 . 76251) (-4375 . 76184) + (-4376 . 76030) (-4377 . 75871) (-4378 . 75477) (-4379 . 75402) + (-4380 . 75296) (-4381 . 75224) (-4382 . 75146) (-4383 . 75073) + (-4384 . 75000) (-4385 . 74927) (-4386 . 74855) (-4387 . 74783) + (-4388 . 74710) (-4389 . 74469) (-4390 . 74129) (-4391 . 73981) + (-4392 . 73908) (-4393 . 73835) (-4394 . 73762) (-4395 . 73508) + (-4396 . 73364) (-4397 . 72028) (-4398 . 71834) (-4399 . 71563) + (-4400 . 71415) (-4401 . 71267) (-4402 . 71027) (-4403 . 70832) + (-4404 . 70562) (-4405 . 70366) (-4406 . 70337) (-4407 . 70236) + (-4408 . 70135) (-4409 . 70034) (-4410 . 69933) (-4411 . 69832) + (-4412 . 69731) (-4413 . 69630) (-4414 . 69529) (-4415 . 69428) + (-4416 . 69327) (-4417 . 69212) (-4418 . 69097) (-4419 . 69046) + (-4420 . 68929) (-4421 . 68871) (-4422 . 68770) (-4423 . 68669) + (-4424 . 68568) (-4425 . 68452) (-4426 . 68423) (-4427 . 67690) + (-4428 . 67565) (-4429 . 67440) (-4430 . 67300) (-4431 . 67182) + (-4432 . 67057) (-4433 . 66902) (-4434 . 65918) (-4435 . 65058) + (-4436 . 65004) (-4437 . 64950) (-4438 . 64742) (-4439 . 64368) + (-4440 . 63954) (-4441 . 63593) (-4442 . 63232) (-4443 . 63079) + (-4444 . 62777) (-4445 . 62621) (-4446 . 62295) (-4447 . 62224) + (-4448 . 62153) (-4449 . 61941) (-4450 . 61134) (-4451 . 60928) + (-4452 . 60554) (-4453 . 60034) (-4454 . 59766) (-4455 . 59282) + (-4456 . 58798) (-4457 . 58672) (-4458 . 57457) (-4459 . 56265) + (-4460 . 55692) (-4461 . 55474) (-4462 . 37057) (-4463 . 36871) + (-4464 . 34770) (-4465 . 32593) (-4466 . 32445) (-4467 . 32263) + (-4468 . 31854) (-4469 . 31553) (-4470 . 31202) (-4471 . 31034) + (-4472 . 30866) (-4473 . 30451) (-4474 . 16372) (-4475 . 15253) (* . 11185) + (-4477 . 10929) (-4478 . 10743) (-4479 . 9781) (-4480 . 9727) (-4481 . 9667) + (-4482 . 9398) (-4483 . 8763) (-4484 . 7481) (-4485 . 6222) (-4486 . 5342) + (-4487 . 4075) (-4488 . 424) (-4489 . 308) (-4490 . 174) (-4491 . 30))
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