diff options
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 1082 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 394 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1341 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9022 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 27073 |
5 files changed, 19462 insertions, 19450 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 04329149..cedbae88 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2267801 . 3480528374) +(2268057 . 3480551177) (-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."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . 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}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4445 . T) (-4443 . T) (-4442 . T) ((-4450 "*") . T) (-4441 . T) (-4446 . T) (-4440 . T)) +((-4446 . T) (-4444 . T) (-4443 . T) ((-4451 "*") . T) (-4442 . T) (-4447 . T) (-4441 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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."))) @@ -63,7 +63,7 @@ NIL (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4448))) +((|HasAttribute| |#1| (QUOTE -4449))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,15 +82,15 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) NIL (-39 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -1674 UP UPUP -4323) +(-40 -1674 UP UPUP -2532) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4441 |has| (-413 |#2|) (-368)) (-4446 |has| (-413 |#2|) (-368)) (-4440 |has| (-413 |#2|) (-368)) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 |has| (-413 |#2|) (-368)) (-4447 |has| (-413 |#2|) (-368)) (-4441 |has| (-413 |#2|) (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2740 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2740 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2740 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2740 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) (-41 R -1674) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-311)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4445 |has| |#1| (-562)) (-4443 . T) (-4442 . T)) +((-4446 |has| |#1| (-562)) (-4444 . T) (-4443 . T)) ((|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-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."))) -((-4448 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2223) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2223) (|devaluate| |#2|))))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2223) (|devaluate| |#2|))))))) +((-4449 . T) (-4450 . T)) +((-2740 (-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|))))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4445 . T)) +((-4446 . T)) NIL (-51 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -158,7 +158,7 @@ NIL NIL (-57 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) NIL (-58 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) @@ -166,65 +166,65 @@ NIL NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-61 -3503) +(-61 -3504) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -3503) +(-62 -3504) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -3503) +(-63 -3504) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -3503) +(-64 -3504) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -3503) +(-65 -3504) ((|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 -3503) +(-66 -3504) ((|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 -3503) +(-67 -3504) ((|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 -3503) +(-68 -3504) ((|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 -3503) +(-69 -3504) ((|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 -3503) +(-70 -3504) ((|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 -3503) +(-71 -3504) ((|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 -3503) +(-72 -3504) ((|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 -3503) +(-73 -3504) ((|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 -3503) +(-74 -3504) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -3503) +(-77 -3504) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -3503) +(-78 -3504) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -3503) +(-79 -3504) ((|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 -3503) +(-80 -3504) ((|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 -3503) +(-81 -3504) ((|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 -3503) +(-82 -3504) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -3503) +(-83 -3504) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3503) +(-84 -3504) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3503) +(-85 -3504) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -3503) +(-86 -3504) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -3503) +(-87 -3504) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -3503) +(-88 -3504) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -3503) +(-89 -3504) ((|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 @@ -294,7 +294,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-368)))) (-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}."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) @@ -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\"."))) -((-4448 . T)) +((-4449 . 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."))) -((-4448 . T) ((-4450 "*") . T) (-4449 . T) (-4445 . T) (-4443 . T) (-4442 . T) (-4441 . T) (-4446 . T) (-4440 . T) (-4439 . T) (-4438 . T) (-4437 . T) (-4436 . T) (-4444 . T) (-4447 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4435 . T)) +((-4449 . T) ((-4451 "*") . T) (-4450 . T) (-4446 . T) (-4444 . T) (-4443 . T) (-4442 . T) (-4447 . T) (-4441 . T) (-4440 . T) (-4439 . T) (-4438 . T) (-4437 . T) (-4445 . T) (-4448 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4436 . 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}."))) -((-4445 . T)) +((-4446 . 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 \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-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 (-4450 "*")))) +((|HasAttribute| |#1| (QUOTE (-4451 "*")))) (-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"))) -((-4448 . T)) +((-4449 . 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."))) @@ -358,11 +358,11 @@ 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."))) -((-4449 . T)) +((-4450 . 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."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2740 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) @@ -370,11 +370,11 @@ NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1109))) (|HasCategory| (-112) (LIST (QUOTE -313) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-112) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-112) (QUOTE (-1109))) (|HasCategory| (-112) (LIST (QUOTE -619) (QUOTE (-868))))) (-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}"))) -((-4443 . T) (-4442 . T)) +((-4444 . T) (-4443 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) @@ -398,16 +398,16 @@ NIL NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-118 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| (-117 |#1|) (QUOTE (-916))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-117 |#1|) (QUOTE (-1031))) (|HasCategory| (-117 |#1|) (QUOTE (-826))) (-2740 (|HasCategory| (-117 |#1|) (QUOTE (-826))) (|HasCategory| (-117 |#1|) (QUOTE (-856)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-1161))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-235))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-311))) (|HasCategory| (-117 |#1|) (QUOTE (-551))) (|HasCategory| (-117 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) (-119 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4449))) +((|HasAttribute| |#1| (QUOTE -4450))) (-120 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -418,7 +418,7 @@ NIL NIL (-122 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"))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) @@ -426,7 +426,7 @@ NIL NIL (-124) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) NIL (-125 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -434,19 +434,19 @@ NIL NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-128 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."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-129) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-2740 (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-130) (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109)))) (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) @@ -470,7 +470,7 @@ NIL NIL (-135) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4450 "*") . T)) +(((-4451 "*") . T)) NIL (-136 |minix| -2408 S T$) ((|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}."))) @@ -498,7 +498,7 @@ NIL NIL (-142) ((|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}."))) -((-4448 . T) (-4438 . T) (-4449 . T)) +((-4449 . T) (-4439 . T) (-4450 . T)) ((-2740 (-12 (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-143 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}\\spad{'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}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) @@ -514,7 +514,7 @@ NIL NIL (-146) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4445 . T)) +((-4446 . T)) NIL (-147 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) @@ -522,7 +522,7 @@ NIL NIL (-148) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4445 . T)) +((-4446 . T)) NIL (-149 -1674 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}."))) @@ -535,14 +535,14 @@ NIL (-151 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasAttribute| |#1| (QUOTE -4448))) +((|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasAttribute| |#1| (QUOTE -4449))) (-152 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL (-153 |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."))) -((-4443 . T) (-4442 . T) (-4445 . T)) +((-4444 . T) (-4443 . T) (-4446 . T)) NIL (-154) ((|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."))) @@ -595,10 +595,10 @@ NIL (-166 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 (-916))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-1011))) (|HasCategory| |#2| (QUOTE (-1211))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4444)) (|HasAttribute| |#2| (QUOTE -4447)) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562)))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-1011))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4445)) (|HasAttribute| |#2| (QUOTE -4448)) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562)))) (-167 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})"))) -((-4441 -2740 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4446 |has| |#1| (-368)) (-4440 |has| |#1| (-368)) (-4444 |has| |#1| (-6 -4444)) (-4447 |has| |#1| (-6 -4447)) (-3035 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 -2740 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4445 |has| |#1| (-6 -4445)) (-4448 |has| |#1| (-6 -4448)) (-3035 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-168 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}."))) -((-4441 -2740 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4446 |has| |#1| (-368)) (-4440 |has| |#1| (-368)) (-4444 |has| |#1| (-6 -4444)) (-4447 |has| |#1| (-6 -4447)) (-3035 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1031)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1211)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| 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T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| 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(|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-916))))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368)))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasAttribute| |#1| (QUOTE -4445)) (|HasAttribute| |#1| (QUOTE -4448)) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-354))))) (-172 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -626,7 +626,7 @@ NIL NIL (-174) ((|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."))) -(((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-175) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -634,7 +634,7 @@ NIL NIL (-176 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4450 "*") . T) (-4441 . T) (-4446 . T) (-4440 . T) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") . T) (-4442 . T) (-4447 . T) (-4441 . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-177) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -806,7 +806,7 @@ NIL NIL (-219) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|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."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2740 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-220) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) @@ -826,11 +826,11 @@ NIL NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-225 |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}."))) -((-4445 . T)) +((-4446 . T)) NIL (-226 R -1674) ((|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."))) @@ -838,7 +838,7 @@ NIL NIL (-227) ((|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}."))) -((-3026 . T) (-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-3026 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-228) ((|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)}.}"))) @@ -846,15 +846,15 @@ NIL NIL (-229 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}"))) -((-4448 . T) (-4449 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4450 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4449 . T) (-4450 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4451 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-230 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 (-231 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."))) -((-4449 . T)) +((-4450 . T)) NIL (-232 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) @@ -862,7 +862,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (-233 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4445 . T)) +((-4446 . T)) NIL (-234 S) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -870,15 +870,15 @@ NIL NIL (-235) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4445 . T)) +((-4446 . T)) NIL (-236 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4448))) +((|HasAttribute| |#1| (QUOTE -4449))) (-237 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}."))) -((-4449 . T)) +((-4450 . T)) NIL (-238) ((|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"))) @@ -887,10 +887,10 @@ NIL (-239 S -2408 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854))) (|HasAttribute| |#3| (QUOTE -4445)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-1109)))) +((|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854))) (|HasAttribute| |#3| (QUOTE -4446)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-1109)))) (-240 -2408 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4442 |has| |#2| (-1058)) (-4443 |has| |#2| (-1058)) (-4445 |has| |#2| (-6 -4445)) ((-4450 "*") |has| |#2| (-174)) (-4448 . T)) +((-4443 |has| |#2| (-1058)) (-4444 |has| |#2| (-1058)) (-4446 |has| |#2| (-6 -4446)) ((-4451 "*") |has| |#2| (-174)) (-4449 . T)) NIL (-241 -2408 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}."))) @@ -898,8 +898,8 @@ NIL NIL (-242 -2408 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."))) -((-4442 |has| |#2| (-1058)) (-4443 |has| |#2| (-1058)) (-4445 |has| |#2| (-6 -4445)) ((-4450 "*") |has| |#2| (-174)) (-4448 . 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(LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2740 (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasAttribute| |#2| (QUOTE -4446)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))))) (-243) ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -910,7 +910,7 @@ NIL NIL (-245) ((|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}."))) -((-4441 . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-246 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) @@ -918,7 +918,7 @@ NIL NIL (-247 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-248 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) @@ -926,8 +926,8 @@ NIL NIL (-249 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4450 "*") |has| |#2| (-174)) (-4441 |has| |#2| (-562)) (-4446 |has| |#2| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . 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T) (-4443 . T) (-4446 . 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(|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (-255 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-235)))) (-256 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) NIL (-257 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}."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) NIL (-258) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g),a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -998,8 +998,8 @@ NIL NIL (-267 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"))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4446)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-268 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1074,7 +1074,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109)))) (-286 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}."))) -((-4449 . T)) +((-4450 . T)) NIL (-287 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}."))) @@ -1095,18 +1095,18 @@ NIL (-291 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 -4449))) +((|HasAttribute| |#1| (QUOTE -4450))) (-292 |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 -(-293 S R |Mod| -4052 -3068 |exactQuo|) +(-293 S R |Mod| -2979 -2727 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-294) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4441 . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-295) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "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"))) @@ -1122,12 +1122,12 @@ NIL NIL (-298 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4445 -2740 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4442 |has| |#1| (-1058)) (-4443 |has| |#1| (-1058))) +((-4446 -2740 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4443 |has| |#1| (-1058)) (-4444 |has| |#1| (-1058))) ((|HasCategory| |#1| (QUOTE (-368))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2740 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-732)))) (|HasCategory| |#1| (QUOTE (-479))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2740 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-306))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-479)))) (-2740 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732)))) (-2740 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-732)))) (-299 |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."))) -((-4448 . T) (-4449 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2223) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4449 . T) (-4450 . T)) +((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-300) ((|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 @@ -1174,7 +1174,7 @@ NIL NIL (-311) ((|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| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-312 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -1198,8 +1198,8 @@ NIL NIL (-317 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))}."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) -((|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-1031))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (-2740 (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-856)))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-1161))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-235))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1262) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (LIST (QUOTE -313) (LIST (QUOTE -1262) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (LIST (QUOTE -290) (LIST (QUOTE -1262) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1262) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-551))) (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-856))) (-12 (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))) (-2740 (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1262 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))))) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1031))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (-2740 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1161))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-235))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -313) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -290) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-551))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))) (-2740 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))))) (-318 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 @@ -1210,7 +1210,7 @@ NIL NIL (-320 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."))) -((-4445 -2740 (-1765 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (-12 (|has| |#1| (-562)) (-2740 (-1765 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (|has| |#1| (-1058)) (|has| |#1| (-479)))) (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4443 |has| |#1| (-174)) (-4442 |has| |#1| (-174)) ((-4450 "*") |has| |#1| (-562)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-562)) (-4440 |has| |#1| (-562))) +((-4446 -2740 (-1765 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (-12 (|has| |#1| (-562)) (-2740 (-1765 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (|has| |#1| (-1058)) (|has| |#1| (-479)))) (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) ((-4451 "*") |has| |#1| (-562)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-562)) (-4441 |has| |#1| (-562))) ((-2740 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (QUOTE (-21))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2740 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (-12 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2740 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-2740 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2740 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-2740 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) (-321 R -1674) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{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)}."))) @@ -1222,8 +1222,8 @@ NIL NIL (-323 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."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-368)) (-4440 |has| |#1| (-368)) (-4442 . T) (-4443 . T) (-4445 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1211))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3555) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1716) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3722) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1713) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-324 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1234,7 +1234,7 @@ NIL NIL (-326 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}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4443 . T) (-4442 . T)) +((-4444 . T) (-4443 . T)) ((|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-798)))) (-327 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}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|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}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1250,11 +1250,11 @@ NIL ((|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174)))) (-330 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-331 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."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-332 S -1674) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) @@ -1262,7 +1262,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-373)))) (-333 -1674) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-334) ((|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."))) @@ -1306,7 +1306,7 @@ NIL NIL (-344 |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| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\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.}"))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-384)))) (|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) (-345 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}."))) @@ -1318,19 +1318,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-368)))) (-347 -1674 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(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."))) -((-4441 |has| (-413 |#2|) (-368)) (-4446 |has| (-413 |#2|) (-368)) (-4440 |has| (-413 |#2|) (-368)) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 |has| (-413 |#2|) (-368)) (-4447 |has| (-413 |#2|) (-368)) (-4441 |has| (-413 |#2|) (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-348 |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."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((-2740 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-349 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((-2740 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-350 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((-2740 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-351 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) @@ -1346,7 +1346,7 @@ NIL NIL (-354) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-355 R UP -1674) ((|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}"))) @@ -1354,23 +1354,23 @@ NIL NIL (-356 |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."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((-2740 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-357 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((-2740 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-358 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((-2740 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-359 |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}."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((-2740 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-360 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((-2740 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-361 -1674 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) @@ -1386,7 +1386,7 @@ NIL NIL (-364 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((-2740 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-365 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) @@ -1394,7 +1394,7 @@ NIL NIL (-366 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}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4445 . T)) +((-4446 . T)) NIL (-367 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1402,7 +1402,7 @@ NIL NIL (-368) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-369 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) @@ -1418,7 +1418,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-562)))) (-372 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4445 |has| |#1| (-562)) (-4443 . T) (-4442 . T)) +((-4446 |has| |#1| (-562)) (-4444 . T) (-4443 . T)) NIL (-373) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1430,7 +1430,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-368)))) (-375 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) NIL (-376 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) @@ -1439,14 +1439,14 @@ NIL (-377 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4449)) (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109)))) +((|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109)))) (-378 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4448 . T)) +((-4449 . T)) NIL (-379 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4443 . T) (-4442 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4444 . T) (-4443 . T)) NIL (-380 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."))) @@ -1458,7 +1458,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-382 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) -((-4445 . T)) +((-4446 . T)) NIL (-383 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1466,7 +1466,7 @@ NIL NIL (-384) ((|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}."))) -((-4431 . T) (-4439 . T) (-3026 . T) (-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4432 . T) (-4440 . T) (-3026 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-385 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1474,11 +1474,11 @@ NIL NIL (-386 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4443 . T) (-4442 . T)) +((-4444 . T) (-4443 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-387 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-4443 . T) (-4442 . T)) +((-4444 . T) (-4443 . T)) NIL (-388) ((|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}."))) @@ -1490,7 +1490,7 @@ NIL NIL (-390 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."))) -((-4443 . T) (-4442 . T)) +((-4444 . T) (-4443 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-391 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1502,7 +1502,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-856)))) (-393) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-394) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1514,7 +1514,7 @@ NIL NIL (-396 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4443 . T) (-4442 . T)) +((-4444 . T) (-4443 . T)) NIL (-397) ((|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"))) @@ -1544,7 +1544,7 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) NIL NIL -(-404 -3503 |returnType| -3890 |symbols|) +(-404 -3504 |returnType| -3890 |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 @@ -1562,15 +1562,15 @@ NIL NIL (-408) ((|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-409 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4431)) (|HasAttribute| |#1| (QUOTE -4439))) +((|HasAttribute| |#1| (QUOTE -4432)) (|HasAttribute| |#1| (QUOTE -4440))) (-410) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-3026 . T) (-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-3026 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-411 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."))) @@ -1582,15 +1582,15 @@ NIL NIL (-413 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4435 -12 (|has| |#1| (-6 -4446)) (|has| |#1| (-458)) (|has| |#1| (-6 -4435))) (-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-2740 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-551))) (-12 (|HasAttribute| |#1| (QUOTE -4446)) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-458)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((-4436 -12 (|has| |#1| (-6 -4447)) (|has| |#1| (-458)) (|has| |#1| (-6 -4436))) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-2740 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-551))) (-12 (|HasAttribute| |#1| (QUOTE -4447)) (|HasAttribute| |#1| (QUOTE -4436)) (|HasCategory| |#1| (QUOTE (-458)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-414 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-415 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) NIL (-416 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1606,7 +1606,7 @@ NIL NIL (-419 R -1674 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4445 . T)) +((-4446 . T)) NIL (-420 R -1674 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) @@ -1622,12 +1622,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-368)))) (-423 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{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."))) -((-4445 |has| |#1| (-562)) (-4443 . T) (-4442 . T)) +((-4446 |has| |#1| (-562)) (-4444 . T) (-4443 . T)) NIL (-424 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) -((|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -313) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1230))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-1230)))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-458)))) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -313) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1231))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-1231)))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-458)))) (-425 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL @@ -1654,7 +1654,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-373)))) (-431 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4448 . T) (-4438 . T) (-4449 . T)) +((-4449 . T) (-4439 . T) (-4450 . T)) NIL (-432 R -1674) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) @@ -1662,8 +1662,8 @@ NIL NIL (-433 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4435 -12 (|has| |#1| (-6 -4435)) (|has| |#2| (-6 -4435))) (-4442 . T) (-4443 . T) (-4445 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4435)) (|HasAttribute| |#2| (QUOTE -4435)))) +((-4436 -12 (|has| |#1| (-6 -4436)) (|has| |#2| (-6 -4436))) (-4443 . T) (-4444 . T) (-4446 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4436)) (|HasAttribute| |#2| (QUOTE -4436)))) (-434 R -1674) ((|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 @@ -1674,7 +1674,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (-436 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|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}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4445 -2740 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4443 |has| |#1| (-174)) (-4442 |has| |#1| (-174)) ((-4450 "*") |has| |#1| (-562)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-562)) (-4440 |has| |#1| (-562))) +((-4446 -2740 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) ((-4451 "*") |has| |#1| (-562)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-562)) (-4441 |has| |#1| (-562))) NIL (-437 R -1674) ((|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."))) @@ -1762,16 +1762,16 @@ NIL NIL (-458) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-459 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"))) -((-4445 |has| (-413 (-959 |#1|)) (-562)) (-4443 . T) (-4442 . T)) +((-4446 |has| (-413 (-959 |#1|)) (-562)) (-4444 . T) (-4443 . T)) ((|HasCategory| (-413 (-959 |#1|)) (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-413 (-959 |#1|)) (QUOTE (-562)))) (-460 |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"))) -(((-4450 "*") |has| |#2| (-174)) (-4441 |has| |#2| (-562)) (-4446 |has| |#2| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4446)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4451 "*") |has| |#2| (-174)) (-4442 |has| |#2| (-562)) (-4447 |has| |#2| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) +((|HasCategory| |#2| (QUOTE (-916))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4447)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-461 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1798,7 +1798,7 @@ NIL NIL (-467 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4443 . T) (-4442 . T)) +((-4444 . T) (-4443 . T)) NIL (-468 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1806,7 +1806,7 @@ NIL NIL (-469 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-868))))) (-470 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) @@ -1846,23 +1846,23 @@ NIL NIL (-479) ((|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}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4445 . T)) +((-4446 . T)) NIL (-480 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-368)) (-4440 |has| |#1| (-368)) (-4442 . T) (-4443 . T) (-4445 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1211))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3555) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1716) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3722) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1713) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-481 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4449 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2223) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109)))) +((-4450 . T)) +((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109)))) (-482 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)}"))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-868))))) (-483) ((|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}."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-484) ((|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'."))) @@ -1870,27 +1870,27 @@ NIL NIL (-485 |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."))) -((-4448 . T) (-4449 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2223) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4449 . T) (-4450 . T)) +((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-486) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-487 |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.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4450 "*") |has| |#2| (-174)) (-4441 |has| |#2| (-562)) (-4446 |has| |#2| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . 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T) (-4443 . T) (-4446 . 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(|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2740 (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasAttribute| |#2| (QUOTE -4446)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))))) (-489) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL NIL (-490 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}."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-491 -1674 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) @@ -1902,12 +1902,12 @@ NIL NIL (-493) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2740 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-494 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4448)) (|HasAttribute| |#1| (QUOTE -4449)) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) +((|HasAttribute| |#1| (QUOTE -4449)) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-495 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1934,15 +1934,15 @@ NIL NIL (-501) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) (-502 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-503 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-504 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"))) @@ -1954,7 +1954,7 @@ NIL NIL (-506 |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}."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1109))) (|HasCategory| (-112) (LIST (QUOTE -313) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-112) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-112) (QUOTE (-1109))) (|HasCategory| (-112) (LIST (QUOTE -619) (QUOTE (-868))))) (-507 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)}."))) @@ -2018,7 +2018,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-798)))) (-522 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-523) ((|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'."))) @@ -2026,28 +2026,28 @@ NIL NIL (-524 |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}."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((-2740 (|HasCategory| (-587 |#1|) (QUOTE (-146))) (|HasCategory| (-587 |#1|) (QUOTE (-373)))) (|HasCategory| (-587 |#1|) (QUOTE (-148))) (|HasCategory| (-587 |#1|) (QUOTE (-373))) (|HasCategory| (-587 |#1|) (QUOTE (-146)))) (-525 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-526 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."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-527 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -4449))) +((|HasAttribute| |#3| (QUOTE -4450))) (-528 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 -4449))) +((|HasAttribute| |#7| (QUOTE -4450))) (-529 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."))) -((-4448 . T) (-4449 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4450 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4449 . T) (-4450 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4451 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-530) ((|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 @@ -2134,7 +2134,7 @@ NIL NIL (-551) ((|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."))) -((-4446 . T) (-4447 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4447 . T) (-4448 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-552) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2154,8 +2154,8 @@ NIL NIL (-556 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4448 . T) (-4449 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2223) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4449 . T) (-4450 . T)) +((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-557 R -1674) ((|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 @@ -2170,7 +2170,7 @@ NIL NIL (-560 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-3026 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-3026 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-561 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."))) @@ -2178,7 +2178,7 @@ NIL NIL (-562) ((|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."))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-563 R -1674) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'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."))) @@ -2210,7 +2210,7 @@ NIL NIL (-570) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4430 . T) (-4436 . T) (-4440 . T) (-4435 . T) (-4446 . T) (-4447 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4431 . T) (-4437 . T) (-4441 . T) (-4436 . T) (-4447 . T) (-4448 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-571) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) @@ -2238,7 +2238,7 @@ NIL NIL (-577 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."))) -((-3026 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-3026 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-578) ((|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}\\spad{'s} exists."))) @@ -2274,11 +2274,11 @@ NIL NIL (-586 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-587 |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."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-373)))) (-588) ((|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."))) @@ -2298,7 +2298,7 @@ NIL NIL (-592 -1674) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) -((-4443 . T) (-4442 . T)) +((-4444 . T) (-4443 . T)) ((|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-593 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) @@ -2326,7 +2326,7 @@ NIL NIL (-599 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-2740 (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-600 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)}."))) @@ -2334,11 +2334,11 @@ NIL NIL (-601 |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}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))) (|HasCategory| (-570) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570)))))) (-602 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4450 "*") |has| |#1| (-562)) (-4441 |has| |#1| (-562)) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-562)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-562)))) (-603) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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"))) @@ -2362,12 +2362,12 @@ NIL NIL (-608 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-609 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 -4449)) (|HasCategory| |#2| (QUOTE (-856))) (|HasAttribute| |#1| (QUOTE -4448)) (|HasCategory| |#3| (QUOTE (-1109)))) +((|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-856))) (|HasAttribute| |#1| (QUOTE -4449)) (|HasCategory| |#3| (QUOTE (-1109)))) (-610 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2382,19 +2382,19 @@ NIL NIL (-613 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4445 -2740 (-1765 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4443 . T) (-4442 . T)) +((-4446 -2740 (-1765 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4444 . T) (-4443 . T)) ((-2740 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-614 |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."))) -((-4448 . T) (-4449 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2223) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4449 . T) (-4450 . T)) +((-12 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-615 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 (-616 |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| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4449 . T)) +((-4450 . T)) NIL (-617 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) @@ -2434,11 +2434,11 @@ NIL NIL (-626 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) -((-4445 . T)) +((-4446 . T)) NIL (-627 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}."))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-854)))) (-628 R -1674) ((|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."))) @@ -2446,7 +2446,7 @@ NIL NIL (-629 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"))) -((-4443 . T) (-4442 . T) ((-4450 "*") . T) (-4441 . T) (-4445 . T)) +((-4444 . T) (-4443 . T) ((-4451 "*") . T) (-4442 . T) (-4446 . T)) ((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (-630 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) @@ -2462,7 +2462,7 @@ NIL NIL (-633 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4445 . T)) +((-4446 . T)) NIL (-634 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) @@ -2482,19 +2482,19 @@ NIL NIL (-638) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4449 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2223) (QUOTE (-52))))))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 (-52))) (QUOTE (-1109)))) +((-4450 . T)) +((-12 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2224) (QUOTE (-52))))))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (QUOTE (-1109)))) (-639 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-368)))) (-640 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4443 . T) (-4442 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4444 . T) (-4443 . T)) NIL (-641 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4445 -2740 (-1765 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4443 . T) (-4442 . T)) +((-4446 -2740 (-1765 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4444 . T) (-4443 . T)) ((-2740 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-642 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))}."))) @@ -2507,10 +2507,10 @@ NIL (-644 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-1754 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) +((-1753 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) (-645 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4445 . T)) +((-4446 . T)) NIL (-646 R) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-linear set if it is stable by dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{Module} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet,{} RightLinearSet."))) @@ -2530,7 +2530,7 @@ NIL NIL (-650 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-651 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) @@ -2542,7 +2542,7 @@ NIL NIL (-653 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-654 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) @@ -2555,7 +2555,7 @@ NIL (-656 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4449))) +((|HasAttribute| |#1| (QUOTE -4450))) (-657 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL @@ -2566,11 +2566,11 @@ NIL NIL (-659 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}}"))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) (-660 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) (-661 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2578,15 +2578,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-368)))) (-662 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}."))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) NIL (-663 -1674 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)))) -(-664 A -2737) +(-664 A -1541) ((|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}}"))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) (-665 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) @@ -2602,7 +2602,7 @@ NIL NIL (-668 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}."))) -((-4443 . T) (-4442 . T)) +((-4444 . T) (-4443 . T)) ((|HasCategory| |#1| (QUOTE (-797)))) (-669 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2610,7 +2610,7 @@ NIL NIL (-670 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4443 . T) (-4442 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4444 . T) (-4443 . T)) ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-174)))) (-671 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}."))) @@ -2618,7 +2618,7 @@ NIL NIL (-672 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}."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) NIL (-673 -1674) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) @@ -2634,8 +2634,8 @@ NIL NIL (-676 |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."))) -((-4445 . T) (-4448 . T) (-4442 . T) (-4443 . T)) -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4450 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562))) (-2740 (|HasAttribute| |#2| (QUOTE (-4450 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((-4446 . T) (-4449 . T) (-4443 . T) (-4444 . T)) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562))) (-2740 (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-677) ((|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 @@ -2699,10 +2699,10 @@ NIL (-692 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4450 "*"))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562)))) +((|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562)))) (-693 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) NIL (-694 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,a,i,j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,a,i,j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) @@ -2710,8 +2710,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562)))) (-695 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."))) -((-4448 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4450 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-4449 . T) (-4450 . T)) +((-2740 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4451 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-696 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2730,11 +2730,11 @@ NIL NIL (-700) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4441 . T) (-4446 |has| (-705) (-368)) (-4440 |has| (-705) (-368)) (-3035 . T) (-4447 |has| (-705) (-6 -4447)) (-4444 |has| (-705) (-6 -4444)) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) -((|HasCategory| (-705) (QUOTE (-148))) (|HasCategory| (-705) (QUOTE (-146))) (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-373))) (|HasCategory| (-705) (QUOTE (-368))) (-2740 (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-235))) (-2740 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (LIST (QUOTE -290) (QUOTE (-705)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -313) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2740 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-705) (QUOTE (-1031))) (|HasCategory| (-705) (QUOTE (-1211))) (-12 (|HasCategory| (-705) (QUOTE (-1011))) (|HasCategory| (-705) (QUOTE (-1211)))) (-2740 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-2740 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (|HasCategory| (-705) (QUOTE (-551))) (-12 (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-1211)))) (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916))) (-2740 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-2740 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-562)))) (-12 (|HasCategory| (-705) (QUOTE (-235))) (|HasCategory| (-705) (QUOTE (-368)))) (-12 (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-562))) (|HasAttribute| (-705) (QUOTE -4447)) (|HasAttribute| (-705) (QUOTE -4444)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-354))))) +((-4442 . 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T)) +((|HasCategory| (-705) (QUOTE (-148))) (|HasCategory| (-705) (QUOTE (-146))) (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-373))) (|HasCategory| (-705) (QUOTE (-368))) (-2740 (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-235))) (-2740 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (LIST (QUOTE -290) (QUOTE (-705)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -313) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2740 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-705) (QUOTE (-1031))) (|HasCategory| (-705) (QUOTE (-1212))) (-12 (|HasCategory| (-705) (QUOTE (-1011))) (|HasCategory| (-705) (QUOTE (-1212)))) (-2740 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-2740 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (|HasCategory| (-705) (QUOTE (-551))) (-12 (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-1212)))) (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916))) (-2740 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-2740 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-562)))) (-12 (|HasCategory| (-705) (QUOTE (-235))) (|HasCategory| (-705) (QUOTE (-368)))) (-12 (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-562))) (|HasAttribute| (-705) (QUOTE -4448)) (|HasAttribute| (-705) (QUOTE -4445)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-354))))) (-701 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}."))) -((-4449 . T)) +((-4450 . T)) NIL (-702 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) @@ -2750,7 +2750,7 @@ NIL NIL (-705) ((|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}"))) -((-3026 . T) (-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-3026 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-706 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."))) @@ -2758,7 +2758,7 @@ NIL NIL (-707) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4447 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4448 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-708 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) @@ -2786,7 +2786,7 @@ NIL NIL (-714 R) ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#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)}.}"))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) NIL (-715 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}."))) @@ -2796,25 +2796,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-717 R |Mod| -4052 -3068 |exactQuo|) +(-717 R |Mod| -2979 -2727 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-718 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4444 |has| |#1| (-368)) (-4446 |has| |#1| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4446)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4445 |has| |#1| (-368)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . 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(|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4443 |has| |#1| (-174)) (-4442 |has| |#1| (-174)) (-4445 . T)) +((-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-721 R |Mod| -4052 -3068 |exactQuo|) +(-721 R |Mod| -2979 -2727 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4445 . T)) +((-4446 . T)) NIL (-722 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2822,11 +2822,11 @@ NIL NIL (-723 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4443 . T) (-4442 . T)) +((-4444 . T) (-4443 . T)) NIL (-724 -1674) ((|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]]}."))) -((-4445 . T)) +((-4446 . T)) NIL (-725 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."))) @@ -2850,7 +2850,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-373)))) (-730 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."))) -((-4441 |has| |#1| (-368)) (-4446 |has| |#1| (-368)) (-4440 |has| |#1| (-368)) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 |has| |#1| (-368)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-731 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."))) @@ -2878,8 +2878,8 @@ NIL NIL (-737 |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."))) -(((-4450 "*") |has| |#2| (-174)) (-4441 |has| |#2| (-562)) (-4446 |has| |#2| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4446)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4451 "*") |has| |#2| (-174)) (-4442 |has| |#2| (-562)) (-4447 |has| |#2| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) +((|HasCategory| |#2| (QUOTE (-916))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4447)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-738 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2894,15 +2894,15 @@ NIL NIL (-741 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4443 |has| |#1| (-174)) (-4442 |has| |#1| (-174)) (-4445 . T)) +((-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) (-4446 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-856)))) (-742 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4438 . T) (-4449 . T)) +((-4439 . T) (-4450 . T)) NIL (-743 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}."))) -((-4448 . T) (-4438 . T) (-4449 . T)) +((-4449 . T) (-4439 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-744) ((|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."))) @@ -2914,7 +2914,7 @@ NIL NIL (-746 |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}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4443 . T) (-4442 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4444 . T) (-4443 . T) (-4446 . T)) NIL (-747 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"))) @@ -2930,7 +2930,7 @@ NIL NIL (-750 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4443 . T) (-4442 . T)) +((-4444 . T) (-4443 . T)) NIL (-751) ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,n,scale,ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,n,scale,ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) @@ -3038,7 +3038,7 @@ NIL NIL (-777) ((|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."))) -(((-4450 "*") . T)) +(((-4451 "*") . T)) NIL (-778 R -1674) ((|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."))) @@ -3074,23 +3074,23 @@ NIL NIL (-786 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186))))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1754 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1754 (|HasCategory| |#1| (QUOTE (-551)))) (-1754 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1754 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570))))) (-1754 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1754 (|HasCategory| |#1| (LIST (QUOTE -1001) (QUOTE (-570))))))) (|HasAttribute| |#1| (QUOTE -4446)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL (-788 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) 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T) (-4443 . T) (-4446 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-789 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-790 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) NIL (-791 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}."))) @@ -3142,7 +3142,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-373)))) (-803 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) NIL (-804 -2740 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) @@ -3150,7 +3150,7 @@ NIL NIL (-805 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-2740 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (-806) ((|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."))) @@ -3214,15 +3214,15 @@ NIL NIL (-821 -2408 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4442 |has| |#2| (-1058)) (-4443 |has| |#2| (-1058)) (-4445 |has| |#2| (-6 -4445)) ((-4450 "*") |has| |#2| (-174)) (-4448 . 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T) (-4443 . T) (-4442 . T)) +(((-4451 "*") |has| |#2| (-368)) (-4442 |has| |#2| (-368)) (-4447 |has| |#2| (-368)) (-4441 |has| |#2| (-368)) (-4446 . T) (-4444 . T) (-4443 . T)) ((|HasCategory| |#2| (QUOTE (-368)))) (-824 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}))."))) @@ -3234,7 +3234,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-856)))) (-826) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-827) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) @@ -3262,7 +3262,7 @@ NIL NIL (-833 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-235)))) (-834) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev, u, true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev, u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u, true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) @@ -3274,7 +3274,7 @@ NIL NIL (-836 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4448 . T) (-4438 . T) (-4449 . T)) +((-4449 . T) (-4439 . T) (-4450 . T)) NIL (-837) ((|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."))) @@ -3286,7 +3286,7 @@ NIL NIL (-839 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."))) -((-4445 |has| |#1| (-854))) +((-4446 |has| |#1| (-854))) ((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2740 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2740 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) (-840 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}."))) @@ -3298,7 +3298,7 @@ NIL NIL (-842 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4443 |has| |#1| (-174)) (-4442 |has| |#1| (-174)) (-4445 . T)) +((-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) (-843) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) @@ -3326,7 +3326,7 @@ NIL NIL (-849 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4445 |has| |#1| (-854))) +((-4446 |has| |#1| (-854))) ((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2740 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2740 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) (-850) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) @@ -3346,7 +3346,7 @@ NIL NIL (-854) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4445 . T)) +((-4446 . T)) NIL (-855 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3362,19 +3362,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174)))) (-858 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) NIL (-859 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) -(-860 R |sigma| -3048) +(-860 R |sigma| -3049) ((|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."))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) -(-861 |x| R |sigma| -3048) +(-861 |x| R |sigma| -3049) ((|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}."))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-368)))) (-862 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..)}."))) @@ -3418,7 +3418,7 @@ NIL NIL (-872 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4443 |has| |#1| (-174)) (-4442 |has| |#1| (-174)) (-4445 . T)) +((-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368)))) (-873 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3430,19 +3430,19 @@ NIL NIL (-875 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-876 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-877 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| (-876 |#1|) (QUOTE (-916))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-148))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-876 |#1|) (QUOTE (-1031))) (|HasCategory| (-876 |#1|) (QUOTE (-826))) (-2740 (|HasCategory| (-876 |#1|) (QUOTE (-826))) (|HasCategory| (-876 |#1|) (QUOTE (-856)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-1161))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-235))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -876) (|devaluate| |#1|)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (QUOTE (-311))) (|HasCategory| (-876 |#1|) (QUOTE (-551))) (|HasCategory| (-876 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))))) (-878 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-826))) (-2740 (|HasCategory| |#2| (QUOTE (-826))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-879 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) @@ -3507,7 +3507,7 @@ NIL (-894 |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 (-1754 (|HasCategory| |#2| (QUOTE (-1058)))) (-1754 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-1754 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) +((-12 (-1753 (|HasCategory| |#2| (QUOTE (-1058)))) (-1753 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-1753 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-895 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3558,7 +3558,7 @@ NIL NIL (-907 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1, n1)..., sn, nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x, s, n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1)..., sn)}.") (($ $ |#1|) "\\spad{D(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x, s, n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}.") (($ $ |#1|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) -((-4445 . T)) +((-4446 . T)) NIL (-908 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) @@ -3570,7 +3570,7 @@ NIL NIL (-910 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p, el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p, el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4445 . T)) +((-4446 . T)) NIL (-911 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3578,7 +3578,7 @@ NIL NIL (-912 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4445 . T)) +((-4446 . T)) ((-2740 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (-913 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."))) @@ -3594,11 +3594,11 @@ NIL ((|HasCategory| |#1| (QUOTE (-146)))) (-916) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-917 |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."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-373)))) (-918 R0 -1674 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"))) @@ -3614,7 +3614,7 @@ NIL NIL (-921 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-922 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."))) @@ -3638,11 +3638,11 @@ NIL NIL (-927) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-928) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4450 "*") . T)) +(((-4451 "*") . T)) NIL (-929 -1674 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) @@ -3730,7 +3730,7 @@ NIL NIL (-950 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-951 |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}."))) @@ -3751,10 +3751,10 @@ NIL (-955 S R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-916))) (|HasAttribute| |#2| (QUOTE -4446)) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#4| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#4| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#4| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasAttribute| |#2| (QUOTE -4447)) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#4| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#4| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#4| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (-956 R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) NIL (-957 E V R P -1674) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) @@ -3766,8 +3766,8 @@ NIL NIL (-959 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}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4446)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-960 E V R P -1674) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL @@ -3790,7 +3790,7 @@ NIL NIL (-965 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-966) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} \\spad{dx}."))) @@ -3810,11 +3810,11 @@ NIL NIL (-970 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}"))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-6 -4446)) (-4442 . T) (-4443 . T) (-4445 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4446))) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4443 . T) (-4444 . T) (-4446 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4447))) (-971 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"))) -((-4445 -12 (|has| |#2| (-479)) (|has| |#1| (-479)))) +((-4446 -12 (|has| |#2| (-479)) (|has| |#1| (-479)))) ((-2740 (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-972) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) @@ -3838,7 +3838,7 @@ NIL NIL (-977 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) NIL (-978 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) @@ -3849,7 +3849,7 @@ NIL NIL NIL (-980) -((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|Integer|) (|PositiveInteger|))) (|List| (|Integer|))) "\\spad{powers(li)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) +((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|Integer|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) NIL NIL (-981 S |Coef| |Expon| |Var|) @@ -3858,7 +3858,7 @@ NIL NIL (-982 |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}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-983) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) @@ -3870,7 +3870,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-562)))) (-985 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4448 . T)) +((-4449 . T)) NIL (-986 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) @@ -3886,7 +3886,7 @@ NIL NIL (-989 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}."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) NIL (-990 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) @@ -3934,7 +3934,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-826))) (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1161)))) (-1001 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}."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-1002 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -3946,7 +3946,7 @@ NIL NIL (-1004 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) NIL (-1005 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}."))) @@ -3954,7 +3954,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-294)))) (-1006 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}."))) -((-4441 |has| |#1| (-294)) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 |has| |#1| (-294)) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-1007 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}."))) @@ -3962,11 +3962,11 @@ NIL NIL (-1008 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.}"))) -((-4441 |has| |#1| (-294)) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 |has| |#1| (-294)) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551)))) (-1009 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}."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1010 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}."))) @@ -3978,11 +3978,11 @@ NIL NIL (-1012 -1674 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4441 |has| (-413 |#2|) (-368)) (-4446 |has| (-413 |#2|) (-368)) (-4440 |has| (-413 |#2|) (-368)) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 |has| (-413 |#2|) (-368)) (-4447 |has| (-413 |#2|) (-368)) (-4441 |has| (-413 |#2|) (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2740 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2740 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2740 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2740 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) (-1013 |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."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2740 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-1014) ((|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}."))) @@ -4003,7 +4003,7 @@ NIL (-1018 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4449)) (|HasCategory| |#2| (QUOTE (-1109)))) +((|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-1109)))) (-1019 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL @@ -4014,7 +4014,7 @@ NIL NIL (-1021) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) -((-4441 . T) (-4446 . T) (-4440 . T) (-4443 . T) (-4442 . T) ((-4450 "*") . T) (-4445 . T)) +((-4442 . T) (-4447 . T) (-4441 . T) (-4444 . T) (-4443 . T) ((-4451 "*") . T) (-4446 . T)) NIL (-1022 R -1674) ((|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."))) @@ -4062,7 +4062,7 @@ NIL NIL (-1033 |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"))) -((-4441 . T) (-4446 . T) (-4440 . T) (-4443 . T) (-4442 . T) ((-4450 "*") . T) (-4445 . T)) +((-4442 . T) (-4447 . T) (-4441 . T) (-4444 . T) (-4443 . T) ((-4451 "*") . T) (-4446 . T)) ((-2740 (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570))))) (-1034 -1674 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}."))) @@ -4074,12 +4074,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1109)))) (-1036 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-868))))) (-1037 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(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{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4450 "*")))) +((|HasAttribute| |#1| (QUOTE (-4451 "*")))) (-1038 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL @@ -4102,12 +4102,12 @@ NIL NIL (-1043 -1674 |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"))) -(((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-1044) ((|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.}"))) -((-4448 . T) (-4449 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2223) (QUOTE (-52))))))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4449 . T) (-4450 . T)) +((-12 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2224) (QUOTE (-52))))))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1045) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4150,7 +4150,7 @@ NIL NIL (-1055 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-12 (|HasCategory| (-786 |#1| (-870 |#2|)) (QUOTE (-1109))) (|HasCategory| (-786 |#1| (-870 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -786) (|devaluate| |#1|) (LIST (QUOTE -870) (|devaluate| |#2|)))))) (|HasCategory| (-786 |#1| (-870 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-786 |#1| (-870 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-870 |#2|) (QUOTE (-373))) (|HasCategory| (-786 |#1| (-870 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-1056) ((|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"))) @@ -4162,7 +4162,7 @@ NIL NIL (-1058) ((|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."))) -((-4445 . T)) +((-4446 . T)) NIL (-1059 |xx| -1674) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) @@ -4178,11 +4178,11 @@ NIL ((|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (QUOTE (-562))) (|HasCategory| |#4| (QUOTE (-174)))) (-1062 |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"))) -((-4448 . T) (-4443 . T) (-4442 . T)) +((-4449 . T) (-4444 . T) (-4443 . T)) NIL (-1063 |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}."))) -((-4448 . T) (-4443 . T) (-4442 . T)) +((-4449 . T) (-4444 . T) (-4443 . T)) ((|HasCategory| |#3| (QUOTE (-174))) (-2740 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868))))) (-1064 |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}."))) @@ -4206,7 +4206,7 @@ NIL NIL (-1069) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-1070 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4214,19 +4214,19 @@ NIL NIL (-1071) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4436 . T) (-4440 . T) (-4435 . T) (-4446 . T) (-4447 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4437 . T) (-4441 . T) (-4436 . T) (-4447 . T) (-4448 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-1072) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) -((-4448 . T) (-4449 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2223) (QUOTE (-52))))))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4449 . T) (-4450 . T)) +((-12 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2224) (QUOTE (-52))))))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1073 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1001) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-1186))))) (-1074 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) NIL (-1075) ((|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'."))) @@ -4250,7 +4250,7 @@ NIL NIL (-1080 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}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) NIL (-1081 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) @@ -4286,7 +4286,7 @@ NIL NIL (-1089 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."))) -((-4441 |has| |#1| (-368)) (-4446 |has| |#1| (-368)) (-4440 |has| |#1| (-368)) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 |has| |#1| (-368)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368))))) (-1090 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) @@ -4314,8 +4314,8 @@ NIL NIL (-1096 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"))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4446)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1097 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4358,7 +4358,7 @@ NIL NIL (-1107 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}."))) -((-4438 . T)) +((-4439 . T)) NIL (-1108 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) @@ -4374,7 +4374,7 @@ NIL NIL (-1111 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) -((-4448 . T) (-4438 . T) (-4449 . T)) +((-4449 . T) (-4439 . T) (-4450 . T)) ((-2740 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-1112 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,...,an), [i1,...,im])} returns \\spad{(a_i1,...,a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,...,an), i)} returns \\spad{ai}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) @@ -4402,7 +4402,7 @@ NIL NIL (-1118 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) NIL (-1119) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em 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."))) @@ -4418,8 +4418,8 @@ NIL NIL (-1122 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4442 |has| |#3| (-1058)) (-4443 |has| |#3| (-1058)) (-4445 |has| |#3| (-6 -4445)) ((-4450 "*") |has| |#3| (-174)) (-4448 . 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says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4446,19 +4446,19 @@ NIL NIL (-1129) ((|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."))) -((-4436 . T) (-4440 . T) (-4435 . T) (-4446 . T) (-4447 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4437 . T) (-4441 . T) (-4436 . T) (-4447 . T) (-4448 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-1130 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) NIL (-1131 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-368))) (|HasAttribute| |#3| (QUOTE (-4450 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) +((|HasCategory| |#3| (QUOTE (-368))) (|HasAttribute| |#3| (QUOTE (-4451 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) (-1132 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-4448 . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4449 . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-1133 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}."))) @@ -4466,15 +4466,15 @@ NIL NIL (-1134 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."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4446)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1135 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4443 . T) (-4442 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4444 . T) (-4443 . T) (-4446 . T)) ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) (-1136 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}"))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) NIL (-1137 UP -1674) ((|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"))) @@ -4530,19 +4530,19 @@ NIL NIL (-1150 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-2740 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) (-1151 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-4445 . T) (-4437 |has| |#2| (-6 (-4450 "*"))) (-4448 . T) (-4442 . T) (-4443 . T)) -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4450 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (-2740 (|HasAttribute| |#2| (QUOTE (-4450 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((-4446 . T) (-4438 |has| |#2| (-6 (-4451 "*"))) (-4449 . T) (-4443 . T) (-4444 . T)) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (-2740 (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-1152 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1153) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) NIL (-1154 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4550,11 +4550,11 @@ NIL NIL (-1155 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-868))))) (-1156 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}."))) -((-4448 . T) (-4449 . T)) +((-4449 . T) (-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1157 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) @@ -4566,8 +4566,8 @@ NIL NIL (-1159 |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."))) -((-4449 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2223) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109)))) +((-4450 . T)) +((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109)))) (-1160) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4594,20 +4594,20 @@ NIL NIL (-1166 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) -((-4449 . T)) +((-4450 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1167) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) NIL (-1168) NIL -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-1169 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4448 . T) (-4449 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2223) (|devaluate| |#1|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4449 . T) (-4450 . T)) +((-12 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#1|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-1170 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 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 \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,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 @@ -4638,8 +4638,8 @@ NIL NIL (-1177 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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T) (-4444 . T) (-4446 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3722) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1713) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1185) ((|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 @@ -4682,8 +4682,8 @@ NIL NIL (-1188 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-6 -4446)) (-4442 . T) (-4443 . T) (-4445 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| (-980) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasAttribute| |#1| (QUOTE -4446))) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4443 . T) (-4444 . T) (-4446 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| (-980) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasAttribute| |#1| (QUOTE -4447))) (-1189) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4726,427 +4726,431 @@ NIL NIL (-1199 |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}"))) -((-4448 . T) (-4449 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2223) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) -(-1200 R) +((-4449 . T) (-4450 . T)) +((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +(-1200 S) +((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) +NIL +NIL +(-1201 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) NIL NIL -(-1201 S |Key| |Entry|) +(-1202 S |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| |#3| |#3| |#3|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\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| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) NIL NIL -(-1202 |Key| |Entry|) +(-1203 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4449 . T)) +((-4450 . T)) NIL -(-1203 |Key| |Entry|) +(-1204 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) NIL NIL -(-1204) +(-1205) ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) NIL NIL -(-1205 S) +(-1206 S) ((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) NIL NIL -(-1206) +(-1207) ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) NIL NIL -(-1207) +(-1208) ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) NIL NIL -(-1208 R) +(-1209 R) ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) NIL NIL -(-1209) +(-1210) ((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1210 S) +(-1211 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1211) +(-1212) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1212 S) +(-1213 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-1213 S) +(-1214 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1214) +(-1215) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1215 R -1674) +(-1216 R -1674) ((|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 -(-1216 R |Row| |Col| M) +(-1217 R |Row| |Col| M) ((|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 -(-1217 R -1674) +(-1218 R -1674) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -893) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -893) (|devaluate| |#1|))))) -(-1218 S R E V P) +(-1219 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} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL ((|HasCategory| |#4| (QUOTE (-373)))) -(-1219 R E V P) +(-1220 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) NIL -(-1220 |Coef|) +(-1221 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4443 . T) (-4442 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4444 . T) (-4443 . T) (-4446 . T)) ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) -(-1221 |Curve|) +(-1222 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL NIL -(-1222) +(-1223) ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,n,b,r,lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,sin(n - 1) a],...,[cos 2 a,sin 2 a],[cos a,sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,x2,x3,c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) NIL NIL -(-1223 S) +(-1224 S) ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-1224 -1674) +(-1225 -1674) ((|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 -(-1225) +(-1226) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1226) +(-1227) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1227 S) +(-1228 S) ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, b, fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a, b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < ai}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) NIL ((|HasCategory| |#1| (QUOTE (-856)))) -(-1228) +(-1229) ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,...,bm], [a1,...,an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,...,bm], [a1,...,an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,...,an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) NIL NIL -(-1229 S) +(-1230 S) ((|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."))) NIL NIL -(-1230) +(-1231) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-1231) +(-1232) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) NIL NIL -(-1232) +(-1233) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL NIL -(-1233) +(-1234) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) NIL NIL -(-1234) +(-1235) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) NIL NIL -(-1235 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1236 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1236 |Coef|) +(-1237 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-368)) (-4440 |has| |#1| (-368)) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-1237 S |Coef| UTS) +(-1238 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)}."))) NIL ((|HasCategory| |#2| (QUOTE (-368)))) -(-1238 |Coef| UTS) +(-1239 |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)}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-368)) (-4440 |has| |#1| (-368)) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-1239 |Coef| UTS) +(-1240 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. 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The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL NIL -(-1242 R S) +(-1243 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) NIL ((|HasCategory| |#1| (QUOTE (-854)))) -(-1243 S) +(-1244 S) ((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) NIL ((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-1109)))) -(-1244 |x| R |y| S) +(-1245 |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 NIL -(-1245 R Q UP) +(-1246 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1246 R UP) +(-1247 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1247 R UP) +(-1248 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1248 R U) +(-1249 R U) ((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all."))) NIL NIL -(-1249 |x| R) +(-1250 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4450 "*") |has| |#2| (-174)) (-4441 |has| |#2| (-562)) (-4444 |has| |#2| (-368)) (-4446 |has| |#2| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE -4446)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) -(-1250 R PR S PS) +(((-4451 "*") |has| |#2| (-174)) (-4442 |has| |#2| (-562)) (-4445 |has| |#2| (-368)) (-4447 |has| |#2| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE -4447)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-1251 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1251 S R) +(-1252 S 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| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\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| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\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| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|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}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1161)))) -(-1252 R) +(-1253 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4444 |has| |#1| (-368)) (-4446 |has| |#1| (-6 -4446)) (-4443 . T) (-4442 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4445 |has| |#1| (-368)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) NIL -(-1253 S |Coef| |Expon|) +(-1254 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3735) (LIST (|devaluate| |#2|) (QUOTE (-1186)))))) -(-1254 |Coef| |Expon|) +(-1255 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-1255 RC P) +(-1256 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1256 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1257 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1257 |Coef|) +(-1258 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-368)) (-4440 |has| |#1| (-368)) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-1258 S |Coef| ULS) +(-1259 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)}."))) NIL NIL -(-1259 |Coef| ULS) +(-1260 |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)}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-368)) (-4440 |has| |#1| (-368)) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-1260 |Coef| ULS) +(-1261 |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)}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-368)) (-4440 |has| |#1| (-368)) (-4442 . T) (-4443 . T) (-4445 . T)) -((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1211))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3555) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1716) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) -(-1261 |Coef| |var| |cen|) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) +((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3722) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1713) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) +(-1262 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4446 |has| |#1| (-368)) (-4440 |has| |#1| (-368)) (-4442 . T) (-4443 . T) (-4445 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1211))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3555) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1716) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) -(-1262 R FE |var| |cen|) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3722) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1713) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +(-1263 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))}."))) -(((-4450 "*") |has| (-1261 |#2| |#3| |#4|) (-174)) (-4441 |has| (-1261 |#2| |#3| |#4|) (-562)) (-4442 . T) (-4443 . T) (-4445 . T)) -((|HasCategory| (-1261 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1261 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1261 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1261 |#2| |#3| |#4|) (QUOTE (-174))) (-2740 (|HasCategory| (-1261 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1261 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| (-1261 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1261 |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1261 |#2| |#3| |#4|) (QUOTE (-368))) (|HasCategory| (-1261 |#2| |#3| |#4|) (QUOTE (-458))) (|HasCategory| (-1261 |#2| |#3| |#4|) (QUOTE (-562)))) -(-1263 A S) +(((-4451 "*") |has| (-1262 |#2| |#3| |#4|) (-174)) (-4442 |has| (-1262 |#2| |#3| |#4|) (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) +((|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-174))) (-2740 (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-368))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-458))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-562)))) +(-1264 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4449))) -(-1264 S) +((|HasAttribute| |#1| (QUOTE -4450))) +(-1265 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1265 |Coef1| |Coef2| UTS1 UTS2) +(-1266 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1266 S |Coef|) +(-1267 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1211))) (|HasSignature| |#2| (LIST (QUOTE -1716) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3555) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) -(-1267 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasSignature| |#2| (LIST (QUOTE -1713) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3722) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) +(-1268 |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."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-1268 |Coef| |var| |cen|) +(-1269 |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| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4450 "*") |has| |#1| (-174)) (-4441 |has| |#1| (-562)) (-4442 . T) (-4443 . T) (-4445 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1211))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3555) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1716) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) -(-1269 |Coef| UTS) +(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3722) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1713) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +(-1270 |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 -(-1270 -1674 UP L UTS) +(-1271 -1674 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 (-562)))) -(-1271) +(-1272) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) NIL NIL -(-1272 |sym|) +(-1273 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1273 S R) +(-1274 S 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| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "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| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|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."))) NIL ((|HasCategory| |#2| (QUOTE (-1011))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1274 R) +(-1275 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) NIL -(-1275 A B) +(-1276 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1276 R) +(-1277 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) -(-1277) +(-1278) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL -(-1278) +(-1279) ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,c1,c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,x,y,z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,dx,dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,sx,sy,sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,rotx,roty,rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,ind,pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL -(-1279) +(-1280) ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL -(-1280) +(-1281) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1281) +(-1282) ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1282 A S) +(-1283 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1283 S) +(-1284 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}."))) -((-4443 . T) (-4442 . T)) +((-4444 . T) (-4443 . T)) NIL -(-1284 R) +(-1285 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1285 K R UP -1674) +(-1286 K R UP -1674) ((|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 -(-1286) +(-1287) ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) NIL NIL -(-1287) +(-1288) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1288 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1289 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4443 |has| |#1| (-174)) (-4442 |has| |#1| (-174)) (-4445 . T)) +((-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368)))) -(-1289 R E V P) +(-1290 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) -((-4449 . T) (-4448 . T)) +((-4450 . T) (-4449 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-868))))) -(-1290 R) +(-1291 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})"))) -((-4442 . T) (-4443 . T) (-4445 . T)) +((-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-1291 |vl| R) +(-1292 |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."))) -((-4445 . T) (-4441 |has| |#2| (-6 -4441)) (-4443 . T) (-4442 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4441))) -(-1292 R |VarSet| XPOLY) +((-4446 . T) (-4442 |has| |#2| (-6 -4442)) (-4444 . T) (-4443 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4442))) +(-1293 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1293 |vl| R) +(-1294 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4441 |has| |#2| (-6 -4441)) (-4443 . T) (-4442 . T) (-4445 . T)) +((-4442 |has| |#2| (-6 -4442)) (-4444 . T) (-4443 . T) (-4446 . T)) NIL -(-1294 S -1674) +(-1295 S -1674) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1295 -1674) +(-1296 -1674) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4440 . T) (-4446 . T) (-4441 . T) ((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-1296 |VarSet| R) +(-1297 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-4441 |has| |#2| (-6 -4441)) (-4443 . T) (-4442 . T) (-4445 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -723) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasAttribute| |#2| (QUOTE -4441))) -(-1297 |vl| R) +((-4442 |has| |#2| (-6 -4442)) (-4444 . T) (-4443 . T) (-4446 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -723) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasAttribute| |#2| (QUOTE -4442))) +(-1298 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4441 |has| |#2| (-6 -4441)) (-4443 . T) (-4442 . T) (-4445 . T)) +((-4442 |has| |#2| (-6 -4442)) (-4444 . T) (-4443 . T) (-4446 . T)) NIL -(-1298 R) +(-1299 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4441 |has| |#1| (-6 -4441)) (-4443 . T) (-4442 . T) (-4445 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4441))) -(-1299 R E) +((-4442 |has| |#1| (-6 -4442)) (-4444 . T) (-4443 . T) (-4446 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4442))) +(-1300 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4445 . T) (-4446 |has| |#1| (-6 -4446)) (-4441 |has| |#1| (-6 -4441)) (-4443 . T) (-4442 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4445)) (|HasAttribute| |#1| (QUOTE -4446)) (|HasAttribute| |#1| (QUOTE -4441))) -(-1300 |VarSet| R) +((-4446 . T) (-4447 |has| |#1| (-6 -4447)) (-4442 |has| |#1| (-6 -4442)) (-4444 . T) (-4443 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4446)) (|HasAttribute| |#1| (QUOTE -4447)) (|HasAttribute| |#1| (QUOTE -4442))) +(-1301 |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."))) -((-4441 |has| |#2| (-6 -4441)) (-4443 . T) (-4442 . T) (-4445 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4441))) -(-1301 A) +((-4442 |has| |#2| (-6 -4442)) (-4444 . T) (-4443 . T) (-4446 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4442))) +(-1302 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) NIL NIL -(-1302 R |ls| |ls2|) +(-1303 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) NIL NIL -(-1303 R) +(-1304 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}\\spad{'s} exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1304 |p|) +(-1305 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4450 "*") . T) (-4442 . T) (-4443 . T) (-4445 . T)) +(((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL NIL NIL @@ -5164,4 +5168,4 @@ NIL NIL NIL NIL -((-3 NIL 2267781 2267786 2267791 2267796) (-2 NIL 2267761 2267766 2267771 2267776) (-1 NIL 2267741 2267746 2267751 2267756) (0 NIL 2267721 2267726 2267731 2267736) (-1304 "ZMOD.spad" 2267530 2267543 2267659 2267716) (-1303 "ZLINDEP.spad" 2266596 2266607 2267520 2267525) (-1302 "ZDSOLVE.spad" 2256541 2256563 2266586 2266591) (-1301 "YSTREAM.spad" 2256036 2256047 2256531 2256536) (-1300 "XRPOLY.spad" 2255256 2255276 2255892 2255961) (-1299 "XPR.spad" 2253051 2253064 2254974 2255073) (-1298 "XPOLY.spad" 2252606 2252617 2252907 2252976) (-1297 "XPOLYC.spad" 2251925 2251941 2252532 2252601) (-1296 "XPBWPOLY.spad" 2250362 2250382 2251705 2251774) (-1295 "XF.spad" 2248825 2248840 2250264 2250357) (-1294 "XF.spad" 2247268 2247285 2248709 2248714) (-1293 "XFALG.spad" 2244316 2244332 2247194 2247263) (-1292 "XEXPPKG.spad" 2243567 2243593 2244306 2244311) (-1291 "XDPOLY.spad" 2243181 2243197 2243423 2243492) (-1290 "XALG.spad" 2242841 2242852 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"STEPAST.spad" 1959783 1959792 1960539 1960544) (-1159 "STBL.spad" 1958309 1958337 1958476 1958491) (-1158 "STAGG.spad" 1957384 1957395 1958299 1958304) (-1157 "STAGG.spad" 1956457 1956470 1957374 1957379) (-1156 "STACK.spad" 1955814 1955825 1956064 1956091) (-1155 "SREGSET.spad" 1953518 1953535 1955460 1955487) (-1154 "SRDCMPK.spad" 1952079 1952099 1953508 1953513) (-1153 "SRAGG.spad" 1947222 1947231 1952047 1952074) (-1152 "SRAGG.spad" 1942385 1942396 1947212 1947217) (-1151 "SQMATRIX.spad" 1940001 1940019 1940917 1941004) (-1150 "SPLTREE.spad" 1934553 1934566 1939437 1939464) (-1149 "SPLNODE.spad" 1931141 1931154 1934543 1934548) (-1148 "SPFCAT.spad" 1929950 1929959 1931131 1931136) (-1147 "SPECOUT.spad" 1928502 1928511 1929940 1929945) (-1146 "SPADXPT.spad" 1920097 1920106 1928492 1928497) (-1145 "spad-parser.spad" 1919562 1919571 1920087 1920092) (-1144 "SPADAST.spad" 1919263 1919272 1919552 1919557) (-1143 "SPACEC.spad" 1903462 1903473 1919253 1919258) (-1142 "SPACE3.spad" 1903238 1903249 1903452 1903457) (-1141 "SORTPAK.spad" 1902787 1902800 1903194 1903199) (-1140 "SOLVETRA.spad" 1900550 1900561 1902777 1902782) (-1139 "SOLVESER.spad" 1899078 1899089 1900540 1900545) (-1138 "SOLVERAD.spad" 1895104 1895115 1899068 1899073) (-1137 "SOLVEFOR.spad" 1893566 1893584 1895094 1895099) (-1136 "SNTSCAT.spad" 1893166 1893183 1893534 1893561) (-1135 "SMTS.spad" 1891438 1891464 1892731 1892828) (-1134 "SMP.spad" 1888913 1888933 1889303 1889430) (-1133 "SMITH.spad" 1887758 1887783 1888903 1888908) (-1132 "SMATCAT.spad" 1885868 1885898 1887702 1887753) (-1131 "SMATCAT.spad" 1883910 1883942 1885746 1885751) (-1130 "SKAGG.spad" 1882873 1882884 1883878 1883905) (-1129 "SINT.spad" 1881813 1881822 1882739 1882868) (-1128 "SIMPAN.spad" 1881541 1881550 1881803 1881808) (-1127 "SIG.spad" 1880871 1880880 1881531 1881536) (-1126 "SIGNRF.spad" 1879989 1880000 1880861 1880866) (-1125 "SIGNEF.spad" 1879268 1879285 1879979 1879984) (-1124 "SIGAST.spad" 1878653 1878662 1879258 1879263) (-1123 "SHP.spad" 1876581 1876596 1878609 1878614) (-1122 "SHDP.spad" 1866292 1866319 1866801 1866932) (-1121 "SGROUP.spad" 1865900 1865909 1866282 1866287) (-1120 "SGROUP.spad" 1865506 1865517 1865890 1865895) (-1119 "SGCF.spad" 1858669 1858678 1865496 1865501) (-1118 "SFRTCAT.spad" 1857599 1857616 1858637 1858664) (-1117 "SFRGCD.spad" 1856662 1856682 1857589 1857594) (-1116 "SFQCMPK.spad" 1851299 1851319 1856652 1856657) (-1115 "SFORT.spad" 1850738 1850752 1851289 1851294) (-1114 "SEXOF.spad" 1850581 1850621 1850728 1850733) (-1113 "SEX.spad" 1850473 1850482 1850571 1850576) (-1112 "SEXCAT.spad" 1848074 1848114 1850463 1850468) (-1111 "SET.spad" 1846398 1846409 1847495 1847534) (-1110 "SETMN.spad" 1844848 1844865 1846388 1846393) (-1109 "SETCAT.spad" 1844170 1844179 1844838 1844843) (-1108 "SETCAT.spad" 1843490 1843501 1844160 1844165) (-1107 "SETAGG.spad" 1840039 1840050 1843470 1843485) (-1106 "SETAGG.spad" 1836596 1836609 1840029 1840034) (-1105 "SEQAST.spad" 1836299 1836308 1836586 1836591) (-1104 "SEGXCAT.spad" 1835455 1835468 1836289 1836294) (-1103 "SEG.spad" 1835268 1835279 1835374 1835379) (-1102 "SEGCAT.spad" 1834193 1834204 1835258 1835263) (-1101 "SEGBIND.spad" 1833951 1833962 1834140 1834145) (-1100 "SEGBIND2.spad" 1833649 1833662 1833941 1833946) (-1099 "SEGAST.spad" 1833363 1833372 1833639 1833644) (-1098 "SEG2.spad" 1832798 1832811 1833319 1833324) (-1097 "SDVAR.spad" 1832074 1832085 1832788 1832793) (-1096 "SDPOL.spad" 1829500 1829511 1829791 1829918) (-1095 "SCPKG.spad" 1827589 1827600 1829490 1829495) (-1094 "SCOPE.spad" 1826742 1826751 1827579 1827584) (-1093 "SCACHE.spad" 1825438 1825449 1826732 1826737) (-1092 "SASTCAT.spad" 1825347 1825356 1825428 1825433) (-1091 "SAOS.spad" 1825219 1825228 1825337 1825342) (-1090 "SAERFFC.spad" 1824932 1824952 1825209 1825214) (-1089 "SAE.spad" 1823107 1823123 1823718 1823853) (-1088 "SAEFACT.spad" 1822808 1822828 1823097 1823102) (-1087 "RURPK.spad" 1820467 1820483 1822798 1822803) (-1086 "RULESET.spad" 1819920 1819944 1820457 1820462) (-1085 "RULE.spad" 1818160 1818184 1819910 1819915) (-1084 "RULECOLD.spad" 1818012 1818025 1818150 1818155) (-1083 "RTVALUE.spad" 1817747 1817756 1818002 1818007) (-1082 "RSTRCAST.spad" 1817464 1817473 1817737 1817742) (-1081 "RSETGCD.spad" 1813842 1813862 1817454 1817459) (-1080 "RSETCAT.spad" 1803778 1803795 1813810 1813837) (-1079 "RSETCAT.spad" 1793734 1793753 1803768 1803773) (-1078 "RSDCMPK.spad" 1792186 1792206 1793724 1793729) (-1077 "RRCC.spad" 1790570 1790600 1792176 1792181) (-1076 "RRCC.spad" 1788952 1788984 1790560 1790565) (-1075 "RPTAST.spad" 1788654 1788663 1788942 1788947) (-1074 "RPOLCAT.spad" 1768014 1768029 1788522 1788649) (-1073 "RPOLCAT.spad" 1747087 1747104 1767597 1767602) (-1072 "ROUTINE.spad" 1742970 1742979 1745734 1745761) (-1071 "ROMAN.spad" 1742298 1742307 1742836 1742965) (-1070 "ROIRC.spad" 1741378 1741410 1742288 1742293) (-1069 "RNS.spad" 1740281 1740290 1741280 1741373) (-1068 "RNS.spad" 1739270 1739281 1740271 1740276) (-1067 "RNG.spad" 1739005 1739014 1739260 1739265) (-1066 "RNGBIND.spad" 1738165 1738179 1738960 1738965) (-1065 "RMODULE.spad" 1737930 1737941 1738155 1738160) (-1064 "RMCAT2.spad" 1737350 1737407 1737920 1737925) (-1063 "RMATRIX.spad" 1736174 1736193 1736517 1736556) (-1062 "RMATCAT.spad" 1731753 1731784 1736130 1736169) (-1061 "RMATCAT.spad" 1727222 1727255 1731601 1731606) (-1060 "RLINSET.spad" 1726616 1726627 1727212 1727217) (-1059 "RINTERP.spad" 1726504 1726524 1726606 1726611) (-1058 "RING.spad" 1725974 1725983 1726484 1726499) (-1057 "RING.spad" 1725452 1725463 1725964 1725969) (-1056 "RIDIST.spad" 1724844 1724853 1725442 1725447) (-1055 "RGCHAIN.spad" 1723427 1723443 1724329 1724356) (-1054 "RGBCSPC.spad" 1723208 1723220 1723417 1723422) (-1053 "RGBCMDL.spad" 1722738 1722750 1723198 1723203) (-1052 "RF.spad" 1720380 1720391 1722728 1722733) (-1051 "RFFACTOR.spad" 1719842 1719853 1720370 1720375) (-1050 "RFFACT.spad" 1719577 1719589 1719832 1719837) (-1049 "RFDIST.spad" 1718573 1718582 1719567 1719572) (-1048 "RETSOL.spad" 1717992 1718005 1718563 1718568) (-1047 "RETRACT.spad" 1717420 1717431 1717982 1717987) (-1046 "RETRACT.spad" 1716846 1716859 1717410 1717415) (-1045 "RETAST.spad" 1716658 1716667 1716836 1716841) (-1044 "RESULT.spad" 1714718 1714727 1715305 1715332) (-1043 "RESRING.spad" 1714065 1714112 1714656 1714713) (-1042 "RESLATC.spad" 1713389 1713400 1714055 1714060) (-1041 "REPSQ.spad" 1713120 1713131 1713379 1713384) (-1040 "REP.spad" 1710674 1710683 1713110 1713115) (-1039 "REPDB.spad" 1710381 1710392 1710664 1710669) (-1038 "REP2.spad" 1700039 1700050 1710223 1710228) (-1037 "REP1.spad" 1694235 1694246 1699989 1699994) (-1036 "REGSET.spad" 1692032 1692049 1693881 1693908) (-1035 "REF.spad" 1691367 1691378 1691987 1691992) (-1034 "REDORDER.spad" 1690573 1690590 1691357 1691362) (-1033 "RECLOS.spad" 1689356 1689376 1690060 1690153) (-1032 "REALSOLV.spad" 1688496 1688505 1689346 1689351) (-1031 "REAL.spad" 1688368 1688377 1688486 1688491) (-1030 "REAL0Q.spad" 1685666 1685681 1688358 1688363) (-1029 "REAL0.spad" 1682510 1682525 1685656 1685661) (-1028 "RDUCEAST.spad" 1682231 1682240 1682500 1682505) (-1027 "RDIV.spad" 1681886 1681911 1682221 1682226) (-1026 "RDIST.spad" 1681453 1681464 1681876 1681881) (-1025 "RDETRS.spad" 1680317 1680335 1681443 1681448) (-1024 "RDETR.spad" 1678456 1678474 1680307 1680312) (-1023 "RDEEFS.spad" 1677555 1677572 1678446 1678451) (-1022 "RDEEF.spad" 1676565 1676582 1677545 1677550) (-1021 "RCFIELD.spad" 1673751 1673760 1676467 1676560) (-1020 "RCFIELD.spad" 1671023 1671034 1673741 1673746) (-1019 "RCAGG.spad" 1668951 1668962 1671013 1671018) (-1018 "RCAGG.spad" 1666806 1666819 1668870 1668875) (-1017 "RATRET.spad" 1666166 1666177 1666796 1666801) (-1016 "RATFACT.spad" 1665858 1665870 1666156 1666161) (-1015 "RANDSRC.spad" 1665177 1665186 1665848 1665853) (-1014 "RADUTIL.spad" 1664933 1664942 1665167 1665172) (-1013 "RADIX.spad" 1661854 1661868 1663400 1663493) (-1012 "RADFF.spad" 1660267 1660304 1660386 1660542) (-1011 "RADCAT.spad" 1659862 1659871 1660257 1660262) (-1010 "RADCAT.spad" 1659455 1659466 1659852 1659857) (-1009 "QUEUE.spad" 1658803 1658814 1659062 1659089) (-1008 "QUAT.spad" 1657384 1657395 1657727 1657792) (-1007 "QUATCT2.spad" 1657004 1657023 1657374 1657379) (-1006 "QUATCAT.spad" 1655174 1655185 1656934 1656999) (-1005 "QUATCAT.spad" 1653095 1653108 1654857 1654862) (-1004 "QUAGG.spad" 1651922 1651933 1653063 1653090) (-1003 "QQUTAST.spad" 1651690 1651699 1651912 1651917) (-1002 "QFORM.spad" 1651154 1651169 1651680 1651685) (-1001 "QFCAT.spad" 1649856 1649867 1651056 1651149) (-1000 "QFCAT.spad" 1648149 1648162 1649351 1649356) (-999 "QFCAT2.spad" 1647842 1647858 1648139 1648144) (-998 "QEQUAT.spad" 1647401 1647409 1647832 1647837) (-997 "QCMPACK.spad" 1642148 1642167 1647391 1647396) (-996 "QALGSET.spad" 1638227 1638259 1642062 1642067) (-995 "QALGSET2.spad" 1636223 1636241 1638217 1638222) (-994 "PWFFINTB.spad" 1633639 1633660 1636213 1636218) (-993 "PUSHVAR.spad" 1632978 1632997 1633629 1633634) (-992 "PTRANFN.spad" 1629106 1629116 1632968 1632973) (-991 "PTPACK.spad" 1626194 1626204 1629096 1629101) (-990 "PTFUNC2.spad" 1626017 1626031 1626184 1626189) (-989 "PTCAT.spad" 1625272 1625282 1625985 1626012) (-988 "PSQFR.spad" 1624579 1624603 1625262 1625267) (-987 "PSEUDLIN.spad" 1623465 1623475 1624569 1624574) (-986 "PSETPK.spad" 1608898 1608914 1623343 1623348) (-985 "PSETCAT.spad" 1602818 1602841 1608878 1608893) (-984 "PSETCAT.spad" 1596712 1596737 1602774 1602779) (-983 "PSCURVE.spad" 1595695 1595703 1596702 1596707) (-982 "PSCAT.spad" 1594478 1594507 1595593 1595690) (-981 "PSCAT.spad" 1593351 1593382 1594468 1594473) (-980 "PRTITION.spad" 1592440 1592448 1593341 1593346) (-979 "PRTDAST.spad" 1592159 1592167 1592430 1592435) (-978 "PRS.spad" 1581721 1581738 1592115 1592120) (-977 "PRQAGG.spad" 1581156 1581166 1581689 1581716) (-976 "PROPLOG.spad" 1580728 1580736 1581146 1581151) (-975 "PROPFUN2.spad" 1580351 1580364 1580718 1580723) (-974 "PROPFUN1.spad" 1579749 1579760 1580341 1580346) (-973 "PROPFRML.spad" 1578317 1578328 1579739 1579744) (-972 "PROPERTY.spad" 1577805 1577813 1578307 1578312) (-971 "PRODUCT.spad" 1575487 1575499 1575771 1575826) (-970 "PR.spad" 1573879 1573891 1574578 1574705) (-969 "PRINT.spad" 1573631 1573639 1573869 1573874) (-968 "PRIMES.spad" 1571884 1571894 1573621 1573626) (-967 "PRIMELT.spad" 1569965 1569979 1571874 1571879) (-966 "PRIMCAT.spad" 1569592 1569600 1569955 1569960) (-965 "PRIMARR.spad" 1568597 1568607 1568775 1568802) (-964 "PRIMARR2.spad" 1567364 1567376 1568587 1568592) (-963 "PREASSOC.spad" 1566746 1566758 1567354 1567359) (-962 "PPCURVE.spad" 1565883 1565891 1566736 1566741) (-961 "PORTNUM.spad" 1565658 1565666 1565873 1565878) (-960 "POLYROOT.spad" 1564507 1564529 1565614 1565619) (-959 "POLY.spad" 1561842 1561852 1562357 1562484) (-958 "POLYLIFT.spad" 1561107 1561130 1561832 1561837) (-957 "POLYCATQ.spad" 1559225 1559247 1561097 1561102) (-956 "POLYCAT.spad" 1552695 1552716 1559093 1559220) (-955 "POLYCAT.spad" 1545503 1545526 1551903 1551908) (-954 "POLY2UP.spad" 1544955 1544969 1545493 1545498) (-953 "POLY2.spad" 1544552 1544564 1544945 1544950) (-952 "POLUTIL.spad" 1543493 1543522 1544508 1544513) (-951 "POLTOPOL.spad" 1542241 1542256 1543483 1543488) (-950 "POINT.spad" 1541079 1541089 1541166 1541193) (-949 "PNTHEORY.spad" 1537781 1537789 1541069 1541074) (-948 "PMTOOLS.spad" 1536556 1536570 1537771 1537776) (-947 "PMSYM.spad" 1536105 1536115 1536546 1536551) (-946 "PMQFCAT.spad" 1535696 1535710 1536095 1536100) (-945 "PMPRED.spad" 1535175 1535189 1535686 1535691) (-944 "PMPREDFS.spad" 1534629 1534651 1535165 1535170) (-943 "PMPLCAT.spad" 1533709 1533727 1534561 1534566) (-942 "PMLSAGG.spad" 1533294 1533308 1533699 1533704) (-941 "PMKERNEL.spad" 1532873 1532885 1533284 1533289) (-940 "PMINS.spad" 1532453 1532463 1532863 1532868) (-939 "PMFS.spad" 1532030 1532048 1532443 1532448) (-938 "PMDOWN.spad" 1531320 1531334 1532020 1532025) (-937 "PMASS.spad" 1530330 1530338 1531310 1531315) (-936 "PMASSFS.spad" 1529297 1529313 1530320 1530325) (-935 "PLOTTOOL.spad" 1529077 1529085 1529287 1529292) (-934 "PLOT.spad" 1524000 1524008 1529067 1529072) (-933 "PLOT3D.spad" 1520464 1520472 1523990 1523995) (-932 "PLOT1.spad" 1519621 1519631 1520454 1520459) (-931 "PLEQN.spad" 1506911 1506938 1519611 1519616) (-930 "PINTERP.spad" 1506533 1506552 1506901 1506906) (-929 "PINTERPA.spad" 1506317 1506333 1506523 1506528) (-928 "PI.spad" 1505926 1505934 1506291 1506312) (-927 "PID.spad" 1504896 1504904 1505852 1505921) (-926 "PICOERCE.spad" 1504553 1504563 1504886 1504891) (-925 "PGROEB.spad" 1503154 1503168 1504543 1504548) (-924 "PGE.spad" 1494771 1494779 1503144 1503149) (-923 "PGCD.spad" 1493661 1493678 1494761 1494766) (-922 "PFRPAC.spad" 1492810 1492820 1493651 1493656) (-921 "PFR.spad" 1489473 1489483 1492712 1492805) (-920 "PFOTOOLS.spad" 1488731 1488747 1489463 1489468) (-919 "PFOQ.spad" 1488101 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1451261 1452646 1452651) (-899 "PATTERN.spad" 1445783 1445793 1451234 1451239) (-898 "PATTERN2.spad" 1445521 1445533 1445773 1445778) (-897 "PATTERN1.spad" 1443857 1443873 1445511 1445516) (-896 "PATRES.spad" 1441432 1441444 1443847 1443852) (-895 "PATRES2.spad" 1441104 1441118 1441422 1441427) (-894 "PATMATCH.spad" 1439301 1439332 1440812 1440817) (-893 "PATMAB.spad" 1438730 1438740 1439291 1439296) (-892 "PATLRES.spad" 1437816 1437830 1438720 1438725) (-891 "PATAB.spad" 1437580 1437590 1437806 1437811) (-890 "PARTPERM.spad" 1434980 1434988 1437570 1437575) (-889 "PARSURF.spad" 1434414 1434442 1434970 1434975) (-888 "PARSU2.spad" 1434211 1434227 1434404 1434409) (-887 "script-parser.spad" 1433731 1433739 1434201 1434206) (-886 "PARSCURV.spad" 1433165 1433193 1433721 1433726) (-885 "PARSC2.spad" 1432956 1432972 1433155 1433160) (-884 "PARPCURV.spad" 1432418 1432446 1432946 1432951) (-883 "PARPC2.spad" 1432209 1432225 1432408 1432413) (-882 "PARAMAST.spad" 1431337 1431345 1432199 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296435 297063 297068) (-247 "DLIST.spad" 295004 295014 295608 295635) (-246 "DLAGG.spad" 293421 293431 294994 294999) (-245 "DIVRING.spad" 292963 292971 293365 293416) (-244 "DIVRING.spad" 292549 292559 292953 292958) (-243 "DISPLAY.spad" 290739 290747 292539 292544) (-242 "DIRPROD.spad" 280319 280335 280959 281090) (-241 "DIRPROD2.spad" 279137 279155 280309 280314) (-240 "DIRPCAT.spad" 278081 278097 279001 279132) (-239 "DIRPCAT.spad" 276754 276772 277676 277681) (-238 "DIOSP.spad" 275579 275587 276744 276749) (-237 "DIOPS.spad" 274575 274585 275559 275574) (-236 "DIOPS.spad" 273545 273557 274531 274536) (-235 "DIFRING.spad" 272841 272849 273525 273540) (-234 "DIFRING.spad" 272145 272155 272831 272836) (-233 "DIFEXT.spad" 271316 271326 272125 272140) (-232 "DIFEXT.spad" 270404 270416 271215 271220) (-231 "DIAGG.spad" 270034 270044 270384 270399) (-230 "DIAGG.spad" 269672 269684 270024 270029) (-229 "DHMATRIX.spad" 267984 267994 269129 269156) (-228 "DFSFUN.spad" 261624 261632 267974 267979) (-227 "DFLOAT.spad" 258355 258363 261514 261619) (-226 "DFINTTLS.spad" 256586 256602 258345 258350) (-225 "DERHAM.spad" 254500 254532 256566 256581) (-224 "DEQUEUE.spad" 253824 253834 254107 254134) (-223 "DEGRED.spad" 253441 253455 253814 253819) (-222 "DEFINTRF.spad" 250978 250988 253431 253436) (-221 "DEFINTEF.spad" 249488 249504 250968 250973) (-220 "DEFAST.spad" 248856 248864 249478 249483) (-219 "DECIMAL.spad" 246962 246970 247323 247416) (-218 "DDFACT.spad" 244775 244792 246952 246957) (-217 "DBLRESP.spad" 244375 244399 244765 244770) (-216 "DBASE.spad" 243039 243049 244365 244370) (-215 "DATAARY.spad" 242501 242514 243029 243034) (-214 "D03FAFA.spad" 242329 242337 242491 242496) (-213 "D03EEFA.spad" 242149 242157 242319 242324) (-212 "D03AGNT.spad" 241235 241243 242139 242144) (-211 "D02EJFA.spad" 240697 240705 241225 241230) (-210 "D02CJFA.spad" 240175 240183 240687 240692) (-209 "D02BHFA.spad" 239665 239673 240165 240170) (-208 "D02BBFA.spad" 239155 239163 239655 239660) (-207 "D02AGNT.spad" 233969 233977 239145 239150) (-206 "D01WGTS.spad" 232288 232296 233959 233964) (-205 "D01TRNS.spad" 232265 232273 232278 232283) (-204 "D01GBFA.spad" 231787 231795 232255 232260) (-203 "D01FCFA.spad" 231309 231317 231777 231782) (-202 "D01ASFA.spad" 230777 230785 231299 231304) (-201 "D01AQFA.spad" 230223 230231 230767 230772) (-200 "D01APFA.spad" 229647 229655 230213 230218) (-199 "D01ANFA.spad" 229141 229149 229637 229642) (-198 "D01AMFA.spad" 228651 228659 229131 229136) (-197 "D01ALFA.spad" 228191 228199 228641 228646) (-196 "D01AKFA.spad" 227717 227725 228181 228186) (-195 "D01AJFA.spad" 227240 227248 227707 227712) (-194 "D01AGNT.spad" 223307 223315 227230 227235) (-193 "CYCLOTOM.spad" 222813 222821 223297 223302) (-192 "CYCLES.spad" 219669 219677 222803 222808) (-191 "CVMP.spad" 219086 219096 219659 219664) (-190 "CTRIGMNP.spad" 217586 217602 219076 219081) (-189 "CTOR.spad" 217277 217285 217576 217581) (-188 "CTORKIND.spad" 216880 216888 217267 217272) (-187 "CTORCAT.spad" 216129 216137 216870 216875) (-186 "CTORCAT.spad" 215376 215386 216119 216124) (-185 "CTORCALL.spad" 214965 214975 215366 215371) (-184 "CSTTOOLS.spad" 214210 214223 214955 214960) (-183 "CRFP.spad" 207934 207947 214200 214205) (-182 "CRCEAST.spad" 207654 207662 207924 207929) (-181 "CRAPACK.spad" 206705 206715 207644 207649) (-180 "CPMATCH.spad" 206209 206224 206630 206635) (-179 "CPIMA.spad" 205914 205933 206199 206204) (-178 "COORDSYS.spad" 200923 200933 205904 205909) (-177 "CONTOUR.spad" 200334 200342 200913 200918) (-176 "CONTFRAC.spad" 196084 196094 200236 200329) (-175 "CONDUIT.spad" 195842 195850 196074 196079) (-174 "COMRING.spad" 195516 195524 195780 195837) (-173 "COMPPROP.spad" 195034 195042 195506 195511) (-172 "COMPLPAT.spad" 194801 194816 195024 195029) (-171 "COMPLEX.spad" 188938 188948 189182 189443) (-170 "COMPLEX2.spad" 188653 188665 188928 188933) (-169 "COMPILER.spad" 188202 188210 188643 188648) (-168 "COMPFACT.spad" 187804 187818 188192 188197) (-167 "COMPCAT.spad" 185876 185886 187538 187799) (-166 "COMPCAT.spad" 183676 183688 185340 185345) (-165 "COMMUPC.spad" 183424 183442 183666 183671) (-164 "COMMONOP.spad" 182957 182965 183414 183419) (-163 "COMM.spad" 182768 182776 182947 182952) (-162 "COMMAAST.spad" 182531 182539 182758 182763) (-161 "COMBOPC.spad" 181446 181454 182521 182526) (-160 "COMBINAT.spad" 180213 180223 181436 181441) (-159 "COMBF.spad" 177595 177611 180203 180208) (-158 "COLOR.spad" 176432 176440 177585 177590) (-157 "COLONAST.spad" 176098 176106 176422 176427) (-156 "CMPLXRT.spad" 175809 175826 176088 176093) (-155 "CLLCTAST.spad" 175471 175479 175799 175804) (-154 "CLIP.spad" 171579 171587 175461 175466) (-153 "CLIF.spad" 170234 170250 171535 171574) (-152 "CLAGG.spad" 166739 166749 170224 170229) (-151 "CLAGG.spad" 163115 163127 166602 166607) (-150 "CINTSLPE.spad" 162446 162459 163105 163110) (-149 "CHVAR.spad" 160584 160606 162436 162441) (-148 "CHARZ.spad" 160499 160507 160564 160579) (-147 "CHARPOL.spad" 160009 160019 160489 160494) (-146 "CHARNZ.spad" 159762 159770 159989 160004) (-145 "CHAR.spad" 157636 157644 159752 159757) (-144 "CFCAT.spad" 156964 156972 157626 157631) (-143 "CDEN.spad" 156160 156174 156954 156959) (-142 "CCLASS.spad" 154309 154317 155571 155610) (-141 "CATEGORY.spad" 153351 153359 154299 154304) (-140 "CATCTOR.spad" 153242 153250 153341 153346) (-139 "CATAST.spad" 152860 152868 153232 153237) (-138 "CASEAST.spad" 152574 152582 152850 152855) (-137 "CARTEN.spad" 147861 147885 152564 152569) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-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 2268037 2268042 2268047 2268052) (-2 NIL 2268017 2268022 2268027 2268032) (-1 NIL 2267997 2268002 2268007 2268012) (0 NIL 2267977 2267982 2267987 2267992) (-1305 "ZMOD.spad" 2267786 2267799 2267915 2267972) (-1304 "ZLINDEP.spad" 2266852 2266863 2267776 2267781) (-1303 "ZDSOLVE.spad" 2256797 2256819 2266842 2266847) (-1302 "YSTREAM.spad" 2256292 2256303 2256787 2256792) (-1301 "XRPOLY.spad" 2255512 2255532 2256148 2256217) (-1300 "XPR.spad" 2253307 2253320 2255230 2255329) (-1299 "XPOLY.spad" 2252862 2252873 2253163 2253232) (-1298 "XPOLYC.spad" 2252181 2252197 2252788 2252857) (-1297 "XPBWPOLY.spad" 2250618 2250638 2251961 2252030) (-1296 "XF.spad" 2249081 2249096 2250520 2250613) (-1295 "XF.spad" 2247524 2247541 2248965 2248970) (-1294 "XFALG.spad" 2244572 2244588 2247450 2247519) (-1293 "XEXPPKG.spad" 2243823 2243849 2244562 2244567) (-1292 "XDPOLY.spad" 2243437 2243453 2243679 2243748) (-1291 "XALG.spad" 2243097 2243108 2243393 2243432) (-1290 "WUTSET.spad" 2238936 2238953 2242743 2242770) (-1289 "WP.spad" 2238135 2238179 2238794 2238861) (-1288 "WHILEAST.spad" 2237933 2237942 2238125 2238130) (-1287 "WHEREAST.spad" 2237604 2237613 2237923 2237928) (-1286 "WFFINTBS.spad" 2235267 2235289 2237594 2237599) (-1285 "WEIER.spad" 2233489 2233500 2235257 2235262) (-1284 "VSPACE.spad" 2233162 2233173 2233457 2233484) (-1283 "VSPACE.spad" 2232855 2232868 2233152 2233157) (-1282 "VOID.spad" 2232532 2232541 2232845 2232850) (-1281 "VIEW.spad" 2230212 2230221 2232522 2232527) (-1280 "VIEWDEF.spad" 2225413 2225422 2230202 2230207) (-1279 "VIEW3D.spad" 2209374 2209383 2225403 2225408) (-1278 "VIEW2D.spad" 2197265 2197274 2209364 2209369) (-1277 "VECTOR.spad" 2195939 2195950 2196190 2196217) (-1276 "VECTOR2.spad" 2194578 2194591 2195929 2195934) (-1275 "VECTCAT.spad" 2192482 2192493 2194546 2194573) (-1274 "VECTCAT.spad" 2190193 2190206 2192259 2192264) (-1273 "VARIABLE.spad" 2189973 2189988 2190183 2190188) (-1272 "UTYPE.spad" 2189617 2189626 2189963 2189968) (-1271 "UTSODETL.spad" 2188912 2188936 2189573 2189578) (-1270 "UTSODE.spad" 2187128 2187148 2188902 2188907) (-1269 "UTS.spad" 2181932 2181960 2185595 2185692) (-1268 "UTSCAT.spad" 2179411 2179427 2181830 2181927) (-1267 "UTSCAT.spad" 2176534 2176552 2178955 2178960) (-1266 "UTS2.spad" 2176129 2176164 2176524 2176529) (-1265 "URAGG.spad" 2170802 2170813 2176119 2176124) (-1264 "URAGG.spad" 2165439 2165452 2170758 2170763) (-1263 "UPXSSING.spad" 2163084 2163110 2164520 2164653) (-1262 "UPXS.spad" 2160238 2160266 2161216 2161365) (-1261 "UPXSCONS.spad" 2157997 2158017 2158370 2158519) (-1260 "UPXSCCA.spad" 2156568 2156588 2157843 2157992) (-1259 "UPXSCCA.spad" 2155281 2155303 2156558 2156563) (-1258 "UPXSCAT.spad" 2153870 2153886 2155127 2155276) (-1257 "UPXS2.spad" 2153413 2153466 2153860 2153865) (-1256 "UPSQFREE.spad" 2151827 2151841 2153403 2153408) (-1255 "UPSCAT.spad" 2149438 2149462 2151725 2151822) (-1254 "UPSCAT.spad" 2146755 2146781 2149044 2149049) (-1253 "UPOLYC.spad" 2141795 2141806 2146597 2146750) (-1252 "UPOLYC.spad" 2136727 2136740 2141531 2141536) (-1251 "UPOLYC2.spad" 2136198 2136217 2136717 2136722) (-1250 "UP.spad" 2133397 2133412 2133784 2133937) (-1249 "UPMP.spad" 2132297 2132310 2133387 2133392) (-1248 "UPDIVP.spad" 2131862 2131876 2132287 2132292) (-1247 "UPDECOMP.spad" 2130107 2130121 2131852 2131857) (-1246 "UPCDEN.spad" 2129316 2129332 2130097 2130102) (-1245 "UP2.spad" 2128680 2128701 2129306 2129311) (-1244 "UNISEG.spad" 2128033 2128044 2128599 2128604) (-1243 "UNISEG2.spad" 2127530 2127543 2127989 2127994) (-1242 "UNIFACT.spad" 2126633 2126645 2127520 2127525) (-1241 "ULS.spad" 2117191 2117219 2118278 2118707) (-1240 "ULSCONS.spad" 2109587 2109607 2109957 2110106) (-1239 "ULSCCAT.spad" 2107324 2107344 2109433 2109582) (-1238 "ULSCCAT.spad" 2105169 2105191 2107280 2107285) (-1237 "ULSCAT.spad" 2103401 2103417 2105015 2105164) (-1236 "ULS2.spad" 2102915 2102968 2103391 2103396) (-1235 "UINT8.spad" 2102792 2102801 2102905 2102910) (-1234 "UINT64.spad" 2102668 2102677 2102782 2102787) (-1233 "UINT32.spad" 2102544 2102553 2102658 2102663) (-1232 "UINT16.spad" 2102420 2102429 2102534 2102539) (-1231 "UFD.spad" 2101485 2101494 2102346 2102415) (-1230 "UFD.spad" 2100612 2100623 2101475 2101480) (-1229 "UDVO.spad" 2099493 2099502 2100602 2100607) (-1228 "UDPO.spad" 2096986 2096997 2099449 2099454) (-1227 "TYPE.spad" 2096918 2096927 2096976 2096981) (-1226 "TYPEAST.spad" 2096837 2096846 2096908 2096913) (-1225 "TWOFACT.spad" 2095489 2095504 2096827 2096832) (-1224 "TUPLE.spad" 2094975 2094986 2095388 2095393) (-1223 "TUBETOOL.spad" 2091842 2091851 2094965 2094970) (-1222 "TUBE.spad" 2090489 2090506 2091832 2091837) (-1221 "TS.spad" 2089088 2089104 2090054 2090151) (-1220 "TSETCAT.spad" 2076215 2076232 2089056 2089083) (-1219 "TSETCAT.spad" 2063328 2063347 2076171 2076176) (-1218 "TRMANIP.spad" 2057694 2057711 2063034 2063039) (-1217 "TRIMAT.spad" 2056657 2056682 2057684 2057689) (-1216 "TRIGMNIP.spad" 2055184 2055201 2056647 2056652) (-1215 "TRIGCAT.spad" 2054696 2054705 2055174 2055179) (-1214 "TRIGCAT.spad" 2054206 2054217 2054686 2054691) (-1213 "TREE.spad" 2052781 2052792 2053813 2053840) (-1212 "TRANFUN.spad" 2052620 2052629 2052771 2052776) (-1211 "TRANFUN.spad" 2052457 2052468 2052610 2052615) (-1210 "TOPSP.spad" 2052131 2052140 2052447 2052452) (-1209 "TOOLSIGN.spad" 2051794 2051805 2052121 2052126) (-1208 "TEXTFILE.spad" 2050355 2050364 2051784 2051789) (-1207 "TEX.spad" 2047501 2047510 2050345 2050350) (-1206 "TEX1.spad" 2047057 2047068 2047491 2047496) (-1205 "TEMUTL.spad" 2046612 2046621 2047047 2047052) (-1204 "TBCMPPK.spad" 2044705 2044728 2046602 2046607) (-1203 "TBAGG.spad" 2043755 2043778 2044685 2044700) (-1202 "TBAGG.spad" 2042813 2042838 2043745 2043750) (-1201 "TANEXP.spad" 2042221 2042232 2042803 2042808) (-1200 "TALGOP.spad" 2041945 2041956 2042211 2042216) (-1199 "TABLE.spad" 2040356 2040379 2040626 2040653) (-1198 "TABLEAU.spad" 2039837 2039848 2040346 2040351) (-1197 "TABLBUMP.spad" 2036640 2036651 2039827 2039832) (-1196 "SYSTEM.spad" 2035868 2035877 2036630 2036635) (-1195 "SYSSOLP.spad" 2033351 2033362 2035858 2035863) (-1194 "SYSPTR.spad" 2033250 2033259 2033341 2033346) (-1193 "SYSNNI.spad" 2032432 2032443 2033240 2033245) (-1192 "SYSINT.spad" 2031836 2031847 2032422 2032427) (-1191 "SYNTAX.spad" 2028042 2028051 2031826 2031831) (-1190 "SYMTAB.spad" 2026110 2026119 2028032 2028037) (-1189 "SYMS.spad" 2022133 2022142 2026100 2026105) (-1188 "SYMPOLY.spad" 2021140 2021151 2021222 2021349) (-1187 "SYMFUNC.spad" 2020641 2020652 2021130 2021135) (-1186 "SYMBOL.spad" 2018144 2018153 2020631 2020636) (-1185 "SWITCH.spad" 2014915 2014924 2018134 2018139) (-1184 "SUTS.spad" 2011820 2011848 2013382 2013479) (-1183 "SUPXS.spad" 2008961 2008989 2009952 2010101) (-1182 "SUP.spad" 2005774 2005785 2006547 2006700) (-1181 "SUPFRACF.spad" 2004879 2004897 2005764 2005769) (-1180 "SUP2.spad" 2004271 2004284 2004869 2004874) (-1179 "SUMRF.spad" 2003245 2003256 2004261 2004266) (-1178 "SUMFS.spad" 2002882 2002899 2003235 2003240) (-1177 "SULS.spad" 1993427 1993455 1994527 1994956) (-1176 "SUCHTAST.spad" 1993196 1993205 1993417 1993422) (-1175 "SUCH.spad" 1992878 1992893 1993186 1993191) (-1174 "SUBSPACE.spad" 1984993 1985008 1992868 1992873) (-1173 "SUBRESP.spad" 1984163 1984177 1984949 1984954) (-1172 "STTF.spad" 1980262 1980278 1984153 1984158) (-1171 "STTFNC.spad" 1976730 1976746 1980252 1980257) (-1170 "STTAYLOR.spad" 1969365 1969376 1976611 1976616) (-1169 "STRTBL.spad" 1967870 1967887 1968019 1968046) (-1168 "STRING.spad" 1967279 1967288 1967293 1967320) (-1167 "STRICAT.spad" 1967067 1967076 1967247 1967274) (-1166 "STREAM.spad" 1963985 1963996 1966592 1966607) (-1165 "STREAM3.spad" 1963558 1963573 1963975 1963980) (-1164 "STREAM2.spad" 1962686 1962699 1963548 1963553) (-1163 "STREAM1.spad" 1962392 1962403 1962676 1962681) (-1162 "STINPROD.spad" 1961328 1961344 1962382 1962387) (-1161 "STEP.spad" 1960529 1960538 1961318 1961323) (-1160 "STEPAST.spad" 1959763 1959772 1960519 1960524) (-1159 "STBL.spad" 1958289 1958317 1958456 1958471) (-1158 "STAGG.spad" 1957364 1957375 1958279 1958284) (-1157 "STAGG.spad" 1956437 1956450 1957354 1957359) (-1156 "STACK.spad" 1955794 1955805 1956044 1956071) (-1155 "SREGSET.spad" 1953498 1953515 1955440 1955467) (-1154 "SRDCMPK.spad" 1952059 1952079 1953488 1953493) (-1153 "SRAGG.spad" 1947202 1947211 1952027 1952054) (-1152 "SRAGG.spad" 1942365 1942376 1947192 1947197) (-1151 "SQMATRIX.spad" 1939981 1939999 1940897 1940984) (-1150 "SPLTREE.spad" 1934533 1934546 1939417 1939444) (-1149 "SPLNODE.spad" 1931121 1931134 1934523 1934528) (-1148 "SPFCAT.spad" 1929930 1929939 1931111 1931116) (-1147 "SPECOUT.spad" 1928482 1928491 1929920 1929925) (-1146 "SPADXPT.spad" 1920077 1920086 1928472 1928477) (-1145 "spad-parser.spad" 1919542 1919551 1920067 1920072) (-1144 "SPADAST.spad" 1919243 1919252 1919532 1919537) (-1143 "SPACEC.spad" 1903442 1903453 1919233 1919238) (-1142 "SPACE3.spad" 1903218 1903229 1903432 1903437) (-1141 "SORTPAK.spad" 1902767 1902780 1903174 1903179) (-1140 "SOLVETRA.spad" 1900530 1900541 1902757 1902762) (-1139 "SOLVESER.spad" 1899058 1899069 1900520 1900525) (-1138 "SOLVERAD.spad" 1895084 1895095 1899048 1899053) (-1137 "SOLVEFOR.spad" 1893546 1893564 1895074 1895079) (-1136 "SNTSCAT.spad" 1893146 1893163 1893514 1893541) (-1135 "SMTS.spad" 1891418 1891444 1892711 1892808) (-1134 "SMP.spad" 1888893 1888913 1889283 1889410) (-1133 "SMITH.spad" 1887738 1887763 1888883 1888888) (-1132 "SMATCAT.spad" 1885848 1885878 1887682 1887733) (-1131 "SMATCAT.spad" 1883890 1883922 1885726 1885731) (-1130 "SKAGG.spad" 1882853 1882864 1883858 1883885) (-1129 "SINT.spad" 1881793 1881802 1882719 1882848) (-1128 "SIMPAN.spad" 1881521 1881530 1881783 1881788) (-1127 "SIG.spad" 1880851 1880860 1881511 1881516) (-1126 "SIGNRF.spad" 1879969 1879980 1880841 1880846) (-1125 "SIGNEF.spad" 1879248 1879265 1879959 1879964) (-1124 "SIGAST.spad" 1878633 1878642 1879238 1879243) (-1123 "SHP.spad" 1876561 1876576 1878589 1878594) (-1122 "SHDP.spad" 1866272 1866299 1866781 1866912) (-1121 "SGROUP.spad" 1865880 1865889 1866262 1866267) (-1120 "SGROUP.spad" 1865486 1865497 1865870 1865875) (-1119 "SGCF.spad" 1858649 1858658 1865476 1865481) (-1118 "SFRTCAT.spad" 1857579 1857596 1858617 1858644) (-1117 "SFRGCD.spad" 1856642 1856662 1857569 1857574) (-1116 "SFQCMPK.spad" 1851279 1851299 1856632 1856637) (-1115 "SFORT.spad" 1850718 1850732 1851269 1851274) (-1114 "SEXOF.spad" 1850561 1850601 1850708 1850713) (-1113 "SEX.spad" 1850453 1850462 1850551 1850556) (-1112 "SEXCAT.spad" 1848054 1848094 1850443 1850448) (-1111 "SET.spad" 1846378 1846389 1847475 1847514) (-1110 "SETMN.spad" 1844828 1844845 1846368 1846373) (-1109 "SETCAT.spad" 1844150 1844159 1844818 1844823) (-1108 "SETCAT.spad" 1843470 1843481 1844140 1844145) (-1107 "SETAGG.spad" 1840019 1840030 1843450 1843465) (-1106 "SETAGG.spad" 1836576 1836589 1840009 1840014) (-1105 "SEQAST.spad" 1836279 1836288 1836566 1836571) (-1104 "SEGXCAT.spad" 1835435 1835448 1836269 1836274) (-1103 "SEG.spad" 1835248 1835259 1835354 1835359) (-1102 "SEGCAT.spad" 1834173 1834184 1835238 1835243) (-1101 "SEGBIND.spad" 1833931 1833942 1834120 1834125) (-1100 "SEGBIND2.spad" 1833629 1833642 1833921 1833926) (-1099 "SEGAST.spad" 1833343 1833352 1833619 1833624) (-1098 "SEG2.spad" 1832778 1832791 1833299 1833304) (-1097 "SDVAR.spad" 1832054 1832065 1832768 1832773) (-1096 "SDPOL.spad" 1829480 1829491 1829771 1829898) (-1095 "SCPKG.spad" 1827569 1827580 1829470 1829475) (-1094 "SCOPE.spad" 1826722 1826731 1827559 1827564) (-1093 "SCACHE.spad" 1825418 1825429 1826712 1826717) (-1092 "SASTCAT.spad" 1825327 1825336 1825408 1825413) (-1091 "SAOS.spad" 1825199 1825208 1825317 1825322) (-1090 "SAERFFC.spad" 1824912 1824932 1825189 1825194) (-1089 "SAE.spad" 1823087 1823103 1823698 1823833) (-1088 "SAEFACT.spad" 1822788 1822808 1823077 1823082) (-1087 "RURPK.spad" 1820447 1820463 1822778 1822783) (-1086 "RULESET.spad" 1819900 1819924 1820437 1820442) (-1085 "RULE.spad" 1818140 1818164 1819890 1819895) (-1084 "RULECOLD.spad" 1817992 1818005 1818130 1818135) (-1083 "RTVALUE.spad" 1817727 1817736 1817982 1817987) (-1082 "RSTRCAST.spad" 1817444 1817453 1817717 1817722) (-1081 "RSETGCD.spad" 1813822 1813842 1817434 1817439) (-1080 "RSETCAT.spad" 1803758 1803775 1813790 1813817) (-1079 "RSETCAT.spad" 1793714 1793733 1803748 1803753) (-1078 "RSDCMPK.spad" 1792166 1792186 1793704 1793709) (-1077 "RRCC.spad" 1790550 1790580 1792156 1792161) (-1076 "RRCC.spad" 1788932 1788964 1790540 1790545) (-1075 "RPTAST.spad" 1788634 1788643 1788922 1788927) (-1074 "RPOLCAT.spad" 1767994 1768009 1788502 1788629) (-1073 "RPOLCAT.spad" 1747067 1747084 1767577 1767582) (-1072 "ROUTINE.spad" 1742950 1742959 1745714 1745741) (-1071 "ROMAN.spad" 1742278 1742287 1742816 1742945) (-1070 "ROIRC.spad" 1741358 1741390 1742268 1742273) (-1069 "RNS.spad" 1740261 1740270 1741260 1741353) (-1068 "RNS.spad" 1739250 1739261 1740251 1740256) (-1067 "RNG.spad" 1738985 1738994 1739240 1739245) (-1066 "RNGBIND.spad" 1738145 1738159 1738940 1738945) (-1065 "RMODULE.spad" 1737910 1737921 1738135 1738140) (-1064 "RMCAT2.spad" 1737330 1737387 1737900 1737905) (-1063 "RMATRIX.spad" 1736154 1736173 1736497 1736536) (-1062 "RMATCAT.spad" 1731733 1731764 1736110 1736149) (-1061 "RMATCAT.spad" 1727202 1727235 1731581 1731586) (-1060 "RLINSET.spad" 1726596 1726607 1727192 1727197) (-1059 "RINTERP.spad" 1726484 1726504 1726586 1726591) (-1058 "RING.spad" 1725954 1725963 1726464 1726479) (-1057 "RING.spad" 1725432 1725443 1725944 1725949) (-1056 "RIDIST.spad" 1724824 1724833 1725422 1725427) (-1055 "RGCHAIN.spad" 1723407 1723423 1724309 1724336) (-1054 "RGBCSPC.spad" 1723188 1723200 1723397 1723402) (-1053 "RGBCMDL.spad" 1722718 1722730 1723178 1723183) (-1052 "RF.spad" 1720360 1720371 1722708 1722713) (-1051 "RFFACTOR.spad" 1719822 1719833 1720350 1720355) (-1050 "RFFACT.spad" 1719557 1719569 1719812 1719817) (-1049 "RFDIST.spad" 1718553 1718562 1719547 1719552) (-1048 "RETSOL.spad" 1717972 1717985 1718543 1718548) (-1047 "RETRACT.spad" 1717400 1717411 1717962 1717967) (-1046 "RETRACT.spad" 1716826 1716839 1717390 1717395) (-1045 "RETAST.spad" 1716638 1716647 1716816 1716821) (-1044 "RESULT.spad" 1714698 1714707 1715285 1715312) (-1043 "RESRING.spad" 1714045 1714092 1714636 1714693) (-1042 "RESLATC.spad" 1713369 1713380 1714035 1714040) (-1041 "REPSQ.spad" 1713100 1713111 1713359 1713364) (-1040 "REP.spad" 1710654 1710663 1713090 1713095) (-1039 "REPDB.spad" 1710361 1710372 1710644 1710649) (-1038 "REP2.spad" 1700019 1700030 1710203 1710208) (-1037 "REP1.spad" 1694215 1694226 1699969 1699974) (-1036 "REGSET.spad" 1692012 1692029 1693861 1693888) (-1035 "REF.spad" 1691347 1691358 1691967 1691972) (-1034 "REDORDER.spad" 1690553 1690570 1691337 1691342) (-1033 "RECLOS.spad" 1689336 1689356 1690040 1690133) (-1032 "REALSOLV.spad" 1688476 1688485 1689326 1689331) (-1031 "REAL.spad" 1688348 1688357 1688466 1688471) (-1030 "REAL0Q.spad" 1685646 1685661 1688338 1688343) (-1029 "REAL0.spad" 1682490 1682505 1685636 1685641) (-1028 "RDUCEAST.spad" 1682211 1682220 1682480 1682485) (-1027 "RDIV.spad" 1681866 1681891 1682201 1682206) (-1026 "RDIST.spad" 1681433 1681444 1681856 1681861) (-1025 "RDETRS.spad" 1680297 1680315 1681423 1681428) (-1024 "RDETR.spad" 1678436 1678454 1680287 1680292) (-1023 "RDEEFS.spad" 1677535 1677552 1678426 1678431) (-1022 "RDEEF.spad" 1676545 1676562 1677525 1677530) (-1021 "RCFIELD.spad" 1673731 1673740 1676447 1676540) (-1020 "RCFIELD.spad" 1671003 1671014 1673721 1673726) (-1019 "RCAGG.spad" 1668931 1668942 1670993 1670998) (-1018 "RCAGG.spad" 1666786 1666799 1668850 1668855) (-1017 "RATRET.spad" 1666146 1666157 1666776 1666781) (-1016 "RATFACT.spad" 1665838 1665850 1666136 1666141) (-1015 "RANDSRC.spad" 1665157 1665166 1665828 1665833) (-1014 "RADUTIL.spad" 1664913 1664922 1665147 1665152) (-1013 "RADIX.spad" 1661834 1661848 1663380 1663473) (-1012 "RADFF.spad" 1660247 1660284 1660366 1660522) (-1011 "RADCAT.spad" 1659842 1659851 1660237 1660242) (-1010 "RADCAT.spad" 1659435 1659446 1659832 1659837) (-1009 "QUEUE.spad" 1658783 1658794 1659042 1659069) (-1008 "QUAT.spad" 1657364 1657375 1657707 1657772) (-1007 "QUATCT2.spad" 1656984 1657003 1657354 1657359) (-1006 "QUATCAT.spad" 1655154 1655165 1656914 1656979) (-1005 "QUATCAT.spad" 1653075 1653088 1654837 1654842) (-1004 "QUAGG.spad" 1651902 1651913 1653043 1653070) (-1003 "QQUTAST.spad" 1651670 1651679 1651892 1651897) (-1002 "QFORM.spad" 1651134 1651149 1651660 1651665) (-1001 "QFCAT.spad" 1649836 1649847 1651036 1651129) (-1000 "QFCAT.spad" 1648129 1648142 1649331 1649336) (-999 "QFCAT2.spad" 1647822 1647838 1648119 1648124) (-998 "QEQUAT.spad" 1647381 1647389 1647812 1647817) (-997 "QCMPACK.spad" 1642128 1642147 1647371 1647376) (-996 "QALGSET.spad" 1638207 1638239 1642042 1642047) (-995 "QALGSET2.spad" 1636203 1636221 1638197 1638202) (-994 "PWFFINTB.spad" 1633619 1633640 1636193 1636198) (-993 "PUSHVAR.spad" 1632958 1632977 1633609 1633614) (-992 "PTRANFN.spad" 1629086 1629096 1632948 1632953) (-991 "PTPACK.spad" 1626174 1626184 1629076 1629081) (-990 "PTFUNC2.spad" 1625997 1626011 1626164 1626169) (-989 "PTCAT.spad" 1625252 1625262 1625965 1625992) (-988 "PSQFR.spad" 1624559 1624583 1625242 1625247) (-987 "PSEUDLIN.spad" 1623445 1623455 1624549 1624554) (-986 "PSETPK.spad" 1608878 1608894 1623323 1623328) (-985 "PSETCAT.spad" 1602798 1602821 1608858 1608873) (-984 "PSETCAT.spad" 1596692 1596717 1602754 1602759) (-983 "PSCURVE.spad" 1595675 1595683 1596682 1596687) (-982 "PSCAT.spad" 1594458 1594487 1595573 1595670) (-981 "PSCAT.spad" 1593331 1593362 1594448 1594453) (-980 "PRTITION.spad" 1592440 1592448 1593321 1593326) (-979 "PRTDAST.spad" 1592159 1592167 1592430 1592435) (-978 "PRS.spad" 1581721 1581738 1592115 1592120) (-977 "PRQAGG.spad" 1581156 1581166 1581689 1581716) (-976 "PROPLOG.spad" 1580728 1580736 1581146 1581151) (-975 "PROPFUN2.spad" 1580351 1580364 1580718 1580723) (-974 "PROPFUN1.spad" 1579749 1579760 1580341 1580346) (-973 "PROPFRML.spad" 1578317 1578328 1579739 1579744) (-972 "PROPERTY.spad" 1577805 1577813 1578307 1578312) (-971 "PRODUCT.spad" 1575487 1575499 1575771 1575826) (-970 "PR.spad" 1573879 1573891 1574578 1574705) (-969 "PRINT.spad" 1573631 1573639 1573869 1573874) (-968 "PRIMES.spad" 1571884 1571894 1573621 1573626) (-967 "PRIMELT.spad" 1569965 1569979 1571874 1571879) (-966 "PRIMCAT.spad" 1569592 1569600 1569955 1569960) (-965 "PRIMARR.spad" 1568597 1568607 1568775 1568802) (-964 "PRIMARR2.spad" 1567364 1567376 1568587 1568592) (-963 "PREASSOC.spad" 1566746 1566758 1567354 1567359) (-962 "PPCURVE.spad" 1565883 1565891 1566736 1566741) (-961 "PORTNUM.spad" 1565658 1565666 1565873 1565878) (-960 "POLYROOT.spad" 1564507 1564529 1565614 1565619) (-959 "POLY.spad" 1561842 1561852 1562357 1562484) (-958 "POLYLIFT.spad" 1561107 1561130 1561832 1561837) (-957 "POLYCATQ.spad" 1559225 1559247 1561097 1561102) (-956 "POLYCAT.spad" 1552695 1552716 1559093 1559220) (-955 "POLYCAT.spad" 1545503 1545526 1551903 1551908) (-954 "POLY2UP.spad" 1544955 1544969 1545493 1545498) (-953 "POLY2.spad" 1544552 1544564 1544945 1544950) (-952 "POLUTIL.spad" 1543493 1543522 1544508 1544513) (-951 "POLTOPOL.spad" 1542241 1542256 1543483 1543488) (-950 "POINT.spad" 1541079 1541089 1541166 1541193) (-949 "PNTHEORY.spad" 1537781 1537789 1541069 1541074) (-948 "PMTOOLS.spad" 1536556 1536570 1537771 1537776) (-947 "PMSYM.spad" 1536105 1536115 1536546 1536551) (-946 "PMQFCAT.spad" 1535696 1535710 1536095 1536100) (-945 "PMPRED.spad" 1535175 1535189 1535686 1535691) (-944 "PMPREDFS.spad" 1534629 1534651 1535165 1535170) (-943 "PMPLCAT.spad" 1533709 1533727 1534561 1534566) (-942 "PMLSAGG.spad" 1533294 1533308 1533699 1533704) (-941 "PMKERNEL.spad" 1532873 1532885 1533284 1533289) (-940 "PMINS.spad" 1532453 1532463 1532863 1532868) (-939 "PMFS.spad" 1532030 1532048 1532443 1532448) (-938 "PMDOWN.spad" 1531320 1531334 1532020 1532025) (-937 "PMASS.spad" 1530330 1530338 1531310 1531315) (-936 "PMASSFS.spad" 1529297 1529313 1530320 1530325) (-935 "PLOTTOOL.spad" 1529077 1529085 1529287 1529292) (-934 "PLOT.spad" 1524000 1524008 1529067 1529072) (-933 "PLOT3D.spad" 1520464 1520472 1523990 1523995) (-932 "PLOT1.spad" 1519621 1519631 1520454 1520459) (-931 "PLEQN.spad" 1506911 1506938 1519611 1519616) (-930 "PINTERP.spad" 1506533 1506552 1506901 1506906) (-929 "PINTERPA.spad" 1506317 1506333 1506523 1506528) (-928 "PI.spad" 1505926 1505934 1506291 1506312) (-927 "PID.spad" 1504896 1504904 1505852 1505921) (-926 "PICOERCE.spad" 1504553 1504563 1504886 1504891) (-925 "PGROEB.spad" 1503154 1503168 1504543 1504548) (-924 "PGE.spad" 1494771 1494779 1503144 1503149) (-923 "PGCD.spad" 1493661 1493678 1494761 1494766) (-922 "PFRPAC.spad" 1492810 1492820 1493651 1493656) (-921 "PFR.spad" 1489473 1489483 1492712 1492805) (-920 "PFOTOOLS.spad" 1488731 1488747 1489463 1489468) 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(-900 "PBWLB.spad" 1451244 1451261 1452646 1452651) (-899 "PATTERN.spad" 1445783 1445793 1451234 1451239) (-898 "PATTERN2.spad" 1445521 1445533 1445773 1445778) (-897 "PATTERN1.spad" 1443857 1443873 1445511 1445516) (-896 "PATRES.spad" 1441432 1441444 1443847 1443852) (-895 "PATRES2.spad" 1441104 1441118 1441422 1441427) (-894 "PATMATCH.spad" 1439301 1439332 1440812 1440817) (-893 "PATMAB.spad" 1438730 1438740 1439291 1439296) (-892 "PATLRES.spad" 1437816 1437830 1438720 1438725) (-891 "PATAB.spad" 1437580 1437590 1437806 1437811) (-890 "PARTPERM.spad" 1434980 1434988 1437570 1437575) (-889 "PARSURF.spad" 1434414 1434442 1434970 1434975) (-888 "PARSU2.spad" 1434211 1434227 1434404 1434409) (-887 "script-parser.spad" 1433731 1433739 1434201 1434206) (-886 "PARSCURV.spad" 1433165 1433193 1433721 1433726) (-885 "PARSC2.spad" 1432956 1432972 1433155 1433160) (-884 "PARPCURV.spad" 1432418 1432446 1432946 1432951) (-883 "PARPC2.spad" 1432209 1432225 1432408 1432413) (-882 "PARAMAST.spad" 1431337 1431345 1432199 1432204) (-881 "PAN2EXPR.spad" 1430749 1430757 1431327 1431332) (-880 "PALETTE.spad" 1429719 1429727 1430739 1430744) (-879 "PAIR.spad" 1428706 1428719 1429307 1429312) (-878 "PADICRC.spad" 1426040 1426058 1427211 1427304) (-877 "PADICRAT.spad" 1424055 1424067 1424276 1424369) (-876 "PADIC.spad" 1423750 1423762 1423981 1424050) (-875 "PADICCT.spad" 1422299 1422311 1423676 1423745) (-874 "PADEPAC.spad" 1420988 1421007 1422289 1422294) (-873 "PADE.spad" 1419740 1419756 1420978 1420983) (-872 "OWP.spad" 1418980 1419010 1419598 1419665) (-871 "OVERSET.spad" 1418553 1418561 1418970 1418975) (-870 "OVAR.spad" 1418334 1418357 1418543 1418548) (-869 "OUT.spad" 1417420 1417428 1418324 1418329) (-868 "OUTFORM.spad" 1406812 1406820 1417410 1417415) (-867 "OUTBFILE.spad" 1406230 1406238 1406802 1406807) (-866 "OUTBCON.spad" 1405236 1405244 1406220 1406225) (-865 "OUTBCON.spad" 1404240 1404250 1405226 1405231) (-864 "OSI.spad" 1403715 1403723 1404230 1404235) (-863 "OSGROUP.spad" 1403633 1403641 1403705 1403710) (-862 "ORTHPOL.spad" 1402118 1402128 1403550 1403555) (-861 "OREUP.spad" 1401571 1401599 1401798 1401837) (-860 "ORESUP.spad" 1400872 1400896 1401251 1401290) (-859 "OREPCTO.spad" 1398729 1398741 1400792 1400797) (-858 "OREPCAT.spad" 1392876 1392886 1398685 1398724) (-857 "OREPCAT.spad" 1386913 1386925 1392724 1392729) (-856 "ORDSET.spad" 1386085 1386093 1386903 1386908) (-855 "ORDSET.spad" 1385255 1385265 1386075 1386080) (-854 "ORDRING.spad" 1384645 1384653 1385235 1385250) (-853 "ORDRING.spad" 1384043 1384053 1384635 1384640) (-852 "ORDMON.spad" 1383898 1383906 1384033 1384038) (-851 "ORDFUNS.spad" 1383030 1383046 1383888 1383893) (-850 "ORDFIN.spad" 1382850 1382858 1383020 1383025) (-849 "ORDCOMP.spad" 1381315 1381325 1382397 1382426) (-848 "ORDCOMP2.spad" 1380608 1380620 1381305 1381310) (-847 "OPTPROB.spad" 1379246 1379254 1380598 1380603) (-846 "OPTPACK.spad" 1371655 1371663 1379236 1379241) (-845 "OPTCAT.spad" 1369334 1369342 1371645 1371650) (-844 "OPSIG.spad" 1368988 1368996 1369324 1369329) (-843 "OPQUERY.spad" 1368537 1368545 1368978 1368983) (-842 "OP.spad" 1368279 1368289 1368359 1368426) (-841 "OPERCAT.spad" 1367745 1367755 1368269 1368274) (-840 "OPERCAT.spad" 1367209 1367221 1367735 1367740) (-839 "ONECOMP.spad" 1365954 1365964 1366756 1366785) (-838 "ONECOMP2.spad" 1365378 1365390 1365944 1365949) (-837 "OMSERVER.spad" 1364384 1364392 1365368 1365373) (-836 "OMSAGG.spad" 1364172 1364182 1364340 1364379) (-835 "OMPKG.spad" 1362788 1362796 1364162 1364167) (-834 "OM.spad" 1361761 1361769 1362778 1362783) (-833 "OMLO.spad" 1361186 1361198 1361647 1361686) (-832 "OMEXPR.spad" 1361020 1361030 1361176 1361181) (-831 "OMERR.spad" 1360565 1360573 1361010 1361015) (-830 "OMERRK.spad" 1359599 1359607 1360555 1360560) (-829 "OMENC.spad" 1358943 1358951 1359589 1359594) (-828 "OMDEV.spad" 1353252 1353260 1358933 1358938) (-827 "OMCONN.spad" 1352661 1352669 1353242 1353247) (-826 "OINTDOM.spad" 1352424 1352432 1352587 1352656) (-825 "OFMONOID.spad" 1350547 1350557 1352380 1352385) (-824 "ODVAR.spad" 1349808 1349818 1350537 1350542) (-823 "ODR.spad" 1349452 1349478 1349620 1349769) (-822 "ODPOL.spad" 1346834 1346844 1347174 1347301) (-821 "ODP.spad" 1336681 1336701 1337054 1337185) (-820 "ODETOOLS.spad" 1335330 1335349 1336671 1336676) (-819 "ODESYS.spad" 1333024 1333041 1335320 1335325) (-818 "ODERTRIC.spad" 1329033 1329050 1332981 1332986) (-817 "ODERED.spad" 1328432 1328456 1329023 1329028) (-816 "ODERAT.spad" 1326047 1326064 1328422 1328427) (-815 "ODEPRRIC.spad" 1323084 1323106 1326037 1326042) (-814 "ODEPROB.spad" 1322341 1322349 1323074 1323079) (-813 "ODEPRIM.spad" 1319675 1319697 1322331 1322336) (-812 "ODEPAL.spad" 1319061 1319085 1319665 1319670) (-811 "ODEPACK.spad" 1305727 1305735 1319051 1319056) (-810 "ODEINT.spad" 1305162 1305178 1305717 1305722) (-809 "ODEIFTBL.spad" 1302557 1302565 1305152 1305157) (-808 "ODEEF.spad" 1298048 1298064 1302547 1302552) (-807 "ODECONST.spad" 1297585 1297603 1298038 1298043) (-806 "ODECAT.spad" 1296183 1296191 1297575 1297580) (-805 "OCT.spad" 1294319 1294329 1295033 1295072) (-804 "OCTCT2.spad" 1293965 1293986 1294309 1294314) (-803 "OC.spad" 1291761 1291771 1293921 1293960) (-802 "OC.spad" 1289282 1289294 1291444 1291449) (-801 "OCAMON.spad" 1289130 1289138 1289272 1289277) (-800 "OASGP.spad" 1288945 1288953 1289120 1289125) (-799 "OAMONS.spad" 1288467 1288475 1288935 1288940) (-798 "OAMON.spad" 1288328 1288336 1288457 1288462) (-797 "OAGROUP.spad" 1288190 1288198 1288318 1288323) (-796 "NUMTUBE.spad" 1287781 1287797 1288180 1288185) (-795 "NUMQUAD.spad" 1275757 1275765 1287771 1287776) (-794 "NUMODE.spad" 1267111 1267119 1275747 1275752) (-793 "NUMINT.spad" 1264677 1264685 1267101 1267106) (-792 "NUMFMT.spad" 1263517 1263525 1264667 1264672) (-791 "NUMERIC.spad" 1255631 1255641 1263322 1263327) (-790 "NTSCAT.spad" 1254139 1254155 1255599 1255626) (-789 "NTPOLFN.spad" 1253690 1253700 1254056 1254061) (-788 "NSUP.spad" 1246736 1246746 1251276 1251429) (-787 "NSUP2.spad" 1246128 1246140 1246726 1246731) (-786 "NSMP.spad" 1242358 1242377 1242666 1242793) (-785 "NREP.spad" 1240736 1240750 1242348 1242353) (-784 "NPCOEF.spad" 1239982 1240002 1240726 1240731) (-783 "NORMRETR.spad" 1239580 1239619 1239972 1239977) (-782 "NORMPK.spad" 1237482 1237501 1239570 1239575) (-781 "NORMMA.spad" 1237170 1237196 1237472 1237477) (-780 "NONE.spad" 1236911 1236919 1237160 1237165) (-779 "NONE1.spad" 1236587 1236597 1236901 1236906) (-778 "NODE1.spad" 1236074 1236090 1236577 1236582) (-777 "NNI.spad" 1234969 1234977 1236048 1236069) (-776 "NLINSOL.spad" 1233595 1233605 1234959 1234964) (-775 "NIPROB.spad" 1232136 1232144 1233585 1233590) (-774 "NFINTBAS.spad" 1229696 1229713 1232126 1232131) (-773 "NETCLT.spad" 1229670 1229681 1229686 1229691) (-772 "NCODIV.spad" 1227886 1227902 1229660 1229665) (-771 "NCNTFRAC.spad" 1227528 1227542 1227876 1227881) (-770 "NCEP.spad" 1225694 1225708 1227518 1227523) (-769 "NASRING.spad" 1225290 1225298 1225684 1225689) (-768 "NASRING.spad" 1224884 1224894 1225280 1225285) (-767 "NARNG.spad" 1224236 1224244 1224874 1224879) (-766 "NARNG.spad" 1223586 1223596 1224226 1224231) (-765 "NAGSP.spad" 1222663 1222671 1223576 1223581) (-764 "NAGS.spad" 1212324 1212332 1222653 1222658) (-763 "NAGF07.spad" 1210755 1210763 1212314 1212319) (-762 "NAGF04.spad" 1205157 1205165 1210745 1210750) (-761 "NAGF02.spad" 1199226 1199234 1205147 1205152) (-760 "NAGF01.spad" 1194987 1194995 1199216 1199221) (-759 "NAGE04.spad" 1188687 1188695 1194977 1194982) (-758 "NAGE02.spad" 1179347 1179355 1188677 1188682) (-757 "NAGE01.spad" 1175349 1175357 1179337 1179342) (-756 "NAGD03.spad" 1173353 1173361 1175339 1175344) (-755 "NAGD02.spad" 1166100 1166108 1173343 1173348) (-754 "NAGD01.spad" 1160393 1160401 1166090 1166095) (-753 "NAGC06.spad" 1156268 1156276 1160383 1160388) (-752 "NAGC05.spad" 1154769 1154777 1156258 1156263) (-751 "NAGC02.spad" 1154036 1154044 1154759 1154764) (-750 "NAALG.spad" 1153577 1153587 1154004 1154031) (-749 "NAALG.spad" 1153138 1153150 1153567 1153572) (-748 "MULTSQFR.spad" 1150096 1150113 1153128 1153133) (-747 "MULTFACT.spad" 1149479 1149496 1150086 1150091) (-746 "MTSCAT.spad" 1147573 1147594 1149377 1149474) (-745 "MTHING.spad" 1147232 1147242 1147563 1147568) (-744 "MSYSCMD.spad" 1146666 1146674 1147222 1147227) (-743 "MSET.spad" 1144624 1144634 1146372 1146411) (-742 "MSETAGG.spad" 1144469 1144479 1144592 1144619) (-741 "MRING.spad" 1141446 1141458 1144177 1144244) (-740 "MRF2.spad" 1141016 1141030 1141436 1141441) (-739 "MRATFAC.spad" 1140562 1140579 1141006 1141011) (-738 "MPRFF.spad" 1138602 1138621 1140552 1140557) (-737 "MPOLY.spad" 1136073 1136088 1136432 1136559) (-736 "MPCPF.spad" 1135337 1135356 1136063 1136068) (-735 "MPC3.spad" 1135154 1135194 1135327 1135332) (-734 "MPC2.spad" 1134800 1134833 1135144 1135149) (-733 "MONOTOOL.spad" 1133151 1133168 1134790 1134795) (-732 "MONOID.spad" 1132470 1132478 1133141 1133146) (-731 "MONOID.spad" 1131787 1131797 1132460 1132465) (-730 "MONOGEN.spad" 1130535 1130548 1131647 1131782) (-729 "MONOGEN.spad" 1129305 1129320 1130419 1130424) (-728 "MONADWU.spad" 1127335 1127343 1129295 1129300) (-727 "MONADWU.spad" 1125363 1125373 1127325 1127330) (-726 "MONAD.spad" 1124523 1124531 1125353 1125358) (-725 "MONAD.spad" 1123681 1123691 1124513 1124518) (-724 "MOEBIUS.spad" 1122417 1122431 1123661 1123676) (-723 "MODULE.spad" 1122287 1122297 1122385 1122412) (-722 "MODULE.spad" 1122177 1122189 1122277 1122282) (-721 "MODRING.spad" 1121512 1121551 1122157 1122172) (-720 "MODOP.spad" 1120177 1120189 1121334 1121401) (-719 "MODMONOM.spad" 1119908 1119926 1120167 1120172) (-718 "MODMON.spad" 1116703 1116719 1117422 1117575) (-717 "MODFIELD.spad" 1116065 1116104 1116605 1116698) (-716 "MMLFORM.spad" 1114925 1114933 1116055 1116060) (-715 "MMAP.spad" 1114667 1114701 1114915 1114920) (-714 "MLO.spad" 1113126 1113136 1114623 1114662) (-713 "MLIFT.spad" 1111738 1111755 1113116 1113121) (-712 "MKUCFUNC.spad" 1111273 1111291 1111728 1111733) (-711 "MKRECORD.spad" 1110877 1110890 1111263 1111268) (-710 "MKFUNC.spad" 1110284 1110294 1110867 1110872) (-709 "MKFLCFN.spad" 1109252 1109262 1110274 1110279) (-708 "MKBCFUNC.spad" 1108747 1108765 1109242 1109247) (-707 "MINT.spad" 1108186 1108194 1108649 1108742) (-706 "MHROWRED.spad" 1106697 1106707 1108176 1108181) (-705 "MFLOAT.spad" 1105217 1105225 1106587 1106692) (-704 "MFINFACT.spad" 1104617 1104639 1105207 1105212) (-703 "MESH.spad" 1102399 1102407 1104607 1104612) (-702 "MDDFACT.spad" 1100610 1100620 1102389 1102394) (-701 "MDAGG.spad" 1099901 1099911 1100590 1100605) (-700 "MCMPLX.spad" 1095912 1095920 1096526 1096727) (-699 "MCDEN.spad" 1095122 1095134 1095902 1095907) (-698 "MCALCFN.spad" 1092244 1092270 1095112 1095117) (-697 "MAYBE.spad" 1091528 1091539 1092234 1092239) (-696 "MATSTOR.spad" 1088836 1088846 1091518 1091523) (-695 "MATRIX.spad" 1087540 1087550 1088024 1088051) (-694 "MATLIN.spad" 1084884 1084908 1087424 1087429) (-693 "MATCAT.spad" 1076613 1076635 1084852 1084879) (-692 "MATCAT.spad" 1068214 1068238 1076455 1076460) (-691 "MATCAT2.spad" 1067496 1067544 1068204 1068209) (-690 "MAPPKG3.spad" 1066411 1066425 1067486 1067491) (-689 "MAPPKG2.spad" 1065749 1065761 1066401 1066406) (-688 "MAPPKG1.spad" 1064577 1064587 1065739 1065744) (-687 "MAPPAST.spad" 1063892 1063900 1064567 1064572) (-686 "MAPHACK3.spad" 1063704 1063718 1063882 1063887) (-685 "MAPHACK2.spad" 1063473 1063485 1063694 1063699) (-684 "MAPHACK1.spad" 1063117 1063127 1063463 1063468) (-683 "MAGMA.spad" 1060907 1060924 1063107 1063112) (-682 "MACROAST.spad" 1060486 1060494 1060897 1060902) (-681 "M3D.spad" 1058206 1058216 1059864 1059869) (-680 "LZSTAGG.spad" 1055444 1055454 1058196 1058201) (-679 "LZSTAGG.spad" 1052680 1052692 1055434 1055439) (-678 "LWORD.spad" 1049385 1049402 1052670 1052675) (-677 "LSTAST.spad" 1049169 1049177 1049375 1049380) (-676 "LSQM.spad" 1047399 1047413 1047793 1047844) (-675 "LSPP.spad" 1046934 1046951 1047389 1047394) (-674 "LSMP.spad" 1045784 1045812 1046924 1046929) (-673 "LSMP1.spad" 1043602 1043616 1045774 1045779) (-672 "LSAGG.spad" 1043271 1043281 1043570 1043597) (-671 "LSAGG.spad" 1042960 1042972 1043261 1043266) (-670 "LPOLY.spad" 1041914 1041933 1042816 1042885) (-669 "LPEFRAC.spad" 1041185 1041195 1041904 1041909) (-668 "LO.spad" 1040586 1040600 1041119 1041146) (-667 "LOGIC.spad" 1040188 1040196 1040576 1040581) (-666 "LOGIC.spad" 1039788 1039798 1040178 1040183) (-665 "LODOOPS.spad" 1038718 1038730 1039778 1039783) (-664 "LODO.spad" 1038102 1038118 1038398 1038437) (-663 "LODOF.spad" 1037148 1037165 1038059 1038064) (-662 "LODOCAT.spad" 1035814 1035824 1037104 1037143) (-661 "LODOCAT.spad" 1034478 1034490 1035770 1035775) (-660 "LODO2.spad" 1033751 1033763 1034158 1034197) (-659 "LODO1.spad" 1033151 1033161 1033431 1033470) (-658 "LODEEF.spad" 1031953 1031971 1033141 1033146) (-657 "LNAGG.spad" 1027785 1027795 1031943 1031948) (-656 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(-637 "LGROBP.spad" 998453 998472 1001090 1001095) (-636 "LF.spad" 997408 997424 998443 998448) (-635 "LFCAT.spad" 996467 996475 997398 997403) (-634 "LEXTRIPK.spad" 991970 991985 996457 996462) (-633 "LEXP.spad" 989973 990000 991950 991965) (-632 "LETAST.spad" 989672 989680 989963 989968) (-631 "LEADCDET.spad" 988070 988087 989662 989667) (-630 "LAZM3PK.spad" 986774 986796 988060 988065) (-629 "LAUPOL.spad" 985467 985480 986367 986436) (-628 "LAPLACE.spad" 985050 985066 985457 985462) (-627 "LA.spad" 984490 984504 984972 985011) (-626 "LALG.spad" 984266 984276 984470 984485) (-625 "LALG.spad" 984050 984062 984256 984261) (-624 "KVTFROM.spad" 983785 983795 984040 984045) (-623 "KTVLOGIC.spad" 983297 983305 983775 983780) (-622 "KRCFROM.spad" 983035 983045 983287 983292) (-621 "KOVACIC.spad" 981758 981775 983025 983030) (-620 "KONVERT.spad" 981480 981490 981748 981753) (-619 "KOERCE.spad" 981217 981227 981470 981475) (-618 "KERNEL.spad" 979872 979882 981001 981006) (-617 "KERNEL2.spad" 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239673 240165 240170) (-208 "D02BBFA.spad" 239155 239163 239655 239660) (-207 "D02AGNT.spad" 233969 233977 239145 239150) (-206 "D01WGTS.spad" 232288 232296 233959 233964) (-205 "D01TRNS.spad" 232265 232273 232278 232283) (-204 "D01GBFA.spad" 231787 231795 232255 232260) (-203 "D01FCFA.spad" 231309 231317 231777 231782) (-202 "D01ASFA.spad" 230777 230785 231299 231304) (-201 "D01AQFA.spad" 230223 230231 230767 230772) (-200 "D01APFA.spad" 229647 229655 230213 230218) (-199 "D01ANFA.spad" 229141 229149 229637 229642) (-198 "D01AMFA.spad" 228651 228659 229131 229136) (-197 "D01ALFA.spad" 228191 228199 228641 228646) (-196 "D01AKFA.spad" 227717 227725 228181 228186) (-195 "D01AJFA.spad" 227240 227248 227707 227712) (-194 "D01AGNT.spad" 223307 223315 227230 227235) (-193 "CYCLOTOM.spad" 222813 222821 223297 223302) (-192 "CYCLES.spad" 219669 219677 222803 222808) (-191 "CVMP.spad" 219086 219096 219659 219664) (-190 "CTRIGMNP.spad" 217586 217602 219076 219081) (-189 "CTOR.spad" 217277 217285 217576 217581) (-188 "CTORKIND.spad" 216880 216888 217267 217272) (-187 "CTORCAT.spad" 216129 216137 216870 216875) (-186 "CTORCAT.spad" 215376 215386 216119 216124) (-185 "CTORCALL.spad" 214965 214975 215366 215371) (-184 "CSTTOOLS.spad" 214210 214223 214955 214960) (-183 "CRFP.spad" 207934 207947 214200 214205) (-182 "CRCEAST.spad" 207654 207662 207924 207929) (-181 "CRAPACK.spad" 206705 206715 207644 207649) (-180 "CPMATCH.spad" 206209 206224 206630 206635) (-179 "CPIMA.spad" 205914 205933 206199 206204) (-178 "COORDSYS.spad" 200923 200933 205904 205909) (-177 "CONTOUR.spad" 200334 200342 200913 200918) (-176 "CONTFRAC.spad" 196084 196094 200236 200329) (-175 "CONDUIT.spad" 195842 195850 196074 196079) (-174 "COMRING.spad" 195516 195524 195780 195837) (-173 "COMPPROP.spad" 195034 195042 195506 195511) (-172 "COMPLPAT.spad" 194801 194816 195024 195029) (-171 "COMPLEX.spad" 188938 188948 189182 189443) (-170 "COMPLEX2.spad" 188653 188665 188928 188933) (-169 "COMPILER.spad" 188202 188210 188643 188648) (-168 "COMPFACT.spad" 187804 187818 188192 188197) (-167 "COMPCAT.spad" 185876 185886 187538 187799) (-166 "COMPCAT.spad" 183676 183688 185340 185345) (-165 "COMMUPC.spad" 183424 183442 183666 183671) (-164 "COMMONOP.spad" 182957 182965 183414 183419) (-163 "COMM.spad" 182768 182776 182947 182952) (-162 "COMMAAST.spad" 182531 182539 182758 182763) (-161 "COMBOPC.spad" 181446 181454 182521 182526) (-160 "COMBINAT.spad" 180213 180223 181436 181441) (-159 "COMBF.spad" 177595 177611 180203 180208) (-158 "COLOR.spad" 176432 176440 177585 177590) (-157 "COLONAST.spad" 176098 176106 176422 176427) (-156 "CMPLXRT.spad" 175809 175826 176088 176093) (-155 "CLLCTAST.spad" 175471 175479 175799 175804) (-154 "CLIP.spad" 171579 171587 175461 175466) (-153 "CLIF.spad" 170234 170250 171535 171574) (-152 "CLAGG.spad" 166739 166749 170224 170229) (-151 "CLAGG.spad" 163115 163127 166602 166607) (-150 "CINTSLPE.spad" 162446 162459 163105 163110) (-149 "CHVAR.spad" 160584 160606 162436 162441) (-148 "CHARZ.spad" 160499 160507 160564 160579) (-147 "CHARPOL.spad" 160009 160019 160489 160494) (-146 "CHARNZ.spad" 159762 159770 159989 160004) (-145 "CHAR.spad" 157636 157644 159752 159757) (-144 "CFCAT.spad" 156964 156972 157626 157631) (-143 "CDEN.spad" 156160 156174 156954 156959) (-142 "CCLASS.spad" 154309 154317 155571 155610) (-141 "CATEGORY.spad" 153351 153359 154299 154304) (-140 "CATCTOR.spad" 153242 153250 153341 153346) (-139 "CATAST.spad" 152860 152868 153232 153237) (-138 "CASEAST.spad" 152574 152582 152850 152855) (-137 "CARTEN.spad" 147861 147885 152564 152569) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-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 diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 0b9aea69..0d70ff12 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,6 +1,6 @@ -(188562 . 3480528381) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))))) +(188596 . 3480551183) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) ((((-570)) . T) (($) -2740 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-570)) . T)) @@ -56,7 +56,7 @@ (((#0=(-876 |#1|) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) ((((-1168)) . T) (((-965 (-130))) . T) (((-868)) . T)) ((((-868)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (|has| |#4| (-373)) (|has| |#3| (-373)) (((|#1|) . T)) @@ -74,7 +74,7 @@ ((((-570)) . T) (((-413 (-570))) -2740 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570))))) ((|#2|) . T) (($) -2740 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-870 |#1|)) . T)) (-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) -((((-2 (|:| -2159 |#1|) (|:| -1907 |#2|))) . T)) +((((-2 (|:| -2160 |#1|) (|:| -3011 |#2|))) . T)) ((($) . T)) ((((-570)) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T) (($) -2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((-1186)) . T)) ((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) @@ -126,12 +126,12 @@ (((|#1|) . T)) (|has| |#1| (-373)) (((|#1|) . T)) -((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1268 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) +((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) (((|#1|) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) (((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) (($) . T)) (-2740 (|has| |#1| (-856)) (|has| |#1| (-1109))) (((|#1|) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((((-570)) . T)) ((((-868)) . T)) (((|#1| |#2|) . T)) @@ -270,8 +270,8 @@ (((|#1|) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) (((|#1|) . T) (((-570)) |has| |#1| (-645 (-570)))) -(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) (|has| |#1| (-562)) ((((-570)) -2740 (|has| |#4| (-174)) (|has| |#4| (-854)) (-12 (|has| |#4| (-1047 (-570))) (|has| |#4| (-1109))) (|has| |#4| (-1058))) ((|#4|) -2740 (|has| |#4| (-174)) (|has| |#4| (-1109))) (((-413 (-570))) -12 (|has| |#4| (-1047 (-413 (-570)))) (|has| |#4| (-1109)))) ((((-570)) -2740 (|has| |#3| (-174)) (|has| |#3| (-854)) (-12 (|has| |#3| (-1047 (-570))) (|has| |#3| (-1109))) (|has| |#3| (-1058))) ((|#3|) -2740 (|has| |#3| (-174)) (|has| |#3| (-1109))) (((-413 (-570))) -12 (|has| |#3| (-1047 (-413 (-570)))) (|has| |#3| (-1109)))) @@ -284,7 +284,7 @@ (|has| |#1| (-562)) ((((-705)) . T)) (((|#1|) . T)) -(-12 (|has| |#1| (-1011)) (|has| |#1| (-1211))) +(-12 (|has| |#1| (-1011)) (|has| |#1| (-1212))) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-413 (-570))) . T)) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) @@ -300,11 +300,11 @@ ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570))))) ((((-868)) . T)) (((|#1| |#2| |#3| |#4|) . T)) -((((-2 (|:| -2159 |#1|) (|:| -1907 |#2|))) . T) (((-868)) . T)) +((((-2 (|:| -2160 |#1|) (|:| -3011 |#2|))) . T) (((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#1| (-620 (-899 (-570))))) (((|#4|) -2740 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) (((|#3|) -2740 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) -((((-2 (|:| -2159 |#1|) (|:| -1907 |#2|))) . T)) +((((-2 (|:| -2160 |#1|) (|:| -3011 |#2|))) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-542)) . T) (((-570)) . T) (((-899 (-570))) . T) (((-384)) . T) (((-227)) . T)) @@ -312,7 +312,7 @@ (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) ((($) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) ((((-413 $) (-413 $)) |has| |#2| (-562)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2223 (-52)))) . T)) +((((-2 (|:| -2013 (-1168)) (|:| -2224 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-916)) ((((-1168) (-52)) . T)) @@ -351,9 +351,9 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1161)) -((((-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))) . T)) -(|has| (-1262 |#1| |#2| |#3| |#4|) (-146)) -(|has| (-1262 |#1| |#2| |#3| |#4|) (-148)) +((((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) +(|has| (-1263 |#1| |#2| |#3| |#4|) (-146)) +(|has| (-1263 |#1| |#2| |#3| |#4|) (-148)) (|has| |#1| (-146)) (|has| |#1| (-148)) ((((-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058)))) @@ -369,10 +369,10 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-1058))) ((((-868)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) (((|#1|) . T)) -((((-1276 (-344 (-3748) (-3748 (QUOTE X)) (-705)))) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) ((#0=(-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) #0#) |has| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (-313 (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))))) +((((-1277 (-344 (-3749) (-3749 (QUOTE X)) (-705)))) . T)) +(((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) ((#0=(-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) #0#) |has| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (-313 (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))))) ((((-868)) . T)) ((((-570) |#1|) . T)) ((((-542)) -12 (|has| |#1| (-620 (-542))) (|has| |#2| (-620 (-542)))) (((-899 (-384))) -12 (|has| |#1| (-620 (-899 (-384)))) (|has| |#2| (-620 (-899 (-384))))) (((-899 (-570))) -12 (|has| |#1| (-620 (-899 (-570)))) (|has| |#2| (-620 (-899 (-570)))))) @@ -386,8 +386,8 @@ ((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-868)) . T)) ((((-868)) . T)) -(|has| (-1261 |#2| |#3| |#4|) (-148)) -(|has| (-1261 |#2| |#3| |#4|) (-146)) +(|has| (-1262 |#2| |#3| |#4|) (-148)) +(|has| (-1262 |#2| |#3| |#4|) (-146)) (((|#2|) |has| |#2| (-1109)) (((-570)) -12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) (((|#1|) . T)) (|has| |#1| (-1109)) @@ -414,7 +414,7 @@ ((((-868)) . T)) ((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-562))) (|has| |#1| (-368)) -(-2740 (-12 (|has| (-1268 |#1| |#2| |#3|) (-235)) (|has| |#1| (-368))) (|has| |#1| (-15 * (|#1| (-570) |#1|)))) +(-2740 (-12 (|has| (-1269 |#1| |#2| |#3|) (-235)) (|has| |#1| (-368))) (|has| |#1| (-15 * (|#1| (-570) |#1|)))) (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-368)) (|has| |#1| (-15 * (|#1| (-777) |#1|))) @@ -433,11 +433,12 @@ ((($) |has| |#1| (-562)) (((-570)) . T)) (-2740 (|has| |#2| (-799)) (|has| |#2| (-854))) (-2740 (|has| |#2| (-799)) (|has| |#2| (-854))) -((((-1268 |#1| |#2| |#3|)) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-570)) . T) ((|#1|) |has| |#1| (-174))) -((((-1272 |#2|)) . T) (((-1268 |#1| |#2| |#3|)) . T) (((-1240 |#1| |#2| |#3|)) . T) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-570)) . T) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562)))) +((((-1269 |#1| |#2| |#3|)) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-570)) . T) ((|#1|) |has| |#1| (-174))) +((((-1273 |#2|)) . T) (((-1269 |#1| |#2| |#3|)) . T) (((-1241 |#1| |#2| |#3|)) . T) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-570)) . T) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) (((-570)) . T)) (((|#1|) . T)) ((((-1186)) -12 (|has| |#3| (-907 (-1186))) (|has| |#3| (-1058)))) +(((|#1|) . T)) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (-12 (|has| |#1| (-368)) (|has| |#2| (-826))) (-2740 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) @@ -446,8 +447,8 @@ (((#0=(-705) (-1182 #0#)) . T)) ((((-587 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) ((((-413 (-570))) . T) (($) . T)) -((((-868)) . T) (((-1276 |#4|)) . T)) -((((-868)) . T) (((-1276 |#3|)) . T)) +((((-868)) . T) (((-1277 |#4|)) . T)) +((((-868)) . T) (((-1277 |#3|)) . T)) ((((-587 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) ((($) . T) (((-413 (-570))) . T)) ((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T) (($) -2740 (|has| |#1| (-174)) (|has| |#1| (-562)))) @@ -455,9 +456,9 @@ ((((-868)) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) ((($) . T)) -((($ $) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((#0=(-413 (-570)) #0#) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((#1=(-1268 |#1| |#2| |#3|) #1#) |has| |#1| (-368)) ((|#1| |#1|) . T)) +((($ $) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((#0=(-413 (-570)) #0#) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((#1=(-1269 |#1| |#2| |#3|) #1#) |has| |#1| (-368)) ((|#1| |#1|) . T)) (((|#1| |#1|) . T) (($ $) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((#0=(-413 (-570)) #0#) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368)))) -((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1268 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) . T)) +((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) . T)) (((|#1|) . T) (($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368)))) (((|#3|) |has| |#3| (-1058))) ((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) @@ -490,12 +491,12 @@ ((((-145)) . T)) (((|#3|) |has| |#3| (-1109)) (((-570)) -12 (|has| |#3| (-1047 (-570))) (|has| |#3| (-1109))) (((-413 (-570))) -12 (|has| |#3| (-1047 (-413 (-570)))) (|has| |#3| (-1109)))) ((((-868)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (((|#1|) . T)) ((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-542)) |has| |#1| (-620 (-542)))) (((|#1|) |has| |#1| (-174))) -((((-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))) . T)) +((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) . T)) (|has| |#1| (-368)) ((((-1191)) . T)) (((|#1|) . T)) @@ -506,13 +507,13 @@ (|has| |#1| (-854)) (-2740 (|has| |#1| (-856)) (|has| |#1| (-1109))) ((((-868)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((((-542)) |has| |#1| (-620 (-542)))) (((|#1| |#2|) . T)) ((((-1186)) -12 (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))))) ((((-1168) |#1|) . T)) (((|#1| |#2| |#3| (-537 |#3|)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (|has| |#1| (-373)) (|has| |#1| (-373)) (|has| |#1| (-373)) @@ -538,7 +539,7 @@ ((((-570) |#3|) . T)) (((|#1|) . T) (((-570)) |has| |#1| (-645 (-570)))) (-2740 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -((((-1262 |#1| |#2| |#3| |#4|)) . T)) +((((-1263 |#1| |#2| |#3| |#4|)) . T)) ((((-413 (-570))) . T) (((-570)) . T)) ((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1| |#1|) . T)) @@ -615,7 +616,7 @@ (((|#1|) . T) (($) . T)) ((((-570)) |has| |#1| (-645 (-570))) ((|#1|) . T)) ((((-1184 |#1| |#2| |#3|)) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-570)) . T) ((|#1|) |has| |#1| (-174))) -((((-1272 |#2|)) . T) (((-1184 |#1| |#2| |#3|)) . T) (((-1177 |#1| |#2| |#3|)) . T) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-570)) . T) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562)))) +((((-1273 |#2|)) . T) (((-1184 |#1| |#2| |#3|)) . T) (((-1177 |#1| |#2| |#3|)) . T) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-570)) . T) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562)))) (((|#4|) . T)) (((|#3|) . T)) ((((-876 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) @@ -721,14 +722,14 @@ ((($ $) . T)) (((|#1| |#1|) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) -((((-1268 |#1| |#2| |#3|) $) -12 (|has| (-1268 |#1| |#2| |#3|) (-290 (-1268 |#1| |#2| |#3|) (-1268 |#1| |#2| |#3|))) (|has| |#1| (-368))) (($ $) . T)) +((((-1269 |#1| |#2| |#3|) $) -12 (|has| (-1269 |#1| |#2| |#3|) (-290 (-1269 |#1| |#2| |#3|) (-1269 |#1| |#2| |#3|))) (|has| |#1| (-368))) (($ $) . T)) ((($ $) . T)) ((($ $) . T)) (((|#1|) . T)) ((((-1149 |#1| |#2|)) |has| (-1149 |#1| |#2|) (-313 (-1149 |#1| |#2|)))) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) (((|#3| |#3|) -12 (|has| |#3| (-313 |#3|)) (|has| |#3| (-1109)))) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) (((|#2|) . T) (((-570)) |has| |#2| (-1047 (-570))) (((-413 (-570))) |has| |#2| (-1047 (-413 (-570))))) (((|#1|) . T)) (((|#1| |#2|) . T)) @@ -737,9 +738,9 @@ (((|#2|) . T)) (((|#3|) . T)) (-2740 (|has| |#1| (-856)) (|has| |#1| (-1109))) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) (((|#2|) . T)) -((((-868)) -2740 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-619 (-868))) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (((-1276 |#2|)) . T)) +((((-868)) -2740 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-619 (-868))) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (((-1277 |#2|)) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((|#1|) . T) (((-570)) . T) (($) . T)) (((|#1|) |has| |#1| (-174))) ((((-570)) . T)) @@ -789,7 +790,7 @@ (-2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((((-868)) . T)) ((((-868)) . T)) -((((-1262 |#1| |#2| |#3| |#4|)) . T)) +((((-1263 |#1| |#2| |#3| |#4|)) . T)) (((|#1|) |has| |#1| (-1058)) (((-570)) -12 (|has| |#1| (-645 (-570))) (|has| |#1| (-1058)))) (((|#1| |#2|) . T)) (-2740 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) @@ -837,9 +838,9 @@ (-2740 (|has| |#1| (-458)) (|has| |#1| (-916))) ((((-570) |#2|) . T)) ((((-868)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((($) -2740 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -2740 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) ((((-570) |#1|) . T)) @@ -854,11 +855,11 @@ (|has| |#1| (-562)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((((-868)) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))) . T)) +((((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) -((((-394) (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))) . T)) +((((-394) (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#2| (-1161)) (-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) @@ -871,7 +872,7 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) -((((-1225)) . T) (((-868)) . T) (((-1191)) . T)) +((((-1226)) . T) (((-868)) . T) (((-1191)) . T)) ((((-117 |#1|)) . T)) ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) @@ -928,7 +929,7 @@ ((($ $) . T)) ((($ $) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) -(((#0=(-1268 |#1| |#2| |#3|) #0#) -12 (|has| (-1268 |#1| |#2| |#3|) (-313 (-1268 |#1| |#2| |#3|))) (|has| |#1| (-368))) (((-1186) #0#) -12 (|has| (-1268 |#1| |#2| |#3|) (-520 (-1186) (-1268 |#1| |#2| |#3|))) (|has| |#1| (-368)))) +(((#0=(-1269 |#1| |#2| |#3|) #0#) -12 (|has| (-1269 |#1| |#2| |#3|) (-313 (-1269 |#1| |#2| |#3|))) (|has| |#1| (-368))) (((-1186) #0#) -12 (|has| (-1269 |#1| |#2| |#3|) (-520 (-1186) (-1269 |#1| |#2| |#3|))) (|has| |#1| (-368)))) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))) (((|#1|) . T)) (((|#1|) . T)) @@ -970,7 +971,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) -(((|#1| (-1276 |#1|) (-1276 |#1|)) . T)) +(((|#1| (-1277 |#1|) (-1277 |#1|)) . T)) ((((-570) (-145)) . T)) ((($) . T)) (-2740 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) @@ -1019,7 +1020,7 @@ (((|#3|) |has| |#3| (-1109))) (|has| |#3| (-373)) ((($) |has| |#1| (-562)) ((|#1|) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) -((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1268 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) ((((-868)) . T)) ((((-868)) . T)) (((|#2|) . T)) @@ -1094,7 +1095,7 @@ (|has| |#2| (-174)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-235)) (|has| |#2| (-1058))) -(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (-2740 (|has| |#3| (-799)) (|has| |#3| (-854))) (-2740 (|has| |#3| (-799)) (|has| |#3| (-854))) ((((-868)) . T)) @@ -1125,10 +1126,10 @@ (((|#1| (-413 (-570))) . T)) (((|#3|) . T) (((-618 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((((-570)) -2740 (|has| |#2| (-174)) (|has| |#2| (-854)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-1058))) ((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) @@ -1137,8 +1138,8 @@ ((((-868)) . T)) ((((-868)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))))) -(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))) |has| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (-313 (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) +(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) |has| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (-313 (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))))) ((((-868)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1154,7 +1155,7 @@ (|has| (-1103 |#1|) (-1109)) (((|#2| |#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($ $) |has| |#2| (-174))) (((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)))) -((((-570) (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T) ((|#1| |#2|) . T)) +((((-570) (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T) ((|#1| |#2|) . T)) (((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) ((((-570)) . T)) ((((-1191)) . T)) @@ -1199,7 +1200,7 @@ (-2740 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (-12 (|has| |#3| (-235)) (|has| |#3| (-1058))) (|has| |#2| (-1161)) -(((#0=(-52)) . T) (((-2 (|:| -2013 (-1186)) (|:| -2223 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2013 (-1186)) (|:| -2224 #0#))) . T)) (((|#1| |#2|) . T)) (-2740 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) (((|#1| (-570) (-1091)) . T)) @@ -1228,7 +1229,7 @@ (((|#4|) . T) (((-868)) . T)) (((|#3|) . T) ((|#2|) . T) (($) -2740 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) (((-570)) . T) ((|#4|) -2740 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) (((|#2|) . T) (($) -2740 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) (((-570)) . T) ((|#3|) -2740 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) (|has| |#1| (-562)) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-868)) . T)) @@ -1288,9 +1289,9 @@ (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) (-2740 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((($) . T) (((-570)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (((|#2|) . T) (($) . T)) -(|has| |#1| (-1211)) +(|has| |#1| (-1212)) (((#0=(-570) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) ((((-413 (-570))) . T) (($) . T)) (((|#4|) |has| |#4| (-1058))) @@ -1319,11 +1320,11 @@ ((($) . T) (((-413 (-570))) -2740 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) (-2740 (|has| |#1| (-174)) (|has| |#1| (-562))) ((($) . T)) -(((#0=(-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) #0#) |has| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (-313 (-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))))) +(((#0=(-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) #0#) |has| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (-313 (-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))))) ((($) . T)) ((($) . T)) (((|#2|) |has| |#2| (-1109))) -((((-868)) -2740 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-619 (-868))) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (((-1276 |#2|)) . T)) +((((-868)) -2740 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-619 (-868))) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (((-1277 |#2|)) . T)) ((($) . T)) ((((-570)) . T) (($) . T) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-1168) (-52)) . T)) @@ -1335,10 +1336,10 @@ ((((-570)) |has| #0=(-413 |#2|) (-645 (-570))) ((#0#) . T)) ((($) . T) (((-570)) . T)) ((((-570) (-145)) . T)) -((((-570) (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T) ((|#1| |#2|) . T)) +((((-570) (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T) ((|#1| |#2|) . T)) ((((-413 (-570))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((((-868)) . T)) ((((-917 |#1|)) . T)) (|has| |#1| (-368)) @@ -1355,7 +1356,7 @@ (|has| |#1| (-854)) ((((-512)) . T)) (((|#1| (-1186)) . T)) -(((|#1| (-1276 |#1|) (-1276 |#1|)) . T)) +(((|#1| (-1277 |#1|) (-1277 |#1|)) . T)) ((((-868)) . T) (((-1191)) . T)) (((|#1| |#2|) . T)) ((($ $) . T)) @@ -1367,7 +1368,7 @@ ((((-868)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-570) (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T) ((|#1| |#2|) . T)) +((((-570) (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) @@ -1384,7 +1385,7 @@ ((((-542)) |has| |#1| (-620 (-542))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#1| (-620 (-899 (-570))))) ((((-868)) . T)) ((((-876 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) -(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((((-512)) . T)) (|has| |#2| (-854)) ((((-512)) . T)) @@ -1409,7 +1410,7 @@ ((((-542)) |has| |#4| (-620 (-542)))) ((((-868)) . T) (((-650 |#4|)) . T)) ((($) |has| |#1| (-854))) -((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1268 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) +((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) ((((-570)) -2740 (|has| |#2| (-174)) (|has| |#2| (-854)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-1058))) ((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) (((|#1|) . T)) (((|#1|) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-570)) . T) (($) . T)) @@ -1419,7 +1420,7 @@ (((|#1|) . T)) ((((-1186)) |has| (-413 |#2|) (-907 (-1186)))) (((|#2|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) ((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2740 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) ((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T) (($) -2740 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) ((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) @@ -1429,14 +1430,14 @@ ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-868)) -2740 (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-619 (-868))) (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-373)) (|has| |#3| (-732)) (|has| |#3| (-799)) (|has| |#3| (-854)) (|has| |#3| (-1058)) (|has| |#3| (-1109))) (((-1276 |#3|)) . T)) +((((-868)) -2740 (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-619 (-868))) (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-373)) (|has| |#3| (-732)) (|has| |#3| (-799)) (|has| |#3| (-854)) (|has| |#3| (-1058)) (|has| |#3| (-1109))) (((-1277 |#3|)) . T)) ((((-570) |#2|) . T)) (-2740 (|has| |#1| (-856)) (|has| |#1| (-1109))) (((|#2| |#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($ $) |has| |#2| (-174))) (((|#2|) . T) (((-570)) . T)) ((((-868)) . T)) ((((-868)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T) ((|#2|) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-1168) (-1186) (-570) (-227) (-868)) . T)) @@ -1527,7 +1528,7 @@ ((((-1008 |#1|)) . T) ((|#1|) . T)) ((((-868)) . T)) ((((-868)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((((-413 (-570))) . T) (((-413 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1182 |#1|)) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1536,7 +1537,7 @@ (((|#1|) . T) (((-570)) . T) (($) . T)) (((|#2|) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))) . T)) +((((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) ((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) |#2|) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) @@ -1549,8 +1550,8 @@ (((|#3|) -12 (|has| |#3| (-313 |#3|)) (|has| |#3| (-1109)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-1268 |#1| |#2| |#3|)) |has| |#1| (-368))) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))))) +((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-1109)) (|has| |#2| (-368)) @@ -1595,7 +1596,7 @@ (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1| |#2|) . T)) ((((-570) (-145)) . T)) -(((#0=(-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) +(((#0=(-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) ((($) -2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (|has| |#1| (-856)) (((|#2| (-777) (-1091)) . T)) @@ -1619,7 +1620,7 @@ ((((-868)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#3|) . T)) -((((-1268 |#1| |#2| |#3|)) |has| |#1| (-368))) +((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) ((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) (((|#1|) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-570)) . T) (($) . T)) @@ -1647,8 +1648,8 @@ ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) ((((-394) (-1168)) . T)) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((((-868)) -2740 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-619 (-868))) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (((-1276 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2013 (-1168)) (|:| -2223 #0#))) . T)) +((((-868)) -2740 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-619 (-868))) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (((-1277 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2013 (-1168)) (|:| -2224 #0#))) . T)) (((|#1|) . T)) ((((-868)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) @@ -1668,7 +1669,7 @@ (|has| |#1| (-854)) ((((-868)) . T)) (((|#2|) . T)) -((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1268 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) (((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) . T) (((-570)) . T) (((-825 |#1|)) . T)) @@ -1699,12 +1700,12 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))) . T)) +((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((((-1186) (-52)) . T)) ((($ $) . T)) (((|#1| (-570)) . T)) @@ -1719,7 +1720,7 @@ ((((-570)) . T)) (|has| |#1| (-856)) ((((-695 |#2|)) . T) (((-868)) . T)) -((((-1268 |#1| |#2| |#3|)) -12 (|has| (-1268 |#1| |#2| |#3|) (-313 (-1268 |#1| |#2| |#3|))) (|has| |#1| (-368)))) +((((-1269 |#1| |#2| |#3|)) -12 (|has| (-1269 |#1| |#2| |#3|) (-313 (-1269 |#1| |#2| |#3|))) (|has| |#1| (-368)))) ((((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1| |#2|) . T)) ((((-413 (-959 |#1|))) . T)) @@ -1754,11 +1755,11 @@ (-2740 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((((-1186)) |has| |#1| (-907 (-1186))) (((-1091)) . T)) (((|#1|) . T)) (|has| |#1| (-854)) -(((#0=(-2 (|:| -2013 (-1168)) (|:| -2223 (-52))) #0#) |has| (-2 (|:| -2013 (-1168)) (|:| -2223 (-52))) (-313 (-2 (|:| -2013 (-1168)) (|:| -2223 (-52)))))) +(((#0=(-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) #0#) |has| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (-313 (-2 (|:| -2013 (-1168)) (|:| -2224 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#1| (-1109)) ((((-868)) . T) (((-1191)) . T)) @@ -1807,11 +1808,11 @@ ((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T) (($) -2740 (|has| |#1| (-174)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) . T)) ((($) |has| |#1| (-854))) -((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1268 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) (|has| |#1| (-916)) ((((-1186)) . T)) ((((-868)) . T)) -((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1268 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) . T)) +((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) . T)) (((|#1|) . T) (($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368)))) (((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) @@ -1819,7 +1820,7 @@ (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) ((#0=(-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) #0#) |has| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (-313 (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))))) +(((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) ((#0=(-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) #0#) |has| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (-313 (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))))) (-2740 (|has| |#2| (-458)) (|has| |#2| (-916))) (-2740 (|has| |#1| (-458)) (|has| |#1| (-916))) (((|#1|) . T) (($) . T)) @@ -1844,7 +1845,7 @@ ((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) (((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((((-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))) . T)) +((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) . T)) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) ((((-678 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1864,11 +1865,11 @@ (-2740 (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-373)) (|has| |#3| (-732)) (|has| |#3| (-799)) (|has| |#3| (-854)) (|has| |#3| (-1058)) (|has| |#3| (-1109))) (-2740 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) -(|has| |#1| (-1211)) -(|has| |#1| (-1211)) +(|has| |#1| (-1212)) +(|has| |#1| (-1212)) (-2740 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) -(|has| |#1| (-1211)) -(|has| |#1| (-1211)) +(|has| |#1| (-1212)) +(|has| |#1| (-1212)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T) ((#1=(-413 |#1|) #1#) . T) ((|#1| |#1|) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) @@ -1922,7 +1923,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((($ $) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((($ $) . T)) ((((-570) (-112)) . T)) ((($) . T)) @@ -1945,14 +1946,14 @@ (((|#1|) . T)) ((((-868)) . T)) (((|#1| (-570)) . T)) -(((|#1| (-1268 |#1| |#2| |#3|)) . T)) +(((|#1| (-1269 |#1| |#2| |#3|)) . T)) (((|#1|) . T)) (((|#1| (-413 (-570))) . T)) -(((|#1| (-1240 |#1| |#2| |#3|)) . T)) +(((|#1| (-1241 |#1| |#2| |#3|)) . T)) (((|#1| (-777)) . T)) (((|#1|) . T)) ((((-868)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (|has| |#1| (-1109)) ((((-1168) |#1|) . T)) ((($) . T)) @@ -1960,8 +1961,8 @@ (|has| |#2| (-146)) (((|#1| (-537 (-824 (-1186))) (-824 (-1186))) . T)) ((((-868)) . T)) -((((-1262 |#1| |#2| |#3| |#4|)) . T)) -((((-1262 |#1| |#2| |#3| |#4|)) . T)) +((((-1263 |#1| |#2| |#3| |#4|)) . T)) +((((-1263 |#1| |#2| |#3| |#4|)) . T)) (((|#1|) |has| |#1| (-1058))) ((((-570) (-112)) . T)) ((((-868)) |has| |#1| (-1109))) @@ -1978,7 +1979,7 @@ (((|#3|) . T)) (-2740 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-868)) . T)) -((((-1261 |#2| |#3| |#4|)) . T) (((-1262 |#1| |#2| |#3| |#4|)) . T)) +((((-1262 |#2| |#3| |#4|)) . T) (((-1263 |#1| |#2| |#3| |#4|)) . T)) ((((-868)) . T)) ((((-48)) -12 (|has| |#1| (-562)) (|has| |#1| (-1047 (-570)))) (((-618 $)) . T) ((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) -2740 (-12 (|has| |#1| (-562)) (|has| |#1| (-1047 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-413 (-959 |#1|))) |has| |#1| (-562)) (((-959 |#1|)) |has| |#1| (-1058)) (((-1186)) . T)) (((|#1|) . T) (($) . T)) @@ -1986,7 +1987,7 @@ (((|#1|) . T)) ((($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) |has| |#1| (-174))) (((|#1|) |has| |#1| (-313 |#1|))) -((((-1262 |#1| |#2| |#3| |#4|)) . T)) +((((-1263 |#1| |#2| |#3| |#4|)) . T)) ((((-570)) |has| |#1| (-893 (-570))) (((-384)) |has| |#1| (-893 (-384)))) (((|#1|) . T)) (((|#1|) . T)) @@ -2000,7 +2001,7 @@ ((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) . T)) (((|#1|) . T) (($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368)))) ((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) (((|#1|) |has| |#1| (-174))) ((((-868)) . T)) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) @@ -2014,7 +2015,7 @@ (((|#3|) |has| |#3| (-1109))) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) (((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)))) -((((-1261 |#2| |#3| |#4|)) . T)) +((((-1262 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-826)) (|has| |#1| (-826)) @@ -2024,7 +2025,7 @@ (|has| |#1| (-854)) (((|#1| (-570) (-1091)) . T)) (-2740 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (((|#1| (-413 (-570)) (-1091)) . T)) (((|#1| (-777) (-1091)) . T)) (|has| |#1| (-856)) @@ -2043,15 +2044,15 @@ (|has| |#1| (-1109)) ((((-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-645 (-570)))) ((|#2|) |has| |#1| (-368))) (-2740 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) -((((-695 (-344 (-3748) (-3748 (QUOTE X) (QUOTE HESS)) (-705)))) . T)) +((((-695 (-344 (-3749) (-3749 (QUOTE X) (QUOTE HESS)) (-705)))) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) |has| |#1| (-174))) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) ((((-868)) . T)) (|has| |#3| (-854)) ((((-868)) . T)) -((((-1261 |#2| |#3| |#4|) (-323 |#2| |#3| |#4|)) . T)) +((((-1262 |#2| |#3| |#4|) (-323 |#2| |#3| |#4|)) . T)) ((((-868)) . T)) (((|#1| |#1|) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058)))) (((|#1|) . T)) @@ -2063,11 +2064,11 @@ ((($) . T) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-368))) (|has| |#1| (-856)) (((|#1|) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (((|#1|) . T) (((-570)) . T)) (((|#2|) . T)) ((((-570)) . T) ((|#3|) . T)) -((((-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))) |has| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (-313 (-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))))) +((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) |has| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (-313 (-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))))) (-2740 (|has| |#1| (-458)) (|has| |#1| (-916))) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) ((((-868)) . T)) @@ -2126,7 +2127,7 @@ ((((-650 |#1|)) . T)) (|has| |#1| (-916)) (((|#2|) |has| |#2| (-1058))) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) (|has| |#1| (-368)) (((|#1|) |has| |#1| (-174))) (((|#1| |#1|) . T)) @@ -2178,7 +2179,7 @@ (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2223 (-52)))) . T)) +((((-2 (|:| -2013 (-1168)) (|:| -2224 (-52)))) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) @@ -2192,7 +2193,7 @@ (((|#2|) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) -2740 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) ((((-570) |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2223 |#2|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) ((((-384)) . T)) ((((-705)) . T)) ((((-413 (-570))) . #0=(|has| |#2| (-368))) (($) . #0#)) @@ -2209,7 +2210,7 @@ (|has| |#1| (-368)) ((((-1186)) |has| |#2| (-907 (-1186)))) ((((-868)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((((-413 (-570))) . T) (($) . T)) (|has| |#1| (-479)) (|has| |#1| (-373)) @@ -2237,12 +2238,12 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-856)) -((((-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))) . T)) +((((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) (|has| |#1| (-148)) (|has| |#1| (-146)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2223 |#2|)))) ((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)))) ((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) (((|#2|) . T)) (((|#3|) . T)) ((((-117 |#1|)) . T)) @@ -2262,10 +2263,10 @@ ((((-542)) |has| |#1| (-620 (-542))) (((-899 (-570))) |has| |#1| (-620 (-899 (-570)))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384)))) (((-384)) . #0=(|has| |#1| (-1031))) (((-227)) . #0#)) (((|#1|) |has| |#1| (-368))) ((((-868)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((($ $) . T) (((-618 $) $) . T)) (-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) -((($) . T) (((-1262 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . T)) +((($) . T) (((-1263 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . T)) ((($) -2740 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-562))) ((($) . T) (((-570)) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) (|has| |#1| (-368)) @@ -2299,11 +2300,11 @@ ((((-570)) . T)) (-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) -(((#0=(-1261 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| #0# (-38 (-413 (-570)))) (($) . T)) +(((#0=(-1262 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| #0# (-38 (-413 (-570)))) (($) . T)) ((((-570)) . T)) (|has| |#1| (-368)) -(-2740 (-12 (|has| (-1268 |#1| |#2| |#3|) (-148)) (|has| |#1| (-368))) (|has| |#1| (-148))) -(-2740 (-12 (|has| (-1268 |#1| |#2| |#3|) (-146)) (|has| |#1| (-368))) (|has| |#1| (-146))) +(-2740 (-12 (|has| (-1269 |#1| |#2| |#3|) (-148)) (|has| |#1| (-368))) (|has| |#1| (-148))) +(-2740 (-12 (|has| (-1269 |#1| |#2| |#3|) (-146)) (|has| |#1| (-368))) (|has| |#1| (-146))) (|has| |#1| (-368)) (|has| |#1| (-146)) (|has| |#1| (-148)) @@ -2335,7 +2336,7 @@ ((((-959 |#1|)) . T) (((-868)) . T)) (((|#3|) . T)) (((|#1| |#1|) . T) (($ $) -2740 (|has| |#1| (-294)) (|has| |#1| (-368))) ((#0=(-413 (-570)) #0#) |has| |#1| (-368))) -((((-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))) . T)) +((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) . T)) ((((-959 |#1|)) . T)) ((($) . T)) ((((-570) |#1|) . T)) @@ -2372,7 +2373,7 @@ ((((-413 (-570))) . T) (($) . T)) ((((-413 (-570))) . T) (($) . T)) ((((-413 (-570))) . T) (($) . T)) -(-2740 (|has| |#1| (-458)) (|has| |#1| (-1230))) +(-2740 (|has| |#1| (-458)) (|has| |#1| (-1231))) ((($) . T)) ((((-413 (-570))) |has| #0=(-413 |#2|) (-1047 (-413 (-570)))) (((-570)) |has| #0# (-1047 (-570))) ((#0#) . T)) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) @@ -2382,7 +2383,7 @@ ((($) -2740 (|has| |#1| (-368)) (|has| |#1| (-354))) (((-413 (-570))) -2740 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) ((((-570)) . T)) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2013 (-1168)) (|:| -2223 (-52)))) |has| (-2 (|:| -2013 (-1168)) (|:| -2223 (-52))) (-313 (-2 (|:| -2013 (-1168)) (|:| -2223 (-52)))))) +((((-2 (|:| -2013 (-1168)) (|:| -2224 (-52)))) |has| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (-313 (-2 (|:| -2013 (-1168)) (|:| -2224 (-52)))))) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#1| (-854)) (|has| |#1| (-38 (-413 (-570)))) @@ -2411,7 +2412,7 @@ ((((-145)) . T)) ((((-786 |#1| (-870 |#2|))) . T)) ((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) -(|has| |#1| (-1211)) +(|has| |#1| (-1212)) ((((-868)) . T)) (((|#1|) . T)) (-2740 (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-373)) (|has| |#3| (-732)) (|has| |#3| (-799)) (|has| |#3| (-854)) (|has| |#3| (-1058)) (|has| |#3| (-1109))) @@ -2425,10 +2426,10 @@ ((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-542)) |has| |#4| (-620 (-542)))) ((((-868)) . T) (((-650 |#4|)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-854)) -(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))) |has| (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|)) (-313 (-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))))) +(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) |has| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (-313 (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))))) (|has| |#1| (-1109)) (|has| |#1| (-368)) (((|#1|) . T)) @@ -2448,7 +2449,7 @@ (|has| |#1| (-148)) (|has| |#1| (-146)) ((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) -((((-1268 |#1| |#2| |#3|)) |has| |#1| (-368))) +((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) (|has| |#1| (-854)) (((|#1| |#2|) . T)) (((|#1|) . T) (((-570)) |has| |#1| (-645 (-570)))) @@ -2473,7 +2474,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) (((|#1|) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)))) @@ -2512,7 +2513,7 @@ (|has| |#1| (-562)) (((|#2|) . T)) ((((-570)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (((|#1|) . T)) (-2740 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) @@ -2523,7 +2524,7 @@ ((($) . T)) (((|#1|) . T)) ((((-868)) . T)) -(((|#2|) |has| |#2| (-6 (-4450 "*")))) +(((|#2|) |has| |#2| (-6 (-4451 "*")))) (((|#1|) . T)) (((|#1|) . T)) ((($) . T)) @@ -2533,7 +2534,7 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#3|) . T) (((-570)) . T)) -((((-1261 |#2| |#3| |#4|)) . T) (((-570)) . T) (((-1262 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-413 (-570))) . T)) +((((-1262 |#2| |#3| |#4|)) . T) (((-570)) . T) (((-1263 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-413 (-570))) . T)) ((((-48)) -12 (|has| |#1| (-562)) (|has| |#1| (-1047 (-570)))) (((-570)) -2740 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1047 (-570))) (|has| |#1| (-1058))) ((|#1|) . T) (((-618 $)) . T) (($) |has| |#1| (-562)) (((-413 (-570))) -2740 (|has| |#1| (-562)) (|has| |#1| (-1047 (-413 (-570))))) (((-413 (-959 |#1|))) |has| |#1| (-562)) (((-959 |#1|)) |has| |#1| (-1058)) (((-1186)) . T)) ((((-413 (-570))) |has| |#2| (-1047 (-413 (-570)))) (((-570)) |has| |#2| (-1047 (-570))) ((|#2|) . T) (((-870 |#1|)) . T)) ((($) . T) (((-117 |#1|)) . T) (((-413 (-570))) . T)) @@ -2549,16 +2550,16 @@ (((|#4|) . T)) (-2740 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1186) (-52)) . T)) -((((-1261 |#2| |#3| |#4|) (-323 |#2| |#3| |#4|)) . T)) +((((-1262 |#2| |#3| |#4|) (-323 |#2| |#3| |#4|)) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) ((((-868)) . T)) (-2740 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) -(((#0=(-1262 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) +(((#0=(-1263 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-174)) ((#0=(-413 (-570)) #0#) |has| |#1| (-562)) (($ $) |has| |#1| (-562))) ((($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) |has| |#1| (-174))) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#1| $) |has| |#1| (-290 |#1| |#1|))) -((((-1262 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . T) (($) . T)) +((((-1263 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-562)) (($) |has| |#1| (-562))) ((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) (|has| |#1| (-368)) @@ -2571,7 +2572,7 @@ (((|#3|) |has| |#3| (-368))) (((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) ((((-1186)) . T)) -((($) . T) (((-1261 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| (-1261 |#2| |#3| |#4|) (-38 (-413 (-570)))) (((-570)) . T)) +((($) . T) (((-1262 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| (-1262 |#2| |#3| |#4|) (-38 (-413 (-570)))) (((-570)) . T)) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) (((|#2| |#3|) . T)) @@ -2586,7 +2587,7 @@ ((((-868)) . T)) (((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)))) (((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) -((($ $) . T) ((#0=(-1261 |#2| |#3| |#4|) #0#) . T) ((#1=(-413 (-570)) #1#) |has| #0# (-38 (-413 (-570))))) +((($ $) . T) ((#0=(-1262 |#2| |#3| |#4|) #0#) . T) ((#1=(-413 (-570)) #1#) |has| #0# (-38 (-413 (-570))))) ((((-917 |#1|)) . T)) (-12 (|has| |#1| (-368)) (|has| |#2| (-826))) ((($) . T) (((-413 (-570))) . T)) @@ -2597,7 +2598,7 @@ (|has| |#1| (-368)) (|has| |#1| (-368)) (((|#1| |#2|) . T)) -((($) . T) ((#0=(-1261 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) +((($) . T) ((#0=(-1262 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) (-2740 (-12 (|has| |#1| (-311)) (|has| |#1| (-916))) (|has| |#1| (-368)) (|has| |#1| (-354))) (-2740 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) @@ -2645,22 +2646,22 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) (((|#2|) . T)) -(((|#2|) -2740 (|has| |#2| (-6 (-4450 "*"))) (|has| |#2| (-174)))) +(((|#2|) -2740 (|has| |#2| (-6 (-4451 "*"))) (|has| |#2| (-174)))) (-2740 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (-2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (|has| |#2| (-916)) (|has| |#1| (-916)) (((|#2|) |has| |#2| (-174))) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) -((((-1268 |#1| |#2| |#3|)) |has| |#1| (-368))) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-868)) . T)) ((((-868)) . T)) ((((-542)) . T) (((-570)) . T) (((-899 (-570))) . T) (((-384)) . T) (((-227)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2223 (-52)))) . T)) +((((-2 (|:| -2013 (-1168)) (|:| -2224 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((((-868)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) @@ -2682,7 +2683,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-189)) . T) (((-868)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -2695,7 +2696,7 @@ ((((-868)) . T)) ((((-1168)) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -((((-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))) . T)) +((((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) (|has| |#1| (-856)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) @@ -2738,7 +2739,7 @@ (((#0=(-917 |#1|) #0#) . T) (($ $) . T) ((#1=(-413 (-570)) #1#) . T)) ((((-413 |#2|)) . T)) (|has| |#1| (-854)) -((((-1212 |#1|)) . T) (((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-1213 |#1|)) . T) (((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) . T) ((#1=(-570) #1#) . T) (($ $) . T)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) |has| |#2| (-1058)) (((-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058)))) @@ -2757,13 +2758,13 @@ (-2740 (|has| |#1| (-146)) (|has| |#1| (-373))) (-2740 (|has| |#1| (-146)) (|has| |#1| (-373))) (-2740 (|has| |#1| (-146)) (|has| |#1| (-373))) -((((-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2013 (-1186)) (|:| -2223 #0#))) . T)) +((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2013 (-1186)) (|:| -2224 #0#))) . T)) (|has| |#1| (-354)) ((((-570)) . T)) ((((-868)) . T)) (((|#1|) . T)) -(((#0=(-1262 |#1| |#2| |#3| |#4|) $) |has| #0# (-290 #0# #0#))) +(((#0=(-1263 |#1| |#2| |#3| |#4|) $) |has| #0# (-290 #0# #0#))) (|has| |#1| (-368)) (((|#1|) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2740 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((-570)) -2740 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) (((#0=(-1091) |#1|) . T) ((#0# $) . T) (($ $) . T)) @@ -2810,7 +2811,7 @@ (((|#1|) . T) (($) . T)) (((|#1|) . T) (((-570)) . T)) (((|#1|) . T) (((-570)) . T)) -(((|#1| (-1276 |#1|) (-1276 |#1|)) . T)) +(((|#1| (-1277 |#1|) (-1277 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#2|) . T)) ((((-868)) . T)) @@ -2844,7 +2845,7 @@ (|has| |#2| (-1031)) ((($) . T)) (|has| |#1| (-916)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2872,7 +2873,7 @@ ((((-413 (-570))) . T)) (-2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((((-1168)) . T) (((-868)) . T)) -(((#0=(-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) #0#) |has| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (-313 (-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))))) +(((#0=(-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) #0#) |has| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (-313 (-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))))) ((((-1168)) . T)) (|has| |#1| (-916)) (|has| |#2| (-368)) @@ -2910,13 +2911,13 @@ (((|#2|) |has| |#1| (-368))) (((|#2|) |has| |#1| (-368))) ((((-570)) . T) (($) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#2|) . T) (((-1186)) -12 (|has| |#1| (-368)) (|has| |#2| (-1047 (-1186)))) (((-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-1047 (-570)))) (((-413 (-570))) -12 (|has| |#1| (-368)) (|has| |#2| (-1047 (-570))))) (((|#2|) . T)) -((((-1186) #0=(-1262 |#1| |#2| |#3| |#4|)) |has| #0# (-520 (-1186) #0#)) ((#0# #0#) |has| #0# (-313 #0#))) +((((-1186) #0=(-1263 |#1| |#2| |#3| |#4|)) |has| #0# (-520 (-1186) #0#)) ((#0# #0#) |has| #0# (-313 #0#))) ((((-413 (-570))) . T) (($) . T) (((-413 |#1|)) . T) ((|#1|) . T)) ((((-618 $) $) . T) (($ $) . T)) ((((-171 (-227))) . T) (((-171 (-384))) . T) (((-1182 (-705))) . T) (((-899 (-384))) . T)) @@ -2956,9 +2957,9 @@ (((|#2|) . T)) (((|#2|) . T)) (-2740 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-413 (-570)))) @@ -3006,6 +3007,7 @@ (|has| |#1| (-797)) ((((-868)) . T)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) +((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) ((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-115)) . T) ((|#1|) . T)) @@ -3013,7 +3015,7 @@ (((|#1|) . T)) ((((-227)) . T) (((-384)) . T) (((-899 (-384))) . T)) ((((-868)) . T)) -((((-1262 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-413 (-570))) . T)) +((((-1263 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-562)) (((-413 (-570))) |has| |#1| (-562))) ((((-868)) . T)) ((((-868)) . T)) @@ -3037,7 +3039,7 @@ ((((-868)) . T)) (|has| |#1| (-148)) (|has| |#1| (-146)) -((($) . T) ((#0=(-1261 |#2| |#3| |#4|)) |has| #0# (-174)) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) +((($) . T) ((#0=(-1262 |#2| |#3| |#4|)) |has| #0# (-174)) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (|has| |#1| (-368)) (|has| |#1| (-368)) @@ -3090,7 +3092,7 @@ (|has| |#2| (-368)) ((((-587 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2223 (-52)))) . T)) +((((-2 (|:| -2013 (-1168)) (|:| -2224 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-570)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) @@ -3116,7 +3118,7 @@ (((#0=(-587 |#1|) #0#) . T) (($ $) . T) ((#1=(-413 (-570)) #1#) . T)) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) (((|#1|) |has| |#1| (-174))) -(((|#1| (-1276 |#1|) (-1276 |#1|)) . T)) +(((|#1| (-1277 |#1|) (-1277 |#1|)) . T)) ((((-587 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) ((($) . T) (((-413 (-570))) . T)) (((|#1|) . T)) @@ -3124,7 +3126,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-413 (-570))) . T)) -(((|#2|) |has| |#2| (-6 (-4450 "*")))) +(((|#2|) |has| |#2| (-6 (-4451 "*")))) (((|#1|) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((|#1|) . T) (((-570)) . T)) (((|#1|) . T)) @@ -3152,7 +3154,7 @@ ((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-868)) . T)) (((|#1|) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2223 |#1|))) . T)) +((((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3182,13 +3184,13 @@ ((((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-562))) ((((-1186)) |has| |#2| (-907 (-1186))) (((-1091)) . T)) ((((-868)) . T)) -((((-1261 |#2| |#3| |#4|)) . T)) +((((-1262 |#2| |#3| |#4|)) . T)) ((((-917 |#1|)) . T)) ((($) . T) (((-413 (-570))) . T)) (-12 (|has| |#1| (-368)) (|has| |#2| (-826))) (-12 (|has| |#1| (-368)) (|has| |#2| (-826))) ((((-868)) . T)) -(|has| |#1| (-1230)) +(|has| |#1| (-1231)) (((|#2|) . T)) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) ((((-1186)) |has| |#1| (-907 (-1186)))) @@ -3237,7 +3239,7 @@ (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) (((|#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) -(((|#2|) -2740 (|has| |#2| (-6 (-4450 "*"))) (|has| |#2| (-174)))) +(((|#2|) -2740 (|has| |#2| (-6 (-4451 "*"))) (|has| |#2| (-174)))) (((|#2|) . T)) (|has| |#1| (-368)) (((|#2|) . T)) @@ -3283,7 +3285,7 @@ (((|#1|) . T)) ((((-868)) . T)) (|has| |#2| (-916)) -((((-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))) . T)) +((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) . T)) ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570))))) ((((-868)) . T)) ((((-868)) . T)) @@ -3309,7 +3311,7 @@ ((((-1191)) . T)) ((((-1191)) . T)) ((((-650 |#1|)) . T)) -((($) . T) (((-570)) . T) (((-1262 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . T)) +((($) . T) (((-570)) . T) (((-1263 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . T)) ((((-570)) -2740 (|has| |#1| (-21)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) (($) -2740 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-562))) ((((-1191)) . T)) ((((-1191)) . T)) @@ -3339,7 +3341,7 @@ ((((-1186)) |has| |#1| (-907 (-1186))) (((-1091)) . T)) (((|#1|) . T) (((-570)) |has| |#1| (-645 (-570)))) (|has| |#1| (-562)) -(((#0=(-1261 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| #0# (-38 (-413 (-570)))) (((-570)) . T) (($) . T)) +(((#0=(-1262 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| #0# (-38 (-413 (-570)))) (((-570)) . T) (($) . T)) ((($) . T) (((-413 (-570))) . T)) ((($) . T)) ((($) . T)) @@ -3362,7 +3364,7 @@ ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T) ((|#2|) . T)) ((((-1091)) . T) ((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) ((((-384)) -12 (|has| |#1| (-893 (-384))) (|has| |#2| (-893 (-384)))) (((-570)) -12 (|has| |#1| (-893 (-570))) (|has| |#2| (-893 (-570))))) -((((-1262 |#1| |#2| |#3| |#4|)) . T)) +((((-1263 |#1| |#2| |#3| |#4|)) . T)) ((((-570) |#1|) . T)) (((|#1| |#1|) . T)) ((($) . T) ((|#2|) . T)) @@ -3446,7 +3448,7 @@ (((|#2|) . T)) ((((-868)) |has| |#1| (-1109))) ((($) . T)) -((((-1262 |#1| |#2| |#3| |#4|)) . T)) +((((-1263 |#1| |#2| |#3| |#4|)) . T)) (((|#1|) . T)) (((|#1|) . T)) (|has| |#2| (-826)) @@ -3474,12 +3476,12 @@ ((((-1191)) . T)) ((((-868)) . T)) ((((-868)) . T) (((-1191)) . T)) -((((-1225)) . T) (((-868)) . T) (((-1191)) . T)) +((((-1226)) . T) (((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) -((((-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))) |has| (-2 (|:| -2013 (-1186)) (|:| -2223 (-52))) (-313 (-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))))) +((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) |has| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (-313 (-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))))) (-2740 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((((-570) |#1|) . T)) ((((-570) |#1|) . T)) @@ -3500,7 +3502,7 @@ ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) (|has| |#1| (-38 (-413 (-570)))) ((((-868)) . T)) -((((-1262 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-413 (-570))) . T)) +((((-1263 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-562)) (((-413 (-570))) |has| |#1| (-562))) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) (|has| |#1| (-368)) @@ -3528,12 +3530,12 @@ ((($) . T) ((|#2|) . T)) ((($) . T) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570))))) (|has| |#2| (-916)) -((($) . T) ((#0=(-1261 |#2| |#3| |#4|)) |has| #0# (-174)) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) +((($) . T) ((#0=(-1262 |#2| |#3| |#4|)) |has| #0# (-174)) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) (((|#1|) |has| |#1| (-174))) ((((-570) |#1|) . T)) (((|#1|) . T)) ((((-1191)) . T)) -(((#0=(-1262 |#1| |#2| |#3| |#4|)) |has| #0# (-313 #0#))) +(((#0=(-1263 |#1| |#2| |#3| |#4|)) |has| #0# (-313 #0#))) ((($) . T)) (((|#1|) . T)) ((($ $) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((#0=(-413 (-570)) #0#) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#2| |#2|) |has| |#1| (-368)) ((|#1| |#1|) . T)) @@ -3558,7 +3560,7 @@ (((|#4|) . T)) (|has| |#1| (-562)) ((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#2|) |has| |#1| (-368)) ((|#1|) . T)) -((((-1186)) -2740 (-12 (|has| (-1268 |#1| |#2| |#3|) (-907 (-1186))) (|has| |#1| (-368))) (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))))) +((((-1186)) -2740 (-12 (|has| (-1269 |#1| |#2| |#3|) (-907 (-1186))) (|has| |#1| (-368))) (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))))) (((|#1|) . T) (($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368)))) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-907 (-1186))))) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-777) |#1|))) (|has| |#1| (-907 (-1186))))) @@ -3575,9 +3577,9 @@ (((|#1|) . T)) (-2740 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (-2740 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799)))) -((((-1268 |#1| |#2| |#3|)) |has| |#1| (-368))) +((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((($) . T) (((-876 |#1|)) . T) (((-413 (-570))) . T)) -((((-1268 |#1| |#2| |#3|)) |has| |#1| (-368))) +((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) (|has| |#1| (-562)) (((|#1|) . T)) (((|#1|) . T)) @@ -3637,12 +3639,12 @@ ((($) . T)) ((($) -2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((($ $) . T) (((-1186) $) . T)) -((((-1268 |#1| |#2| |#3|)) . T)) +((((-1269 |#1| |#2| |#3|)) . T)) (|has| |#2| (-916)) -((((-1268 |#1| |#2| |#3|)) |has| |#1| (-368))) +((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) (|has| |#1| (-368)) (((|#1|) . T)) -((((-1268 |#1| |#2| |#3|)) . T) (((-1240 |#1| |#2| |#3|)) . T)) +((((-1269 |#1| |#2| |#3|)) . T) (((-1241 |#1| |#2| |#3|)) . T)) ((((-1186)) . T) (((-868)) . T)) (|has| |#1| (-916)) (((|#1|) . T)) @@ -3653,10 +3655,10 @@ ((((-1191)) . T)) (((|#1|) |has| |#1| (-174))) ((((-1191)) . T)) -((((-1262 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-413 (-570))) . T)) +((((-1263 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-562)) (((-413 (-570))) |has| |#1| (-562))) ((((-1191)) . T)) -((((-1262 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . T) (($) . T)) +((((-1263 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-562)) (($) |has| |#1| (-562))) ((((-413 (-570))) . T) (($) . T)) (((|#1| (-570)) . T)) @@ -3691,7 +3693,7 @@ (-2740 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799)))) ((((-570)) . T)) ((((-570)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) (-2740 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) @@ -3702,12 +3704,12 @@ (|has| |#1| (-368)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) -((($) . T) ((#0=(-1261 |#2| |#3| |#4|)) |has| #0# (-174)) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) +((($) . T) ((#0=(-1262 |#2| |#3| |#4|)) |has| #0# (-174)) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) (|has| |#1| (-235)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) ((($) . T) (((-570)) . T)) ((($) . T) (((-570)) . T)) -((($) . T) ((#0=(-1261 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) +((($) . T) ((#0=(-1262 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) ((((-868)) . T)) (((|#1| (-777) (-1091)) . T)) ((((-570) |#1|) . T)) @@ -3798,11 +3800,11 @@ ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-1149 |#1| |#2|)) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) -((((-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1031)) -(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) ((((-868)) . T)) ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570)))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-384)) . #0=(|has| |#2| (-1031))) (((-227)) . #0#)) ((((-298 |#3|)) . T)) @@ -3857,7 +3859,7 @@ ((((-868)) . T)) ((((-868)) . T)) (((|#1| (-537 |#2|)) . T)) -((((-2 (|:| -2013 (-1186)) (|:| -2223 (-52)))) . T)) +((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) . T)) ((((-570) (-130)) . T)) (((|#1| (-570)) . T)) (((|#1| (-413 (-570))) . T)) @@ -3894,7 +3896,7 @@ (((|#1| |#2|) . T)) ((((-1168) |#1|) . T)) ((((-413 |#2|)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2223 |#2|))) . T)) +((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) (|has| |#1| (-562)) (|has| |#1| (-562)) ((($) . T) ((|#2|) . T)) @@ -3907,10 +3909,10 @@ (((|#1| (-650 |#1|)) |has| |#1| (-854))) (-2740 (|has| |#1| (-235)) (|has| |#1| (-354))) (-2740 (|has| |#1| (-368)) (|has| |#1| (-354))) -((((-1272 |#1|)) . T) (((-570)) . T) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-1047 (-413 (-570))))) +((((-1273 |#1|)) . T) (((-570)) . T) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-1047 (-413 (-570))))) (|has| |#1| (-1109)) (((|#1|) . T)) -((((-1272 |#1|)) . T) (((-570)) . T) (($) -2740 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-1091)) . T) ((|#2|) . T) (((-413 (-570))) -2740 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570)))))) +((((-1273 |#1|)) . T) (((-570)) . T) (($) -2740 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-1091)) . T) ((|#2|) . T) (((-413 (-570))) -2740 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570)))))) ((((-413 (-570))) . T) (($) . T)) ((((-1008 |#1|)) . T) ((|#1|) . T) (((-570)) -2740 (|has| (-1008 |#1|) (-1047 (-570))) (|has| |#1| (-1047 (-570)))) (((-413 (-570))) -2740 (|has| (-1008 |#1|) (-1047 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) @@ -3928,10 +3930,10 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1149 |#1| |#2|) #0#) |has| (-1149 |#1| |#2|) (-313 (-1149 |#1| |#2|)))) (((|#1|) . 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T)) -(((-484 . -1109) T) ((-267 . -520) 188453) ((-249 . -520) 188396) ((-247 . -1109) 188346) ((-577 . -111) 188331) ((-537 . -23) T) ((-134 . -1109) T) ((-139 . -1109) T) ((-118 . -313) 188288) ((-138 . -1109) T) ((-485 . -520) 188080) ((-683 . -622) 188064) ((-700 . -102) T) ((-1150 . -520) 187983) ((-396 . -132) T) ((-1289 . -985) 187952) ((-1033 . -1060) 187889) ((-31 . -93) T) ((-608 . -495) 187873) ((-1033 . -646) 187810) ((-627 . -132) T) ((-825 . -852) T) ((-529 . -57) 187760) ((-525 . -520) 187693) ((-359 . -1060) 187638) ((-59 . -520) 187571) ((-522 . -520) 187504) ((-424 . -907) 187463) ((-171 . -1058) T) ((-503 . -520) 187396) ((-502 . -520) 187329) ((-359 . -646) 187274) ((-805 . -1047) 187054) ((-705 . -38) 187019) ((-1249 . -622) 186767) ((-348 . -354) T) ((-1103 . -1102) 186751) ((-1103 . -1109) 186729) ((-861 . -622) 186626) ((-171 . -245) 186577) ((-171 . -235) 186528) ((-1103 . -1104) 186486) ((-878 . -290) 186444) ((-227 . -801) T) ((-227 . -798) T) ((-700 . -288) 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. -294) T) ((-357 . -294) T) ((-349 . -294) T) ((-267 . -294) 185610) ((-249 . -294) 185541) ((-1045 . -619) 185507) ((-1033 . -102) T) ((-1028 . -619) 185473) ((-632 . -496) 185454) ((-419 . -732) T) ((-118 . -38) 185399) ((-489 . -496) 185380) ((-632 . -619) 185346) ((-419 . -479) T) ((-220 . -496) 185327) ((-489 . -619) 185293) ((-359 . -102) T) ((-220 . -619) 185259) ((-1220 . -1067) T) ((-348 . -652) 185189) ((-717 . -1067) T) ((-1184 . -47) 185166) ((-1183 . -47) 185136) ((-1177 . -47) 185113) ((-129 . -292) 185088) ((-1044 . -152) 185034) ((-917 . -294) T) ((-1135 . -47) 185006) ((-700 . -313) NIL) ((-521 . -619) 184988) ((-516 . -619) 184970) ((-514 . -619) 184952) ((-331 . -1109) 184902) ((-718 . -458) 184833) ((-48 . -102) T) ((-1260 . -290) 184818) ((-1239 . -290) 184738) ((-650 . -672) 184722) ((-650 . -657) 184706) ((-344 . -21) T) ((-344 . -25) T) ((-40 . -354) NIL) ((-176 . -21) T) ((-176 . -25) T) ((-650 . -378) 184690) ((-611 . -496) 184672) ((-608 . -290) 184649) 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T) ((-651 . -93) T) ((-326 . -1065) 181999) ((-254 . -797) 181978) ((-254 . -800) 181929) ((-31 . -496) 181910) ((-254 . -799) 181889) ((-253 . -797) 181868) ((-253 . -800) 181819) ((-253 . -799) 181798) ((-31 . -619) 181764) ((-50 . -1067) T) ((-254 . -732) 181674) ((-253 . -732) 181584) ((-1220 . -1109) T) ((-676 . -23) T) ((-587 . -1067) T) ((-524 . -1067) T) ((-384 . -1065) 181549) ((-326 . -111) 181524) ((-73 . -388) T) ((-73 . -401) T) ((-1033 . -38) 181461) ((-700 . -406) 181443) ((-99 . -102) T) ((-717 . -1109) T) ((-1304 . -1060) 181430) ((-1012 . -146) 181402) ((-1012 . -148) 181374) ((-876 . -652) 181346) ((-384 . -111) 181302) ((-323 . -1230) 181281) ((-480 . -1011) 181247) ((-359 . -38) 181212) ((-40 . -375) 181184) ((-879 . -619) 181056) ((-128 . -126) 181040) ((-122 . -126) 181024) ((-842 . -1065) 180994) ((-839 . -21) 180946) ((-833 . -1065) 180930) ((-839 . -25) 180882) ((-323 . -562) 180833) ((-523 . -622) 180814) ((-570 . -834) T) ((-242 . -1226) T) ((-1043 . -622) 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176248) ((-487 . -916) 176227) ((-1240 . -1047) 176193) ((-1220 . -520) 176160) ((-1096 . -723) 176009) ((-1071 . -654) 175996) ((-959 . -654) 175921) ((-603 . -496) 175902) ((-591 . -496) 175883) ((-788 . -723) 175712) ((-603 . -619) 175678) ((-591 . -619) 175644) ((-542 . -619) 175626) ((-542 . -620) 175607) ((-786 . -723) 175456) ((-1086 . -102) T) ((-386 . -25) T) ((-629 . -652) 175428) ((-386 . -21) T) ((-487 . -654) 175353) ((-467 . -723) 175324) ((-460 . -723) 175173) ((-996 . -102) T) ((-1199 . -620) NIL) ((-1199 . -619) 175155) ((-1151 . -1132) 175100) ((-743 . -102) T) ((-118 . -652) 175030) ((-611 . -622) 175012) ((-1055 . -1219) 174941) ((-908 . -313) 174879) ((-537 . -25) T) ((-882 . -93) T) ((-720 . -622) 174833) ((-687 . -93) T) ((-651 . -496) 174814) ((-142 . -102) T) ((-44 . -132) T) ((-682 . -93) T) ((-670 . -619) 174796) ((-348 . -1067) T) ((-293 . -1121) T) ((-651 . -619) 174749) ((-484 . -93) T) ((-360 . -619) 174731) ((-357 . -619) 174713) ((-349 . -619) 174695) 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-1121) T) ((-1084 . -102) T) ((-1066 . -619) 171423) ((-934 . -962) T) ((-743 . -313) 171361) ((-75 . -1226) T) ((-670 . -387) 171333) ((-171 . -916) 171286) ((-30 . -962) T) ((-112 . -850) T) ((-1 . -619) 171268) ((-1012 . -415) 171240) ((-129 . -657) 171222) ((-50 . -626) 171206) ((-700 . -652) 171141) ((-601 . -907) 171054) ((-444 . -102) T) ((-129 . -378) 171036) ((-142 . -313) NIL) ((-878 . -1058) T) ((-839 . -856) 171015) ((-81 . -1226) T) ((-717 . -294) T) ((-40 . -1067) T) ((-587 . -174) T) ((-524 . -174) T) ((-517 . -619) 170997) ((-171 . -654) 170907) ((-513 . -619) 170889) ((-356 . -148) 170871) ((-356 . -146) T) ((-364 . -1121) T) ((-358 . -1121) T) ((-350 . -1121) T) ((-1013 . -311) T) ((-921 . -311) T) ((-878 . -245) T) ((-108 . -1121) T) ((-878 . -235) 170850) ((-1260 . -111) 170671) ((-1239 . -111) 170460) ((-247 . -1264) 170444) ((-570 . -854) T) ((-364 . -23) T) ((-359 . -354) T) ((-320 . -313) 170431) ((-317 . -313) 170372) ((-358 . -23) T) ((-323 . -132) T) ((-350 . -23) T) ((-1013 . -1031) T) ((-31 . -622) 170353) ((-108 . -23) T) ((-660 . -1060) 170337) ((-247 . -610) 170314) ((-337 . -1109) T) ((-660 . -646) 170284) ((-1262 . -38) 170176) ((-1249 . -916) 170155) ((-112 . -1109) T) ((-1044 . -102) T) ((-1249 . -654) 170080) ((-877 . -800) NIL) ((-861 . -654) 170054) ((-877 . -797) NIL) ((-822 . -893) NIL) ((-877 . -732) T) ((-1096 . -520) 169927) ((-788 . -520) 169874) ((-786 . -520) 169826) ((-577 . -654) 169813) ((-822 . -1047) 169641) ((-460 . -520) 169584) ((-394 . -395) T) ((-1260 . -622) 169397) ((-1239 . -622) 169145) ((-60 . -1226) T) ((-627 . -856) 169124) ((-506 . -667) T) ((-1155 . -985) 169093) ((-1033 . -652) 169030) ((-1012 . -458) T) ((-705 . -854) T) ((-516 . -798) T) ((-480 . -1065) 168865) ((-506 . -113) T) ((-348 . -1109) T) ((-317 . -1161) NIL) ((-293 . -132) T) ((-400 . -1109) T) ((-876 . -1067) T) ((-700 . -375) 168832) ((-359 . -652) 168762) ((-225 . -626) 168739) ((-331 . -290) 168716) ((-480 . -111) 168537) ((-1260 . 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163999) ((-591 . -622) 163980) ((-542 . -624) 163883) ((-348 . -174) T) ((-88 . -619) 163865) ((-153 . -21) T) ((-153 . -25) T) ((-917 . -111) 163821) ((-40 . -723) 163766) ((-876 . -1109) T) ((-670 . -622) 163743) ((-651 . -622) 163724) ((-360 . -622) 163661) ((-357 . -622) 163598) ((-553 . -1109) T) ((-349 . -622) 163535) ((-331 . -620) 163496) ((-331 . -619) 163408) ((-267 . -622) 163161) ((-249 . -622) 162946) ((-1239 . -798) 162899) ((-1239 . -801) 162852) ((-254 . -382) 162821) ((-253 . -382) 162790) ((-660 . -38) 162760) ((-614 . -34) T) ((-488 . -1121) 162670) ((-481 . -34) T) ((-1122 . -132) 162540) ((-971 . -25) 162351) ((-917 . -622) 162301) ((-880 . -619) 162283) ((-971 . -21) 162238) ((-821 . -21) 162148) ((-821 . -25) 161999) ((-1232 . -373) T) ((-629 . -1067) T) ((-1188 . -562) 161978) ((-1182 . -47) 161955) ((-360 . -1058) T) ((-357 . -1058) T) ((-488 . -23) 161825) ((-349 . -1058) T) ((-267 . -1058) T) ((-249 . -1058) T) ((-1134 . -47) 161797) ((-118 . -1067) T) 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T) ((-570 . -1109) T) ((-501 . -1109) T) ((-247 . -292) 160897) ((-317 . -233) 160858) ((-1182 . -893) NIL) ((-55 . -1109) T) ((-1134 . -893) 160717) ((-130 . -856) T) ((-1182 . -1047) 160597) ((-1134 . -1047) 160480) ((-185 . -619) 160462) ((-860 . -1047) 160358) ((-788 . -290) 160285) ((-823 . -1121) T) ((-1043 . -732) T) ((-608 . -657) 160269) ((-1055 . -985) 160198) ((-1008 . -102) T) ((-823 . -23) T) ((-718 . -1161) 160176) ((-700 . -1067) T) ((-608 . -378) 160160) ((-356 . -458) T) ((-348 . -294) T) ((-1277 . -1109) T) ((-250 . -1109) T) ((-405 . -102) T) ((-293 . -21) T) ((-293 . -25) T) ((-366 . -732) T) ((-716 . -1109) T) ((-705 . -1109) T) ((-366 . -479) T) ((-1220 . -619) 160142) ((-1182 . -382) 160126) ((-1134 . -382) 160110) ((-1033 . -417) 160072) ((-142 . -231) 160054) ((-384 . -800) T) ((-384 . -797) T) ((-876 . -174) T) ((-384 . -732) T) ((-717 . -619) 160036) ((-718 . -38) 159865) ((-1276 . -1274) 159849) ((-356 . -408) T) ((-1276 . -1109) 159799) ((-586 . -723) 159786) ((-570 . -723) 159773) ((-501 . -723) 159738) ((-1262 . -652) 159628) ((-320 . -635) 159607) ((-842 . -732) T) ((-833 . -732) T) ((-650 . -1226) T) ((-1089 . -645) 159555) ((-1182 . -907) 159498) ((-1134 . -907) 159482) ((-668 . -1065) 159466) ((-108 . -645) 159448) ((-488 . -132) 159318) ((-1188 . -1121) T) ((-959 . -47) 159287) ((-629 . -1109) T) ((-668 . -111) 159266) ((-497 . -619) 159232) ((-331 . -292) 159209) ((-487 . -47) 159166) ((-1188 . -23) T) ((-118 . -1109) T) ((-103 . -102) 159144) ((-1288 . -1121) T) ((-554 . -856) T) ((-1063 . -132) T) ((-1033 . -1067) T) ((-825 . -1047) 159128) ((-1012 . -730) 159100) ((-1288 . -23) T) ((-705 . -723) 159065) ((-592 . -619) 159047) ((-392 . -1047) 159031) ((-359 . -1067) T) ((-390 . -132) T) ((-328 . -1047) 159015) ((-1206 . -619) 158997) ((-1129 . -834) T) ((-1114 . -1109) T) ((-227 . -893) 158979) ((-1013 . -927) T) ((-91 . -34) T) ((-1013 . -826) T) ((-921 . -927) T) ((-1089 . -21) T) ((-1089 . -25) T) ((-493 . -1230) T) 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. -657) 151889) ((-664 . -111) 151868) ((-592 . -622) 151852) ((-320 . -417) 151836) ((-247 . -378) 151820) ((-1169 . -237) 151767) ((-1008 . -233) 151751) ((-74 . -1226) T) ((-48 . -174) T) ((-707 . -393) T) ((-707 . -144) T) ((-1299 . -102) T) ((-1206 . -622) 151733) ((-1096 . -1065) 151576) ((-267 . -916) 151555) ((-249 . -916) 151534) ((-788 . -1065) 151357) ((-786 . -1065) 151200) ((-614 . -1226) T) ((-1174 . -619) 151182) ((-1096 . -111) 151011) ((-1055 . -102) T) ((-481 . -1226) T) ((-467 . -1065) 150982) ((-460 . -1065) 150825) ((-670 . -654) 150809) ((-877 . -311) T) ((-788 . -111) 150618) ((-786 . -111) 150447) ((-360 . -654) 150399) ((-357 . -654) 150351) ((-349 . -654) 150303) ((-267 . -654) 150228) ((-249 . -654) 150153) ((-1168 . -856) T) ((-1097 . -1047) 150137) ((-467 . -111) 150098) ((-460 . -111) 149927) ((-1085 . -1047) 149904) ((-1009 . -34) T) ((-973 . -619) 149886) ((-965 . -1226) T) ((-127 . -1019) 149870) ((-970 . -1121) T) ((-877 . -1031) NIL) ((-741 . -1121) T) ((-721 . -1121) T) ((-664 . -622) 149788) ((-1276 . -495) 149772) ((-1151 . -38) 149732) ((-970 . -23) T) ((-917 . -654) 149697) ((-871 . -1109) T) ((-849 . -102) T) ((-823 . -21) T) ((-641 . -1060) 149681) ((-613 . -1060) 149665) ((-823 . -25) T) ((-741 . -23) T) ((-721 . -23) T) ((-641 . -646) 149649) ((-110 . -667) T) ((-613 . -646) 149633) ((-587 . -1065) 149598) ((-524 . -1065) 149543) ((-229 . -57) 149501) ((-459 . -23) T) ((-413 . -102) T) ((-266 . -102) T) ((-110 . -113) T) ((-700 . -294) T) ((-872 . -38) 149471) ((-587 . -111) 149427) ((-524 . -111) 149356) ((-1096 . -622) 149092) ((-424 . -1121) T) ((-320 . -1067) 148982) ((-317 . -1067) T) ((-129 . -1226) T) ((-788 . -622) 148730) ((-786 . -622) 148496) ((-664 . -1058) T) ((-1304 . -1109) T) ((-460 . -622) 148281) ((-171 . -311) 148212) ((-424 . -23) T) ((-40 . -619) 148194) ((-40 . -620) 148178) ((-108 . -1001) 148160) ((-117 . -875) 148144) ((-655 . -622) 148128) ((-48 . -520) 148094) ((-1212 . -1019) 148078) ((-1191 . 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147236) ((-50 . -1058) T) ((-1288 . -21) T) ((-1288 . -25) T) ((-1184 . -562) 147215) ((-1183 . -1230) 147194) ((-1183 . -562) 147145) ((-587 . -1058) T) ((-524 . -1058) T) ((-1177 . -1230) 147124) ((-366 . -1047) 147108) ((-326 . -1047) 147092) ((-1033 . -294) T) ((-384 . -893) 147074) ((-1177 . -562) 147025) ((-1012 . -38) 146970) ((-1008 . -652) 146893) ((-805 . -1121) T) ((-917 . -732) T) ((-587 . -245) T) ((-587 . -235) T) ((-524 . -235) T) ((-524 . -245) T) ((-1135 . -562) 146872) ((-359 . -294) T) ((-653 . -701) 146856) ((-384 . -1047) 146816) ((-298 . -1060) 146737) ((-1129 . -1067) T) ((-103 . -126) 146721) ((-298 . -646) 146663) ((-805 . -23) T) ((-1298 . -1293) 146639) ((-1276 . -290) 146616) ((-413 . -313) 146581) ((-1296 . -1293) 146560) ((-1262 . -1109) T) ((-876 . -619) 146542) ((-842 . -1047) 146511) ((-205 . -793) T) ((-204 . -793) T) ((-203 . -793) T) ((-202 . -793) T) ((-201 . -793) T) ((-200 . -793) T) ((-199 . -793) T) ((-198 . -793) T) ((-197 . -793) T) ((-196 . 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128566) ((-1260 . -927) 128545) ((-1239 . -927) 128524) ((-876 . -732) T) ((-171 . -562) 128435) ((-586 . -654) 128422) ((-570 . -654) 128409) ((-413 . -1109) T) ((-266 . -1109) T) ((-215 . -619) 128391) ((-501 . -654) 128356) ((-227 . -23) T) ((-1239 . -826) 128309) ((-1298 . -102) T) ((-359 . -1295) 128286) ((-1296 . -102) T) ((-1262 . -111) 128178) ((-821 . -1060) 128075) ((-821 . -646) 128017) ((-145 . -619) 127999) ((-1002 . -132) T) ((-44 . -102) T) ((-242 . -856) 127950) ((-1249 . -1230) 127929) ((-103 . -495) 127913) ((-1299 . -723) 127883) ((-1096 . -47) 127844) ((-1071 . -1121) T) ((-959 . -1121) T) ((-128 . -34) T) ((-122 . -34) T) ((-788 . -47) 127821) ((-786 . -47) 127793) ((-1249 . -562) 127704) ((-359 . -373) T) ((-487 . -1121) T) ((-1182 . -132) T) ((-1134 . -132) T) ((-460 . -47) 127683) ((-877 . -368) T) ((-860 . -132) T) ((-153 . -102) T) ((-1071 . -23) T) ((-959 . -23) T) ((-577 . -562) T) ((-822 . -25) T) ((-822 . -21) T) ((-1151 . -520) 127616) ((-598 . -1092) T) 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. -111) 121668) ((-1151 . -495) 121652) ((-1300 . -652) 121611) ((-386 . -652) 121580) ((-821 . -38) 121550) ((-63 . -447) T) ((-63 . -401) T) ((-1169 . -102) T) ((-877 . -132) T) ((-490 . -102) 121528) ((-1304 . -373) T) ((-1089 . -102) T) ((-1070 . -102) T) ((-356 . -723) 121473) ((-737 . -148) 121452) ((-737 . -146) 121431) ((-660 . -622) 121349) ((-1033 . -654) 121286) ((-529 . -1109) 121264) ((-364 . -102) T) ((-358 . -102) T) ((-350 . -102) T) ((-108 . -102) T) ((-510 . -1109) T) ((-359 . -654) 121209) ((-1182 . -645) 121157) ((-1134 . -645) 121105) ((-390 . -515) 121084) ((-839 . -854) 121063) ((-384 . -1230) T) ((-700 . -732) T) ((-1240 . -1001) 121015) ((-344 . -1067) T) ((-112 . -1226) T) ((-176 . -1067) T) ((-103 . -619) 120947) ((-1184 . -146) 120926) ((-1184 . -148) 120905) ((-384 . -562) T) ((-1183 . -148) 120884) ((-1183 . -146) 120863) ((-1177 . -146) 120770) ((-413 . -294) T) ((-1177 . -148) 120677) ((-1135 . -148) 120656) ((-1135 . -146) 120635) ((-323 . -38) 120476) 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119492) ((-271 . -102) T) ((-214 . -102) T) ((-213 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-205 . -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) ((-195 . -102) T) ((-359 . -732) T) ((-718 . -111) 119301) ((-676 . -233) 119285) ((-587 . -311) T) ((-524 . -311) T) ((-298 . -520) 119234) ((-108 . -313) NIL) ((-72 . -401) T) ((-1122 . -102) 119024) ((-839 . -417) 119008) ((-1129 . -801) T) ((-1129 . -798) T) ((-707 . -1109) T) ((-584 . -619) 118990) ((-384 . -368) T) ((-171 . -499) 118968) ((-224 . -619) 118900) ((-135 . -1109) T) ((-117 . -1109) T) ((-973 . -1226) T) ((-48 . -732) T) ((-1055 . -495) 118865) ((-142 . -431) 118847) ((-142 . -373) T) ((-1036 . -102) T) ((-518 . -515) 118826) ((-718 . -622) 118582) ((-482 . -102) T) ((-469 . -102) T) ((-1043 . -1121) T) ((-1233 . -619) 118564) ((-1191 . -1047) 118500) ((-1184 . -35) 118466) ((-1184 . -95) 118432) ((-1184 . -1214) 118398) ((-1184 . -1211) 118364) ((-1168 . -313) NIL) ((-89 . -402) T) ((-89 . -401) T) ((-1089 . -1161) 118343) ((-1183 . -1211) 118309) ((-1183 . -1214) 118275) ((-1043 . -23) T) ((-1183 . -95) 118241) ((-577 . -499) T) ((-1183 . -35) 118207) ((-1177 . -1211) 118173) ((-1177 . -1214) 118139) ((-1177 . -95) 118105) ((-366 . -1121) T) ((-364 . -1161) 118084) ((-358 . -1161) 118063) ((-350 . -1161) 118042) ((-1177 . -35) 118008) ((-1135 . -35) 117974) ((-1135 . -95) 117940) ((-108 . -1161) T) ((-1135 . -1214) 117906) ((-839 . -1067) 117885) ((-653 . -313) 117823) ((-638 . -313) 117674) ((-1135 . -1211) 117640) ((-718 . -1058) T) ((-1071 . -645) 117622) ((-1089 . -38) 117490) ((-959 . -645) 117438) ((-1013 . -148) T) ((-1013 . -146) NIL) ((-384 . -1121) T) ((-328 . -25) T) ((-326 . -23) T) ((-950 . -856) 117417) ((-718 . -330) 117394) ((-487 . -645) 117342) ((-40 . -1047) 117230) ((-718 . -235) T) ((-707 . -723) 117217) ((-344 . 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((-1055 . -620) 112740) ((-1055 . -619) 112683) ((-317 . -916) NIL) ((-1234 . -850) T) ((-705 . -1047) 112628) ((-717 . -927) T) ((-480 . -1230) 112607) ((-1183 . -458) 112586) ((-1177 . -458) 112565) ((-334 . -102) T) ((-878 . -1121) T) ((-323 . -652) 112447) ((-320 . -654) 112268) ((-317 . -654) 112197) ((-480 . -562) 112148) ((-344 . -520) 112114) ((-556 . -152) 112064) ((-40 . -311) T) ((-849 . -619) 112046) ((-707 . -294) T) ((-878 . -23) T) ((-384 . -499) T) ((-1089 . -233) 112016) ((-518 . -102) T) ((-413 . -620) 111823) ((-413 . -619) 111805) ((-266 . -619) 111787) ((-117 . -294) T) ((-1262 . -732) T) ((-1260 . -368) 111766) ((-1239 . -368) 111745) ((-1289 . -34) T) ((-1234 . -1109) T) ((-118 . -1226) T) ((-108 . -233) 111727) ((-1188 . -102) T) ((-483 . -1109) T) ((-529 . -495) 111711) ((-743 . -34) T) ((-659 . -1060) 111695) ((-488 . -38) 111665) ((-659 . -646) 111635) ((-142 . -34) T) ((-118 . -891) 111612) ((-118 . -893) NIL) ((-629 . -1047) 111495) ((-650 . -856) 111474) 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T) ((-137 . -1047) 98523) ((-227 . -95) T) ((-171 . -148) 98502) ((-75 . -447) T) ((0 . -619) 98484) ((-75 . -401) T) ((-171 . -146) 98435) ((-227 . -35) T) ((-49 . -619) 98417) ((-483 . -1067) T) ((-493 . -233) 98399) ((-490 . -977) 98383) ((-488 . -854) 98362) ((-219 . -233) 98344) ((-81 . -447) T) ((-81 . -401) T) ((-1155 . -34) T) ((-821 . -174) 98323) ((-737 . -102) T) ((-659 . -652) 98282) ((-1035 . -619) 98249) ((-506 . -290) 98224) ((-320 . -382) 98193) ((-317 . -382) 98154) ((-317 . -343) 98115) ((-1094 . -619) 98097) ((-822 . -956) 98044) ((-668 . -132) T) ((-1249 . -146) 98023) ((-1249 . -148) 98002) ((-1184 . -102) T) ((-1183 . -102) T) ((-1177 . -102) T) ((-1169 . -1109) T) ((-1135 . -102) T) ((-224 . -34) T) ((-293 . -723) 97989) ((-1169 . -616) 97965) ((-599 . -313) NIL) ((-490 . -1109) 97943) ((-1159 . -231) 97893) ((-396 . -619) 97875) ((-516 . -856) T) ((-1129 . -1226) T) ((-1268 . -1267) 97859) ((-1268 . -1254) 97836) ((-1261 . -1259) 97797) ((-1261 . -1254) 97767) 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. -723) 95587) ((-1013 . -1060) 95537) ((-1013 . -646) 95487) ((-950 . -989) 95471) ((-921 . -646) 95423) ((-921 . -1060) 95375) ((-917 . -21) T) ((-917 . -25) T) ((-878 . -856) 95326) ((-872 . -654) 95286) ((-717 . -1121) T) ((-717 . -23) T) ((-293 . -174) T) ((-707 . -1058) T) ((-315 . -93) T) ((-707 . -235) T) ((-653 . -1109) 95264) ((-638 . -616) 95239) ((-638 . -1109) T) ((-587 . -1230) T) ((-587 . -562) T) ((-524 . -1230) T) ((-524 . -562) T) ((-493 . -652) 95189) ((-433 . -1060) 95173) ((-433 . -646) 95157) ((-364 . -723) 95109) ((-358 . -723) 95061) ((-344 . -1065) 95045) ((-350 . -723) 94997) ((-344 . -111) 94976) ((-176 . -1065) 94908) ((-219 . -652) 94858) ((-176 . -111) 94769) ((-108 . -723) 94719) ((-277 . -1109) T) ((-276 . -1109) T) ((-275 . -1109) T) ((-274 . -1109) T) ((-273 . -1109) T) ((-272 . -1109) T) ((-271 . -1109) T) ((-214 . -1109) T) ((-213 . -1109) T) ((-171 . -1214) 94697) ((-171 . -1211) 94675) ((-211 . -1109) T) ((-210 . -1109) T) ((-117 . -1058) T) ((-209 . -1109) T) ((-208 . -1109) T) ((-205 . -1109) T) ((-204 . -1109) T) ((-203 . -1109) T) ((-202 . -1109) T) ((-201 . -1109) T) ((-200 . -1109) T) ((-199 . -1109) T) ((-198 . -1109) T) ((-197 . -1109) T) ((-196 . -1109) T) ((-195 . -1109) T) ((-242 . -102) 94465) ((-171 . -35) 94443) ((-171 . -95) 94421) ((-660 . -1047) 94317) ((-488 . -1067) 94247) ((-1122 . -1109) 94037) ((-1151 . -34) T) ((-676 . -495) 94021) ((-73 . -1226) T) ((-105 . -619) 94003) ((-1300 . -619) 93985) ((-386 . -619) 93967) ((-344 . -622) 93919) ((-176 . -622) 93836) ((-1225 . -496) 93817) ((-737 . -38) 93666) ((-577 . -1214) T) ((-577 . -1211) T) ((-537 . -619) 93648) ((-526 . -313) 93586) ((-506 . -619) 93568) ((-506 . -620) 93550) ((-1225 . -619) 93516) ((-1177 . -1161) NIL) ((-1036 . -1080) 93485) ((-1036 . -1109) T) ((-1013 . -102) T) ((-980 . -102) T) ((-921 . -102) T) ((-900 . -1047) 93462) ((-1151 . -732) T) ((-1012 . -654) 93407) ((-482 . -1109) T) ((-469 . -1109) T) ((-592 . -23) T) ((-577 . -35) T) ((-577 . -95) T) ((-433 . -102) T) ((-1072 . -231) 93353) ((-1184 . -38) 93250) ((-872 . -732) T) ((-700 . -927) T) ((-517 . -25) T) ((-513 . -21) T) ((-513 . -25) T) ((-1183 . -38) 93091) ((-344 . -1058) T) ((-1177 . -38) 92887) ((-1089 . -174) T) ((-176 . -1058) T) ((-1135 . -38) 92784) ((-718 . -47) 92761) ((-364 . -174) T) ((-358 . -174) T) ((-525 . -57) 92735) ((-503 . -57) 92685) ((-356 . -1295) 92662) ((-227 . -458) T) ((-323 . -294) 92613) ((-350 . -174) T) ((-176 . -245) T) ((-1239 . -856) 92512) ((-108 . -174) T) ((-878 . -1001) 92496) ((-664 . -1121) T) ((-587 . -368) T) ((-587 . -333) 92483) ((-524 . -333) 92460) ((-524 . -368) T) ((-320 . -311) 92439) ((-317 . -311) T) ((-608 . -856) 92418) ((-1122 . -723) 92360) ((-526 . -286) 92344) ((-664 . -23) T) ((-424 . -233) 92328) ((-317 . -1031) NIL) ((-341 . -23) T) ((-103 . -1019) 92312) ((-45 . -36) 92291) ((-618 . -1109) T) ((-356 . -373) T) ((-530 . -102) T) ((-501 . -27) T) ((-242 . -313) 92229) ((-1096 . -1121) T) ((-1299 . -654) 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. -23) T) ((-717 . -132) T) ((-718 . -1047) 90222) ((-587 . -23) T) ((-108 . -520) NIL) ((-524 . -23) T) ((-171 . -415) 90193) ((-1149 . -1109) T) ((-1291 . -1290) 90177) ((-707 . -801) T) ((-707 . -798) T) ((-1129 . -311) T) ((-384 . -148) T) ((-284 . -619) 90159) ((-283 . -619) 90141) ((-1239 . -1001) 90111) ((-48 . -927) T) ((-681 . -495) 90095) ((-254 . -1283) 90065) ((-253 . -1283) 90035) ((-1186 . -856) T) ((-1122 . -174) 90014) ((-1129 . -1031) T) ((-1055 . -34) T) ((-842 . -148) 89993) ((-842 . -146) 89972) ((-743 . -107) 89956) ((-618 . -133) T) ((-488 . -1109) 89746) ((-1188 . -1067) T) ((-877 . -458) T) ((-85 . -1226) T) ((-242 . -38) 89716) ((-142 . -107) 89698) ((-718 . -382) 89682) ((-839 . -622) 89550) ((-1299 . -732) T) ((-1288 . -1067) T) ((-1129 . -551) T) ((-585 . -102) T) ((-130 . -496) 89532) ((-1268 . -102) T) ((-396 . -1065) 89516) ((-1261 . -102) T) ((-1182 . -956) 89485) ((-130 . -619) 89452) ((-52 . -619) 89434) ((-1134 . -956) 89401) ((-659 . -417) 89385) 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. -458) T) ((-501 . -520) 156381) ((-493 . -368) T) ((-360 . -373) 156360) ((-357 . -373) 156339) ((-349 . -373) 156318) ((-720 . -732) T) ((-219 . -368) T) ((-117 . -458) T) ((-1300 . -1291) 156302) ((-877 . -891) 156279) ((-877 . -893) NIL) ((-971 . -856) 156178) ((-821 . -856) 156129) ((-1234 . -102) T) ((-660 . -662) 156113) ((-1213 . -34) T) ((-173 . -619) 156095) ((-1122 . -21) 156005) ((-1122 . -25) 155856) ((-877 . -1047) 155833) ((-959 . -907) 155814) ((-1250 . -47) 155791) ((-917 . -373) T) ((-59 . -657) 155775) ((-522 . -657) 155759) ((-487 . -907) 155736) ((-71 . -447) T) ((-71 . -401) T) ((-502 . -657) 155720) ((-59 . -378) 155704) ((-629 . -174) T) ((-522 . -378) 155688) ((-502 . -378) 155672) ((-833 . -714) 155656) ((-1182 . -311) 155635) ((-1188 . -132) T) ((-1151 . -1060) 155619) ((-118 . -174) T) ((-1151 . -646) 155551) ((-1155 . -313) 155489) ((-171 . -1227) T) ((-1289 . -132) T) ((-872 . -1060) 155459) ((-641 . -750) 155443) ((-613 . -750) 155427) ((-1262 . -927) 155406) ((-1241 . -927) 155385) ((-1241 . -826) NIL) ((-872 . -646) 155355) ((-700 . -723) 155305) ((-1240 . -916) 155258) ((-1033 . -1109) T) ((-877 . -382) 155235) ((-877 . -343) 155212) ((-912 . -1121) T) ((-171 . -891) 155196) ((-171 . -893) 155121) ((-493 . -1121) T) ((-359 . -1109) T) ((-219 . -1121) T) ((-76 . -447) T) ((-76 . -401) T) ((-171 . -1047) 155017) ((-323 . -856) T) ((-1277 . -520) 154950) ((-1261 . -654) 154847) ((-1240 . -654) 154717) ((-878 . -800) 154696) ((-878 . -797) 154675) ((-878 . -732) T) ((-493 . -23) T) ((-225 . -619) 154657) ((-176 . -458) T) ((-224 . -313) 154595) ((-86 . -447) T) ((-86 . -401) T) ((-219 . -23) T) ((-1301 . -1294) 154574) ((-683 . -1047) 154558) ((-586 . -294) T) ((-570 . -294) T) ((-501 . -294) T) ((-137 . -476) 154513) ((-660 . -652) 154472) ((-48 . -1109) T) ((-718 . -233) 154456) ((-877 . -907) NIL) ((-1250 . -893) NIL) ((-896 . -102) T) ((-892 . -102) T) ((-394 . -1109) T) ((-171 . -382) 154440) ((-171 . -343) 154424) ((-1250 . 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. -622) 152769) ((-112 . -619) 152751) ((-112 . -620) 152733) ((-724 . -479) T) ((-717 . -622) 152683) ((-1300 . -1060) 152667) ((-488 . -21) 152577) ((-128 . -495) 152561) ((-122 . -495) 152545) ((-488 . -25) 152396) ((-1300 . -646) 152366) ((-629 . -294) T) ((-592 . -1065) 152341) ((-443 . -1109) T) ((-1071 . -311) T) ((-118 . -294) T) ((-1113 . -102) T) ((-1012 . -102) T) ((-592 . -111) 152309) ((-1151 . -313) 152247) ((-1221 . -1058) T) ((-1071 . -1031) T) ((-66 . -1227) T) ((-1063 . -25) T) ((-1063 . -21) T) ((-717 . -1058) T) ((-390 . -21) T) ((-390 . -25) T) ((-700 . -520) NIL) ((-1033 . -174) T) ((-717 . -245) T) ((-1071 . -551) T) ((-718 . -652) 152157) ((-512 . -102) T) ((-508 . -102) T) ((-359 . -174) T) ((-348 . -619) 152139) ((-413 . -1060) 152091) ((-400 . -619) 152073) ((-1129 . -854) T) ((-480 . -732) T) ((-899 . -1047) 152041) ((-413 . -646) 151993) ((-108 . -856) T) ((-664 . -1065) 151977) ((-493 . -132) T) ((-1263 . -1067) T) ((-219 . -132) T) ((-1166 . -102) 151955) 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. -562) T) ((-822 . -25) T) ((-822 . -21) T) ((-1151 . -520) 127632) ((-598 . -1092) T) ((-592 . -1047) 127616) ((-1263 . -622) 127490) ((-487 . -23) T) ((-356 . -1067) T) ((-1221 . -907) 127471) ((-676 . -313) 127409) ((-1122 . -1284) 127379) ((-705 . -654) 127344) ((-1012 . -174) T) ((-970 . -146) 127323) ((-641 . -1109) T) ((-613 . -1109) T) ((-970 . -148) 127302) ((-1013 . -856) T) ((-741 . -148) 127281) ((-741 . -146) 127260) ((-980 . -856) T) ((-839 . -652) 127177) ((-480 . -927) 127156) ((-323 . -1060) 126991) ((-320 . -1065) 126901) ((-317 . -1065) 126830) ((-1008 . -290) 126788) ((-413 . -723) 126740) ((-323 . -646) 126581) ((-707 . -854) T) ((-1263 . -1058) T) ((-320 . -111) 126477) ((-317 . -111) 126390) ((-971 . -102) T) ((-821 . -102) 126180) ((-718 . -620) NIL) ((-718 . -619) 126162) ((-664 . -1047) 126058) ((-1263 . -330) 126002) ((-1044 . -292) 125977) ((-586 . -732) T) ((-570 . -800) T) ((-171 . -368) 125928) ((-570 . -797) T) ((-570 . -732) T) ((-501 . -732) T) 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117358) ((-40 . -1047) 117246) ((-718 . -235) T) ((-707 . -723) 117233) ((-344 . -1109) T) ((-176 . -1109) T) ((-335 . -856) T) ((-424 . -458) 117183) ((-384 . -23) T) ((-364 . -38) 117148) ((-358 . -38) 117113) ((-350 . -38) 117078) ((-80 . -447) T) ((-80 . -401) T) ((-227 . -25) T) ((-227 . -21) T) ((-842 . -1121) T) ((-108 . -38) 117028) ((-833 . -1121) T) ((-780 . -1109) T) ((-117 . -723) 117015) ((-678 . -1047) 116999) ((-618 . -102) T) ((-842 . -23) T) ((-833 . -23) T) ((-1166 . -290) 116976) ((-1122 . -313) 116914) ((-488 . -1060) 116811) ((-1111 . -237) 116795) ((-64 . -402) T) ((-64 . -401) T) ((-1160 . -102) T) ((-110 . -102) T) ((-488 . -646) 116737) ((-40 . -382) 116714) ((-96 . -102) T) ((-659 . -858) 116698) ((-1144 . -1092) T) ((-1071 . -21) T) ((-1071 . -25) T) ((-1063 . -1060) 116682) ((-821 . -233) 116651) ((-959 . -25) T) ((-959 . -21) T) ((-1063 . -646) 116593) ((-627 . -1067) T) ((-1129 . -373) T) ((-1036 . -313) 116531) ((-676 . -652) 116490) ((-487 . -25) T) 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. -891) 111628) ((-118 . -893) NIL) ((-629 . -1047) 111511) ((-650 . -856) 111490) ((-1289 . -102) T) ((-299 . -102) T) ((-718 . -373) 111469) ((-118 . -1047) 111446) ((-396 . -723) 111430) ((-627 . -723) 111414) ((-45 . -313) 111218) ((-822 . -146) 111197) ((-822 . -148) 111176) ((-293 . -652) 111148) ((-1300 . -387) 111127) ((-825 . -856) T) ((-1279 . -1109) T) ((-1169 . -231) 111074) ((-392 . -856) 111053) ((-1269 . -1215) 111019) ((-1269 . -1212) 110985) ((-1262 . -1212) 110951) ((-521 . -132) T) ((-1262 . -1215) 110917) ((-1241 . -1212) 110883) ((-1241 . -1215) 110849) ((-1269 . -35) 110815) ((-1269 . -95) 110781) ((-641 . -619) 110750) ((-613 . -619) 110719) ((-227 . -856) T) ((-1262 . -95) 110685) ((-1262 . -35) 110651) ((-1261 . -1121) T) ((-1129 . -654) 110638) ((-1241 . -95) 110604) ((-1240 . -1121) T) ((-599 . -152) 110586) ((-1089 . -354) 110565) ((-176 . -294) T) ((-118 . -382) 110542) ((-118 . -343) 110519) ((-1241 . -35) 110485) ((-876 . -311) T) ((-317 . -800) NIL) 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. -654) 93423) ((-482 . -1109) T) ((-469 . -1109) T) ((-592 . -23) T) ((-577 . -35) T) ((-577 . -95) T) ((-433 . -102) T) ((-1072 . -231) 93369) ((-1184 . -38) 93266) ((-872 . -732) T) ((-700 . -927) T) ((-517 . -25) T) ((-513 . -21) T) ((-513 . -25) T) ((-1183 . -38) 93107) ((-344 . -1058) T) ((-1177 . -38) 92903) ((-1089 . -174) T) ((-176 . -1058) T) ((-1135 . -38) 92800) ((-718 . -47) 92777) ((-364 . -174) T) ((-358 . -174) T) ((-525 . -57) 92751) ((-503 . -57) 92701) ((-356 . -1296) 92678) ((-227 . -458) T) ((-323 . -294) 92629) ((-350 . -174) T) ((-176 . -245) T) ((-1240 . -856) 92528) ((-108 . -174) T) ((-878 . -1001) 92512) ((-664 . -1121) T) ((-587 . -368) T) ((-587 . -333) 92499) ((-524 . -333) 92476) ((-524 . -368) T) ((-320 . -311) 92455) ((-317 . -311) T) ((-608 . -856) 92434) ((-1122 . -723) 92376) ((-526 . -286) 92360) ((-664 . -23) T) ((-424 . -233) 92344) ((-317 . -1031) NIL) ((-341 . -23) T) ((-103 . -1019) 92328) ((-45 . -36) 92307) ((-618 . -1109) T) ((-356 . -373) 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. -652) 88259) ((-921 . -38) 88211) ((-849 . -800) 88190) ((-849 . -797) 88169) ((-849 . -732) 88148) ((-364 . -294) T) ((-358 . -294) T) ((-350 . -294) T) ((-171 . -458) 88079) ((-433 . -38) 88063) ((-108 . -294) T) ((-225 . -23) T) ((-413 . -800) 88042) ((-413 . -797) 88021) ((-413 . -732) T) ((-506 . -292) 87996) ((-483 . -1065) 87961) ((-664 . -132) T) ((-627 . -622) 87930) ((-1122 . -520) 87863) ((-341 . -132) T) ((-171 . -408) 87842) ((-488 . -723) 87784) ((-821 . -290) 87761) ((-483 . -111) 87717) ((-659 . -1067) T) ((-822 . -1060) 87560) ((-1288 . -1092) T) ((-1250 . -458) 87491) ((-822 . -646) 87340) ((-1287 . -1092) T) ((-1096 . -132) T) ((-1063 . -723) 87282) ((-788 . -132) T) ((-786 . -132) T) ((-577 . -458) T) ((-1036 . -520) 87215) ((-627 . -1058) T) ((-598 . -1109) T) ((-539 . -175) T) ((-467 . -132) T) ((-460 . -132) T) ((-45 . -1109) T) ((-390 . -723) 87185) ((-823 . -1109) T) ((-482 . -520) 87118) ((-469 . -520) 87051) ((-459 . -372) 87021) ((-45 . -616) 87000) ((-320 . -306) T) ((-483 . -622) 86950) ((-1241 . -313) 86835) ((-676 . -619) 86797) ((-59 . -856) 86776) ((-1013 . -406) 86758) ((-554 . -619) 86740) ((-805 . -652) 86699) ((-821 . -610) 86676) ((-522 . -856) 86655) ((-502 . -856) 86634) ((-40 . -1231) T) ((-1008 . -1047) 86530) ((-50 . -132) T) ((-587 . -132) T) ((-524 . -132) T) ((-298 . -654) 86390) ((-348 . -333) 86367) ((-348 . -368) T) ((-326 . -327) 86344) ((-323 . -290) 86329) ((-40 . -562) T) ((-384 . -1212) T) ((-384 . -1215) T) ((-1044 . -1203) 86304) ((-1199 . -237) 86254) ((-1177 . -233) 86206) ((-334 . -1109) T) ((-384 . -95) T) ((-384 . -35) T) ((-1044 . -107) 86152) ((-483 . -1058) T) ((-1301 . -1065) 86136) ((-485 . -237) 86086) ((-1169 . -495) 86020) ((-1292 . -1060) 86004) ((-386 . -1065) 85988) ((-1292 . -646) 85958) ((-483 . -245) T) ((-822 . -102) T) ((-720 . -148) 85937) ((-720 . -146) 85916) ((-490 . -495) 85900) ((-491 . -340) 85869) ((-1301 . -111) 85848) ((-518 . -1109) T) ((-488 . -174) 85827) ((-1008 . -382) 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82763) ((-1166 . -1019) 82747) ((-950 . -102) 82697) ((-356 . -732) T) ((-867 . -619) 82679) ((-1183 . -652) 82561) ((-1177 . -652) 82398) ((-1135 . -652) 82308) ((-1241 . -406) 82260) ((-1122 . -495) 82244) ((-60 . -313) 82182) ((-335 . -102) T) ((-1221 . -21) T) ((-1221 . -25) T) ((-40 . -1121) T) ((-717 . -21) T) ((-633 . -619) 82164) ((-521 . -327) 82143) ((-717 . -25) T) ((-445 . -102) T) ((-108 . -290) NIL) ((-928 . -1121) T) ((-40 . -23) T) ((-777 . -1121) T) ((-570 . -1231) T) ((-501 . -1231) T) ((-323 . -619) 82125) ((-1013 . -233) 82107) ((-171 . -167) 82091) ((-586 . -562) T) ((-570 . -562) T) ((-501 . -562) T) ((-777 . -23) T) ((-1261 . -148) 82070) ((-1169 . -610) 82046) ((-1261 . -146) 82025) ((-1036 . -495) 82009) ((-1240 . -146) 81934) ((-1240 . -148) 81859) ((-1292 . -1298) 81838) ((-482 . -495) 81822) ((-469 . -495) 81806) ((-529 . -34) T) ((-659 . -723) 81776) ((-112 . -976) T) ((-668 . -856) 81755) ((-1188 . -174) 81706) ((-370 . -102) T) ((-242 . -240) 81685) 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. -1109) T) ((-825 . -619) 16818) ((-872 . -21) T) ((-872 . -25) T) ((-805 . -732) T) ((-176 . -1231) T) ((-587 . -38) 16783) ((-524 . -38) 16748) ((-392 . -619) 16730) ((-337 . -102) T) ((-328 . -619) 16712) ((-171 . -290) 16670) ((-63 . -1227) T) ((-112 . -102) T) ((-878 . -1109) T) ((-176 . -562) T) ((-720 . -723) 16640) ((-298 . -132) 16523) ((-227 . -619) 16505) ((-227 . -620) 16435) ((-1012 . -645) 16374) ((-1292 . -1058) T) ((-1129 . -148) T) ((-638 . -1203) 16349) ((-737 . -916) 16328) ((-599 . -34) T) ((-653 . -107) 16312) ((-638 . -107) 16258) ((-1250 . -290) 16185) ((-737 . -654) 16110) ((-299 . -1227) T) ((-1188 . -1047) 16006) ((-950 . -624) 15983) ((-583 . -582) T) ((-583 . -533) T) ((-535 . -533) T) ((-1177 . -916) NIL) ((-1071 . -620) 15898) ((-1071 . -619) 15880) ((-959 . -619) 15862) ((-719 . -496) 15812) ((-348 . -102) T) ((-254 . -1065) 15709) ((-253 . -1065) 15606) ((-400 . -102) T) ((-31 . -1109) T) ((-959 . -620) 15467) ((-719 . -619) 15402) ((-1290 . -1220) 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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 f1408d2a..7bf8a3b8 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3480528372) -(4451 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3480551175) +(4452 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -438,19 +438,19 @@ |SymmetricPolynomial| |TheSymbolTable| |SymbolTable| |Syntax| |SystemInteger| |SystemNonNegativeInteger| |SystemPointer| |SystemSolvePackage| |System| |TableauxBumpers| |Tableau| |Table| - |TangentExpansions| |TableAggregate&| |TableAggregate| - |TabulatedComputationPackage| |TemplateUtilities| |TexFormat1| - |TexFormat| |TextFile| |ToolsForSign| |TopLevelThreeSpace| - |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| - |Tree| |TrigonometricFunctionCategory&| - |TrigonometricFunctionCategory| |TrigonometricManipulations| - |TriangularMatrixOperations| |TranscendentalManipulations| - |TriangularSetCategory&| |TriangularSetCategory| |TaylorSeries| - |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| |TypeAst| |Type| - |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| - |UniqueFactorizationDomain&| |UniqueFactorizationDomain| |UInt16| - |UInt32| |UInt64| |UInt8| |UnivariateLaurentSeriesFunctions2| - |UnivariateLaurentSeriesCategory| + |TermAlgebraOperator| |TangentExpansions| |TableAggregate&| + |TableAggregate| |TabulatedComputationPackage| |TemplateUtilities| + |TexFormat1| |TexFormat| |TextFile| |ToolsForSign| + |TopLevelThreeSpace| |TranscendentalFunctionCategory&| + |TranscendentalFunctionCategory| |Tree| + |TrigonometricFunctionCategory&| |TrigonometricFunctionCategory| + |TrigonometricManipulations| |TriangularMatrixOperations| + |TranscendentalManipulations| |TriangularSetCategory&| + |TriangularSetCategory| |TaylorSeries| |TubePlot| |TubePlotTools| + |Tuple| |TwoFactorize| |TypeAst| |Type| |UserDefinedPartialOrdering| + |UserDefinedVariableOrdering| |UniqueFactorizationDomain&| + |UniqueFactorizationDomain| |UInt16| |UInt32| |UInt64| |UInt8| + |UnivariateLaurentSeriesFunctions2| |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesConstructorCategory| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeries| @@ -484,660 +484,663 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |f04qaf| |d01anf| |f02ajf| |spherical| |subNode?| - |pi| |listConjugateBases| |logGamma| |upperBound| |doublyTransitive?| - |viewZoomDefault| |OMsetEncoding| |hconcat| |even?| |quasiRegular| - 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|realEigenvalues| |messagePrint| |normalizedAssociate| - |findCycle| |endSubProgram| |OMReadError?| |adjoint| - |inputOutputBinaryFile| |numberOfFractionalTerms| |stoseInvertible?| - |jordanAdmissible?| |nextColeman| |normalElement| |lflimitedint| - |e02ddf| |Is| |phiCoord| |external?| |monicModulo| |realElementary| - |separateFactors| |makeRecord| |nthFractionalTerm| |factorPolynomial| - |lo| |noKaratsuba| |fortranLiteralLine| |tanintegrate| |makeUnit| - |genericRightMinimalPolynomial| |An| |numberOfIrreduciblePoly| - |s21bdf| |dmpToHdmp| |xCoord| |ricDsolve| |incr| |acsch| |credPol| - |label| |prime| |pdct| |gethi| |palgint| |initial| |UP2ifCan| - |recolor| |nthExpon| |d01akf| |algebraicVariables| |positive?| - |zeroDimPrimary?| |Lazard| |uncouplingMatrices| |plus!| |readByte!| - |yellow| |tubePlot| |laplacian| |mathieu22| |lfinfieldint| - |positiveRemainder| |stoseInvertibleSetreg| |rightRecip| |triangular?| - |unary?| |harmonic| |sequences| |OMputAtp| |writeLine!| |cartesian| - |c06ekf| |outputGeneral| |crest| |screenResolution3D| Y |cyclicCopy| - |mergeFactors| |monomial?| |genericLeftNorm| |prime?| |failed?| - |printCode| |maxColIndex| |unitsColorDefault| |aromberg| |extend| - |outputForm| |bumprow| |goodPoint| |compBound| |chvar| - |OMencodingSGML| |nodeOf?| |is?| |unrankImproperPartitions0| |df2mf| - |basisOfMiddleNucleus| |contains?| |e04dgf| |numFunEvals| |tail| - |regime| |upperCase| |removeZeroes| |RemainderList| |inconsistent?| - |constructor| |s17acf| |rules| |ffactor| |pmintegrate| |bothWays| - |completeSmith| |c05adf| |capacity| |getZechTable| |idealiserMatrix| - |expPot| |select!| |sncndn| |complement| |nothing| |meshPar1Var| - |isTimes| |list?| |option| |imagk| |removeRedundantFactorsInPols| - |degree| |s13aaf| |pointSizeDefault| |showSummary| - |numberOfOperations| |normalizeAtInfinity| |minColIndex| - |LyndonWordsList| |writeBytes!| |basisOfLeftNucloid| |c06gbf| - |brillhartTrials| |medialSet| FG2F |forLoop| |oblateSpheroidal| - |iiacsch| |sortConstraints| |normalizeIfCan| |constantToUnaryFunction| - |toseLastSubResultant| |factorGroebnerBasis| |perfectNthRoot| - |restorePrecision| |showAttributes| |LowTriBddDenomInv| - |constantOperator| |setProperties| |d02bhf| |imagI| |sdf2lst| - |unknown| |coHeight| |getRef| |semiResultantReduitEuclidean| - |taylorRep| |macroExpand| |minimalPolynomial| |showIntensityFunctions| - |rightScalarTimes!| |cycles| |updateStatus!| |rightTrim| |mapCoef| - |nullity| |minPoly| |ran| |pointPlot| |schwerpunkt| |iiasech| - |chiSquare| |cotIfCan| |leftTrim| |solve| |setStatus!| |digit| - |exponents| |completeEchelonBasis| |solveLinearPolynomialEquation| - |genericRightNorm| |zeroDimPrime?| |addmod| |cAcoth| |normalForm| - |PollardSmallFactor| |possiblyNewVariety?| |gradient| |omError| - |rotatex| |say| |every?| |characteristicSerie| |f01rcf| F |Aleph| - |rightFactorIfCan| |makeFloatFunction| |distance| |factors| - |OMmakeConn| |associates?| |setMinPoints| |dflist| |rarrow| |dark| - |SturmHabicht| |flexible?| |curry| |eof?| |acotIfCan| |cAcsc| - |semiDegreeSubResultantEuclidean| |screenResolution| |removeCosSq| - |initiallyReduce| |multisect| |bottom!| |in?| |nonLinearPart| - |eigenvector| |startTable!| |remove| |function| |multivariate| - |edf2efi| |gcdcofactprim| |thetaCoord| |adaptive| |viewDefaults| - |fortranCarriageReturn| |fortran| |unravel| |f02bbf| - |genericLeftTraceForm| |coefficient| |variables| |result| |inf| - |iiacsc| |fixPredicate| |functorData| |mainCoefficients| |zeroOf| - |stoseIntegralLastSubResultant| |nary?| |linearAssociatedLog| |open| - |last| |e04ycf| |eval| |reset| |unitNormalize| |unit| - |internalZeroSetSplit| |generalizedInverse| |constantRight| |assoc| - |principal?| |null| |mapmult| |compose| |extractIndex| |enumerate| - |OMputEndAttr| |comparison| |strongGenerators| |OMputInteger| - |removeSuperfluousCases| |iicosh| |setFieldInfo| |rightDivide| - |pattern| |limitedIntegrate| |not| |leftExtendedGcd| |write| - |superscript| |lazyPrem| |structuralConstants| |OMUnknownSymbol?| - |quatern| |chebyshevU| |bandedHessian| |hostByteOrder| |and| |replace| - |calcRanges| |save| |palglimint0| |eigenvalues| |hasTopPredicate?| - |rightFactorCandidate| |modifyPointData| |operations| |leftMult| - |pointColor| |cPower| |or| |deepestInitial| |finiteBound| |taylor| - |radicalOfLeftTraceForm| |subset?| |writeByte!| |bat1| |aQuartic| - |d01bbf| |measure| |xor| |squareFree| |laurent| |intensity| - |fixedDivisor| |polygamma| |isobaric?| |lastSubResultantElseSplit| - |mergeDifference| |f01mcf| |message| |rectangularMatrix| |besselY| - |case| |insertBottom!| |puiseux| |setErrorBound| |copyInto!| - |coordinates| |reduceByQuasiMonic| |d02bbf| |sub| |OMencodingXML| - |Zero| |symmetric?| |power!| |iicsch| |evaluate| |cyclicSubmodule| - |hi| |positiveSolve| |minPoints3D| |unknownEndian| |rightUnit| |One| - |outputArgs| |inv| |partialDenominators| |optional?| |integral?| - |clearTheFTable| |critB| |torsion?| |solveid| |viewpoint| |ground?| - |lazyResidueClass| |bitTruth| |square?| |att2Result| |secIfCan| - |randnum| |newTypeLists| |ground| |unparse| |mainVariable?| |lcm| - |s20acf| |knownInfBasis| |internal?| |clipBoolean| - |genericRightDiscriminant| |extension| |makeSin| |plotPolar| - |simplifyExp| |leadingMonomial| |selectsecond| |critpOrder| - |primextendedint| |before?| |stoseSquareFreePart| |rationalPoint?| - |append| |moreAlgebraic?| |leadingCoefficient| |hue| |close!| |gderiv| - |npcoef| |nonQsign| |sizePascalTriangle| |showTheFTable| |ptFunc| - |primitiveMonomials| |gcd| |subNodeOf?| |elt| |output| - |symmetricTensors| |pastel| |mathieu11| |simpleBounds?| |delete!| - |swapColumns!| |LazardQuotient| |factorSquareFreePolynomial| |hcrf| - |quadraticNorm| |halfExtendedSubResultantGcd2| |false| |reductum| - |supRittWu?| |collectQuasiMonic| |arity| |middle| |presub| |bat| - |deleteProperty!| |bfKeys| |extract!| |curveColor| |axesColorDefault| - |decimal| |latex| |inrootof| |roughEqualIdeals?| |expressIdealMember| - |exponent| |polyred| |OMgetSymbol| |ParCond| |irreducible?| - |relativeApprox| |normalizedDivide| |closeComponent| |graphState| - |sylvesterSequence| |getGraph| |charthRoot| |pushup| - |perfectNthPower?| |modifyPoint| |functionIsFracPolynomial?| - |createNormalPoly| |rootPower| |mapMatrixIfCan| |s13acf| |alphabetic?| - |aLinear| |laguerreL| |prem| |firstSubsetGray| |dihedralGroup| - |numberOfVariables| |constantKernel| |twoFactor| |linSolve| - |fortranCompilerName| |showTheIFTable| |resultant| |goto| |categories| - |infieldIntegrate| |dimensionOfIrreducibleRepresentation| |hexDigit?| - |solid| |iExquo| |viewWriteAvailable| |elRow1!| |s17aff| - |semiSubResultantGcdEuclidean1| |clipWithRanges| |fill!| |minimize| - |resetBadValues| |generic| |typeLists| |topPredicate| |create| - |factorials| |antiCommutator| |monomialIntegrate| |c06gsf| |tab| - |bsolve| |fractionPart| |difference| |s17dhf| |nextPrime| - |mightHaveRoots| |primitivePart!| |perspective| |checkRur| - |cyclePartition| |particularSolution| |setEmpty!| |stFunc2| - |cyclotomicDecomposition| |nextsubResultant2| |cLog| |c06fqf| - |plusInfinity| |minset| |internalSubPolSet?| |getIdentifier| - |algebraicCoefficients?| |irreducibleFactors| |conical| |extendedint| - |generalizedEigenvector| |diagonalMatrix| |minusInfinity| - |rationalApproximation| |environment| |df2st| |LazardQuotient2| - |d02ejf| |e02zaf| |OMUnknownCD?| |usingTable?| |curryLeft| |iiacos| - |combineFeatureCompatibility| |trapezoidal| |belong?| |dmp2rfi| - |allRootsOf| |cyclic| |realSolve| |separant| |expextendedint| - |lexTriangular| |univariatePolynomial| |key| |c05nbf| |divideIfCan!| - |child?| |genericPosition| |refine| |matrixConcat3D| |delay| |mapUp!| - |listexp| |nextSubsetGray| |mappingAst| |factorSquareFreeByRecursion| - |brillhartIrreducible?| |gcdcofact| |viewport2D| |noLinearFactor?| - |dominantTerm| |filename| |euler| |realEigenvectors| |accuracyIF| - |constantLeft| |primitive?| |removeSuperfluousQuasiComponents| - |partialNumerators| |type| |d02raf| |multiEuclidean| |quadratic| - |minGbasis| |extendedEuclidean| |LiePolyIfCan| |palgint0| |supersub| - |complexForm| |represents| |parse| |besselI| |cosh2sech| - |tubePointsDefault| |leviCivitaSymbol| |companionBlocks| |cAcsch| - |stoseLastSubResultant| |eigenMatrix| |transform| - |extractSplittingLeaf| |qualifier| |next| |parametersOf| |divisor| - |readIfCan!| |problemPoints| |getOrder| |lllip| |sinIfCan| - |lfintegrate| |lowerCase!| |rewriteSetWithReduction| |graphImage| - |f07fdf| |e04jaf| |string?| |f02awf| |e02def| |iisqrt3| |expintegrate| - |one?| |useEisensteinCriterion| |imports| |checkPrecision| |rational?| - |monicRightDivide| |nil?| |s21bbf| |e01sef| |voidMode| |makeMulti| - |cothIfCan| |singularitiesOf| |algint| |OMgetEndApp| |fmecg| |e01saf| - EQ |nativeModuleExtension| |getProperty| |saturate| |minrank| - |resetVariableOrder| |basisOfCommutingElements| |separate| |cAtanh| - |currentSubProgram| |sqfrFactor| |encodingDirectory| |copy!| - 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|optimize| |infix| |commutativeEquality| - |stoseInternalLastSubResultant| |enterInCache| |probablyZeroDim?| - |computePowers| |seed| |cos2sec| |translate| |bivariateSLPEBR| - |cyclicGroup| |stirling1| |figureUnits| - |createLowComplexityNormalBasis| = |doubleComplex?| |primeFactor| - |groebner?| |principalAncestors| |perfectSqrt| |printInfo!| |print| - |bindings| |getVariableOrder| |cAtan| |c02aff| |supDimElseRittWu?| - |nextItem| |definingPolynomial| |operation| |resolve| |f02aff| - |invertible?| |genericRightTrace| |OMwrite| |rightTraceMatrix| < - |rotate!| |nthCoef| |rk4| |setColumn!| |OMgetVariable| |laguerre| - |readable?| |sinhcosh| |f04faf| > |packageCall| - |reduceBasisAtInfinity| |midpoints| |internalDecompose| - |nextIrreduciblePoly| |fracPart| |ipow| |getConstant| <= |reduced?| - |balancedBinaryTree| |standardBasisOfCyclicSubmodule| |htrigs| - |fglmIfCan| |fullDisplay| |stronglyReduced?| |rootKerSimp| - |signAround| |countable?| >= |composites| |OMencodingUnknown| - 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|e02ahf| |e04mbf| |ScanRoman| |fractRadix| |rootOf| |lighting| - |iilog| |li| |solveLinear| |radicalEigenvectors| |e01bhf| |acoth| - |asimpson| |dual| |completeEval| |pureLex| |numberOfPrimitivePoly| - |assign| |mkcomm| |outputFixed| |maxPoints3D| |groebnerIdeal| |asech| - |scalarTypeOf| |iiabs| |padecf| |implies| |relerror| |coleman| - |e02bcf| |argumentList!| |insertTop!| |d02kef| |lllp| - |decreasePrecision| |createMultiplicationTable| |host| - |exponentialOrder| |reducedSystem| |elaborateFile| |coord| |multiple| - |rewriteIdealWithQuasiMonicGenerators| |mesh?| |SFunction| |input| - |cfirst| |approxSqrt| |primPartElseUnitCanonical| |cCos| - |subQuasiComponent?| |operators| |applyQuote| |box| |blankSeparate| - |augment| |fortranTypeOf| |scripted?| |library| |meatAxe| - |showArrayValues| |stronglyReduce| |iiacoth| |readLine!| - |colorFunction| |tanh2coth| |rewriteIdealWithHeadRemainder| |uniform| - |maxdeg| |semiLastSubResultantEuclidean| |totalGroebner| |Lazard2| - |maximumExponent| |internalInfRittWu?| |antiCommutative?| - |interpretString| |bipolar| |ksec| |ignore?| |bernoulliB| - |setLegalFortranSourceExtensions| |rightGcd| - |createNormalPrimitivePoly| |exprToUPS| |zeroVector| |leadingIdeal| - |s17def| |ruleset| |controlPanel| |completeHermite| |e02dff| - |simplify| |dequeue| |pole?| |leftZero| |f02aef| |expintfldpoly| - |subTriSet?| |irreducibleRepresentation| |OMgetString| |nullSpace| - |set| |closedCurve| |sin2csc| GF2FG |f04jgf| |entries| |wholeRadix| - |attributeData| |leftQuotient| |test| |alphanumeric| |id| - |whatInfinity| |printingInfo?| |sorted?| |reducedDiscriminant| - |setright!| |rightOne| |acoshIfCan| |suchThat| |inverse| |whileLoop| - |f02adf| |mesh| |getPickedPoints| |leftCharacteristicPolynomial| - |radicalEigenvector| |expenseOfEvaluation| |OMputEndObject| - |OMputAttr| |pquo| |readBytes!| |recur| |character?| |complex?| - |squareFreeLexTriangular| |table| |shallowExpand| |seriesToOutputForm| - |arrayStack| |collectUpper| |submod| |duplicates| |subst| - |solveLinearPolynomialEquationByFractions| |insert| |new| - |idealSimplify| |halfExtendedSubResultantGcd1| |pointColorPalette| - |rightDiscriminant| |toroidal| |obj| |alphabetic| - |indiceSubResultantEuclidean| |iiperm| |leadingBasisTerm| |shiftRoots| - |nextPartition| |unvectorise| |eq| |coth2trigh| |makeCrit| |prefix| - |rotatez| |notelem| |cache| |weights| |rangePascalTriangle| |sPol| - |iter| |bubbleSort!| |OMputEndBVar| |asinIfCan| |checkForZero| |iiexp| - |iitan| |lintgcd| |monomRDE| |bitLength| |delete| |trigs| |signature| - |modulus| |dualSignature| |d01apf| |pToDmp| |direction| - |linearDependenceOverZ| |maxIndex| |endOfFile?| |vertConcat| |s17ahf| - |kovacic| |genus| |deriv| |outputBinaryFile| |overlabel| |iiasinh| - |sizeLess?| |nsqfree| |minimumDegree| |linearPolynomials| - |changeWeightLevel| |monomRDEsys| |factorset| |cyclotomic| |reseed| - |objects| |removeCoshSq| |iiatan| |normDeriv2| |rightUnits| - |sturmVariationsOf| |basisOfRightNucloid| 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|unit?| + |OMgetEndApp| |nextSublist| |outerProduct| |bitior| |draw| + |squareFree| |qfactor| |OMgetInteger| |morphism| |iidsum| + |messagePrint| |deref| |solveRetract| |fmecg| |Beta| |expand| + |intensity| |superHeight| |stoseInvertible?reg| |setClipValue| + |rowEchLocal| |elliptic?| |currentEnv| |normalizedAssociate| |e01saf| + |root?| |removeRoughlyRedundantFactorsInPols| |filterWhile| + |fixedDivisor| |f04arf| |invertibleSet| |e02aef| |initTable!| + |multinomial| |fortranCharacter| |findCycle| |findBinding| + |nativeModuleExtension| |filterUntil| |symbol| |internalIntegrate0| + |polygamma| |evaluateInverse| |rename!| |convert| F2FG |simpsono| + |generalizedContinuumHypothesisAssumed| |getProperty| |endSubProgram| + |cSin| |points| |select| |expression| |makeObject| |isobaric?| + |iCompose| |writeInt8!| |untab| |minimumExponent| |e02ahf| |saturate| + |height| |OMReadError?| |decompose| |cCot| |OMclose| |OMputError| + |integer| |coef| |setleft!| |lastSubResultantElseSplit| |shrinkable| + |e04mbf| |listLoops| |constantCoefficientRicDE| |adjoint| + |selectOptimizationRoutines| |minrank| |numFunEvals3D| |makeCos| + |psolve| |oneDimensionalArray| |mergeDifference| |elaborate| + |fortranDoubleComplex| |ScanRoman| |leftRemainder| + |inputOutputBinaryFile| |rightExactQuotient| |resetVariableOrder| + |redPol| |corrPoly| |irVar| |f01mcf| |elem?| ** |fractRadix| + |monomials| |numberOfFractionalTerms| |basisOfCommutingElements| + |slex| |roughSubIdeal?| |getOperands| |rectangularMatrix| + |partialQuotients| |elColumn2!| |rootOf| |tanIfCan| |stoseInvertible?| + |associator| |separate| |iibinom| |internalAugment| |besselY| + |stiffnessAndStabilityFactor| |clikeUniv| |lighting| |conjug| + |separateDegrees| |jordanAdmissible?| |cAtanh| |makeRecord| |power| + |permutationGroup| |lo| |insertBottom!| |complexNumericIfCan| + |certainlySubVariety?| |iilog| |internalSubQuasiComponent?| + |nextColeman| |lazyVariations| |currentSubProgram| |initials| + |wholeRagits| |incr| |acsch| |setErrorBound| |label| |exists?| + |prologue| |solveLinear| |setOrder| |initial| |normalElement| + |sqfrFactor| |nilFactor| |definingInequation| |hasHi| |copyInto!| + |PDESolve| |bivariatePolynomials| |topFortranOutputStack| + |radicalEigenvectors| |lflimitedint| |splitLinear| |encodingDirectory| + |trace2PowMod| |subSet| |coordinates| |acscIfCan| |cycleLength| + |e01bhf| |clearDenominator| |e02ddf| |copy!| |qqq| |diff| + |complexElementary| |generalPosition| |reduceByQuasiMonic| |invmod| + |prepareDecompose| |asimpson| Y |Is| |components| |makeSUP| + |bezoutResultant| |maxrow| |d02bbf| |integralBasisAtInfinity| + |zeroSetSplit| |choosemon| |dual| |phiCoord| |minPoints| |move| + |OMgetApp| |connect| |sub| |nthFlag| |transcendenceDegree| + |completeEval| |pop!| |external?| |derivative| |df2ef| |setProperty| + |OMlistCDs| |tail| |OMencodingXML| |beauzamyBound| |elRow2!| |pureLex| + |OMsupportsCD?| |constructor| |monicModulo| |rules| + |euclideanNormalForm| |hessian| |csch2sinh| |more?| |symmetric?| + |squareFreePrim| |changeBase| |numberOfPrimitivePoly| + |LagrangeInterpolation| |totalDifferential| |realElementary| |nothing| + |roughBasicSet| |dihedral| |dioSolve| |f04qaf| |option| |power!| + |tubeRadius| |iterationVar| |assign| |eyeDistance| |showSummary| + |separateFactors| |numerator| |leastMonomial| |characteristic| + |csubst| |d01anf| |iicsch| |disjunction| |bumptab| |mkcomm| + |nthFractionalTerm| |systemSizeIF| |insertionSort!| |critBonD| + |fixedPointExquo| |f02ajf| |evaluate| |doubleResultant| |OMgetAtp| + |outputFixed| |showAttributes| |factorPolynomial| |sylvesterMatrix| + |lepol| |reducedContinuedFraction| |f01brf| |spherical| |unknown| + |cyclicSubmodule| |d01gaf| |atrapezoidal| |maxPoints3D| |macroExpand| + |clearTheIFTable| |noKaratsuba| |compactFraction| |pToHdmp| + |degreeSubResultantEuclidean| |rightTrim| |subNode?| |positiveSolve| + |escape| |s21bcf| |groebnerIdeal| |fortranLiteralLine| |leftTrim| + |legendre| |monicRightFactorIfCan| |clearTable!| |removeSinhSq| + |listConjugateBases| |minPoints3D| |linkToFortran| |mapBivariate| + |scalarTypeOf| |tanintegrate| |quoted?| |currentCategoryFrame| + |horizConcat| |s20adf| |logGamma| |unknownEndian| |constantIfCan| + |leftDivide| |iiabs| |say| |primintfldpoly| |makeUnit| F + |unrankImproperPartitions1| |f02abf| |dmpToP| |upperBound| |rightUnit| + |rombergo| |pushdown| |padecf| |genericRightMinimalPolynomial| + |integralDerivationMatrix| |s14baf| |iiasec| |selectFiniteRoutines| + |doublyTransitive?| |outputArgs| |factorAndSplit| |gcdPrimitive| + |implies| |An| |jacobiIdentity?| |setAdaptive3D| |df2fi| + |numberOfComponents| |partialDenominators| |viewZoomDefault| + |relerror| |insertMatch| |removeIrreducibleRedundantFactors| |remove| + |function| |multivariate| |numberOfIrreduciblePoly| |primlimitedint| + |oddlambert| |localAbs| |prod| |fortran| |OMsetEncoding| |variables| + |optional?| |OMputVariable| |wordInGenerators| |coleman| |result| + |s21bdf| |nextPrimitivePoly| |d01amf| |reciprocalPolynomial| + |startPolynomial| |integral?| |hconcat| |open| |reorder| |generators| + |last| |e02bcf| |eval| |reset| |dmpToHdmp| |lieAlgebra?| |totalLex| + |prinshINFO| |KrullNumber| |assoc| |even?| |clearTheFTable| |null| + |discriminantEuclidean| |column| |argumentList!| |xCoord| + |simplifyPower| |fullPartialFraction| |primintegrate| |lazyIntegrate| + |critB| |quasiRegular| |pattern| |not| |factorSFBRlcUnit| |baseRDEsys| + |insertTop!| |write| |ricDsolve| |rst| |polygon?| + |generalizedEigenvectors| |d01aqf| |pseudoQuotient| |torsion?| |and| + |isList| |primitivePart| |d02kef| |save| |credPol| |deepestTail| + |cyclicParents| |leadingTerm| |negative?| |operations| + |complementaryBasis| |solveid| |or| |setPredicates| |zoom| |taylor| + |lllp| |lifting| |cycleRagits| |style| |d02gaf| |f01qdf| |jacobian| + |viewpoint| |xor| |expandTrigProducts| |decreasePrecision| |laurent| + |low| |preprocess| |pointLists| |s18aff| |innerint| |e02daf| |message| + |lazyResidueClass| |closedCurve?| |case| |createMultiplicationTable| + |puiseux| |leftRegularRepresentation| |f04mbf| |OMputFloat| + |getBadValues| |initiallyReduced?| |bitTruth| |normFactors| + |degreeSubResultant| |Zero| |host| |hypergeometric0F1| + |removeRoughlyRedundantFactorsInContents| |shade| |hi| |monicDivide| + |iicot| |setAttributeButtonStep| |measure2Result| |One| + |exponentialOrder| |inv| |copies| |imagj| |extendedIntegrate| + |OMopenFile| |initiallyReduce| |variationOfParameters| |binaryTree| + |trigs2explogs| |ground?| |reducedSystem| |rightRemainder| |ref| + |inverseLaplace| |createRandomElement| |multisect| |collect| + |elaborateFile| |legendreP| |rroot| |ground| |lcm| |lookupFunction| + |mapUnivariate| |setRow!| |inverseColeman| |bottom!| + |trailingCoefficient| |edf2ef| |var1StepsDefault| |coord| + |leadingMonomial| |variable?| |leaf?| |in?| |pointData| |groebgen| + |append| |selectPDERoutines| |leadingCoefficient| + |rewriteIdealWithQuasiMonicGenerators| |resultantReduit| |delay| + |charClass| |LyndonWordsList1| |nonLinearPart| |primitiveMonomials| + |interReduce| |gcd| |constDsolve| |multiplyExponents| |elt| |output| + |mesh?| |mapUp!| |compound?| |rationalPoints| |leftTraceMatrix| + |safetyMargin| |eigenvector| |squareMatrix| |SFunction| + |hasPredicate?| |contours| |false| |reductum| |times!| |listexp| + |push| |rowEchelonLocal| |startTable!| RF2UTS |cfirst| + |reducedQPowers| |nextSubsetGray| |primeFrobenius| + |removeRoughlyRedundantFactorsInPol| |edf2efi| + |getMultiplicationMatrix| |mappingMode| |tableau| |approxSqrt| + |mappingAst| |unaryFunction| |ParCondList| |partition| |gcdcofactprim| + |indicialEquations| |meshPar2Var| |f01qcf| |primPartElseUnitCanonical| + |d01alf| |factorSquareFreeByRecursion| |swap| |headRemainder| + |ratPoly| |thetaCoord| |HermiteIntegrate| |s19aaf| |cCos| + |brillhartIrreducible?| |fractRagits| |adaptive| |moduloP| + |numberOfComputedEntries| |hostPlatform| |subQuasiComponent?| + |gcdcofact| |graphCurves| |magnitude| |showRegion| |cAsec| + |viewDefaults| |semiResultantEuclidean2| |mainForm| |operators| + |categories| |exprHasAlgebraicWeight| |viewport2D| + |parabolicCylindrical| |ranges| |fortranCarriageReturn| |sechIfCan| + |applyRules| |tanQ| |blankSeparate| |noLinearFactor?| + |OMconnOutDevice| |cAcosh| |isPlus| |unravel| |splitSquarefree| |odd?| + |selectfirst| |palgRDE0| |dominantTerm| |OMputApp| |ceiling| + |computeInt| |f02bbf| |externalList| |open?| |infieldint| |euler| + |lagrange| |resetAttributeButtons| |normal01| |genericLeftTraceForm| + |cTanh| |balancedFactorisation| |finite?| |removeSinSq| |build| + |realEigenvectors| |Nul| |f04maf| |plusInfinity| |coefficient| + |partialFraction| |meshFun2Var| |OMencodingBinary| |s17aef| + |accuracyIF| |fillPascalTriangle| |range| |row| |minusInfinity| |inf| + |OMconnInDevice| |cosIfCan| |addiag| |constantLeft| + |nextsousResultant2| |isAtom| |BumInSepFFE| |irreducibleFactor| + |iiacsc| |basis| |exponential| |equiv| |primitive?| |bivariate?| + |distribute| |romberg| |cot2trig| |Ei| |fixPredicate| |key| + |drawStyle| |algebraicDecompose| |absolutelyIrreducible?| + |removeSuperfluousQuasiComponents| |createLowComplexityTable| |aCubic| + |lfunc| |functorData| |denomRicDE| |diagonalProduct| |commutative?| + |partialNumerators| |invertIfCan| |logIfCan| |basicSet| + |alphanumeric?| |filename| |mainCoefficients| |irDef| |printStats!| + |bytes| |innerEigenvectors| |d02raf| |subResultantGcd| |shiftRight| + |permutation| |type| |zeroOf| |mat| |cTan| |iitanh| |multiEuclidean| + |symmetricGroup| |listOfMonoms| |algebraic?| |makeTerm| + |multiEuclideanTree| |stoseIntegralLastSubResultant| + |genericRightTraceForm| |parse| |tensorProduct| |minRowIndex| + |quadratic| |moduleSum| |viewThetaDefault| |lyndon?| |nary?| + |makeprod| |unexpand| |next| |printStatement| |minGbasis| + |shallowCopy| |gramschmidt| |lastSubResultant| |leftScalarTimes!| + |linearAssociatedLog| |algintegrate| |Vectorise| |heap| + |extendedEuclidean| |fractionFreeGauss!| |flexibleArray| + |UpTriBddDenomInv| |leftTrace| |e04ycf| |myDegree| |s18dcf| + |lfextlimint| |index?| |rowEch| |quasiAlgebraicSet| |LiePolyIfCan| + |checkPrecision| |OMunhandledSymbol| |quoByVar| |unitNormalize| + |bitCoef| |gcdPolynomial| |rationalFunction| |associatedEquations| + |numerators| |palgint0| |cyclicEntries| |overset?| EQ + |derivationCoordinates| |unit| |palgLODE| |setMaxPoints| + |musserTrials| |pmComplexintegrate| |supersub| |symbol?| + |triangularSystems| |parabolic| |showAll?| |internalZeroSetSplit| + |lhs| |less?| |hermiteH| |hdmpToDmp| |complexForm| |finiteBasis| + |dimensionsOf| |addPoint2| |rootSplit| |generalizedInverse| |indices| + |rhs| |basisOfRightNucleus| |represents| |fortranComplex| |e01bff| + |evenInfiniteProduct| |factorByRecursion| |constantRight| |weight| + |curve| |selectAndPolynomials| |ddFact| |besselI| |c06ecf| |s19abf| + |iiasin| |principal?| |read!| |Ci| |mapDown!| |badValues| |cosh2sech| + |iroot| |iiacosh| |getProperties| |rule| |mapmult| |nodes| |csc2sin| + |orbit| |children| |tubePointsDefault| |ef2edf| |createThreeSpace| + |kmax| |setPosition| |compose| |index| |internalLastSubResultant| + |pushuconst| |leviCivitaSymbol| |complexRoots| |e01sff| + |karatsubaDivide| |selectODEIVPRoutines| |extractIndex| + |nextNormalPrimitivePoly| |schema| |ScanFloatIgnoreSpaces| + |representationType| |companionBlocks| |SturmHabichtCoefficients| + |setTex!| |totalfract| |enumerate| |center| |biRank| + |nextLatticePermutation| |indicialEquationAtInfinity| |complexExpand| + |cAcsch| |flagFactor| |generalLambert| |recoverAfterFail| |has?| + |OMputEndAttr| |putColorInfo| |pair| |stoseInvertibleSet| |inspect| + |rk4qc| |stoseLastSubResultant| |c06frf| |value| |modularGcdPrimitive| + |comparison| |trueEqual| |totalDegree| |OMputObject| + |selectPolynomials| |eigenMatrix| |approxNthRoot| |lazyPseudoDivide| + |mapExponents| |strongGenerators| |alternative?| |s17agf| + |semiDiscriminantEuclidean| |transform| |whitePoint| |OMputEndBind| + |characteristicSet| |infiniteProduct| |OMputInteger| |e04naf| + |member?| |createGenericMatrix| |rational| |extractSplittingLeaf| + |max| |stoseInvertible?sqfreg| |entry| |generateIrredPoly| + |removeSuperfluousCases| |pow| |hitherPlane| |child| |setlast!| + |qualifier| |localUnquote| |bigEndian| |iipow| |iicosh| |polyRicDE| + |possiblyInfinite?| |raisePolynomial| |prefixRagits| |parametersOf| + |toseInvertible?| |printHeader| |elliptic| |setFieldInfo| + |currentScope| |returnTypeOf| |realZeros| |divisor| |sign| |s14aaf| + |printTypes| |useSingleFactorBound?| |rightDivide| |stFunc1| + |viewWriteDefault| |ratDenom| |sn| |clipParametric| |palginfieldint| + |readIfCan!| |reverse| |mindegTerm| |useEisensteinCriterion?| + |limitedIntegrate| |binding| |idealiser| |e04ucf| |problemPoints| + |makeResult| |critMTonD1| |cSinh| |replaceKthElement| |extractTop!| + |leftExtendedGcd| |call| |satisfy?| |pushNewContour| |central?| + |getOrder| |OMgetBVar| |areEquivalent?| |bumptab1| |leaves| |tree| + |superscript| |heapSort| |univariatePolynomials| |mkAnswer| |lllip| + |showAllElements| |cCsc| |numberOfMonomials| |setref| |lazyPrem| + |numericIfCan| |readLineIfCan!| |randomLC| |lazyEvaluate| |sinIfCan| + |f02bjf| |s18aef| |subResultantsChain| |structuralConstants| + |getButtonValue| |geometric| |exteriorDifferential| |lfintegrate| + |cycleTail| |OMputSymbol| |showScalarValues| |imagE| |algSplitSimple| + |OMUnknownSymbol?| |normInvertible?| |init| |mainMonomial| + |primlimintfrac| |lowerCase!| |exp1| |resultantReduitEuclidean| + |extendedResultant| |quatern| |removeConstantTerm| |imagK| |cAcot| + |nlde| |rewriteSetWithReduction| |nullary| |extendIfCan| |repeating| + |chebyshevU| |lookup| |setScreenResolution3D| |explicitEntries?| + |lieAdmissible?| |graphImage| |setRealSteps| |key?| |bandedHessian| + |generator| |bezoutMatrix| |laplace| |eulerE| |f07fdf| |cyclic?| + |bits| |reverse!| |hostByteOrder| |bfEntry| |numberOfNormalPoly| + |c06eaf| |rootOfIrreduciblePoly| |e04jaf| |component| |setchildren!| + |replace| |fixedPoint| |monicLeftDivide| |mindeg| |search| |zCoord| + |string?| |root| |iteratedInitials| |exprex| |randomR| |OMgetEndAtp| + |stack| |bombieriNorm| |f02awf| |determinant| |rem| |cycle| |getRef| + |continuedFraction| |roughBase?| |divideExponents| |curveColorPalette| + |e02def| |lprop| |singRicDE| |quo| |semiResultantReduitEuclidean| + |putProperty| |startStats!| |internalIntegrate| |condition| |iisqrt3| + |univariatePolynomialsGcds| |useSingleFactorBound| |roughUnitIdeal?| + |taylorRep| |OMsupportsSymbol?| |setPrologue!| + |getSyntaxFormsFromFile| |div| |routines| |symmetricDifference| + |minimalPolynomial| |OMgetObject| |sturmSequence| |cAcos| + |monomialIntegrate| |tan2cot| |nthRootIfCan| |exquo| + |solveLinearlyOverQ| |dim| |showIntensityFunctions| |bringDown| + |quasiRegular?| |lifting1| |c06gsf| |point?| |doubleRank| + |genericLeftDiscriminant| ~= |rightScalarTimes!| + |tryFunctionalDecomposition?| |frst| |setFormula!| |newLine| |tab| + |lastSubResultantEuclidean| |resize| |#| |matrix| |cycles| |dec| + |Gamma| |bsolve| |fintegrate| |byteBuffer| ~ |traverse| + |firstUncouplingMatrix| |updateStatus!| |sech2cosh| |concat| + |upperCase?| |acschIfCan| |fractionPart| |regularRepresentation| + |readInt8!| |mapCoef| |OMsend| |removeRedundantFactors| |wreath| + |difference| |getOperator| |mvar| |subPolSet?| |printInfo| |nullity| + |presuper| |interpolate| |clearCache| |infRittWu?| |s17dhf| + |diophantineSystem| |level| |minPoly| |pushdterm| |OMputString| + |scalarMatrix| |realRoots| |nextPrime| |basisOfNucleus| |hermite| + |ran| |iisin| |revert| |toScale| |hexDigit| |zeroSquareMatrix| + |mightHaveRoots| |intPatternMatch| |substring?| |pointPlot| + |divisorCascade| |minordet| |equality| |char| |matrixDimensions| + |failed| |primitivePart!| |f02akf| |conjugate| |schwerpunkt| |plot| + |acosIfCan| |linearPart| |rightLcm| |perspective| |parametric?| + |suffix?| |iiasech| |closed| |isPower| + |unprotectedRemoveRedundantFactors| |checkRur| |imagi| |setleaves!| + |cyclicEqual?| |chiSquare| |paren| UTS2UP |leftRankPolynomial| + |appendPoint| |compile| |cyclePartition| |tanSum| |divisors| |prefix?| + |status| |cotIfCan| |factor1| |resetNew| |symmetricProduct| + |createNormalElement| |particularSolution| |commutator| |tanNa| + |solve| |outputAsTex| |pseudoDivide| |isEquiv| |bit?| |setEmpty!| + |algDsolve| |froot| |modulus| |second| |setStatus!| |dictionary| + |moebius| |erf| |symFunc| |float| |complete| |stFunc2| + |increasePrecision| |stFuncN| |dualSignature| |third| |digit| + |euclideanSize| |showTheRoutinesTable| |maxint| + |cyclotomicDecomposition| |OMconnectTCP| |nullary?| |qinterval| + |d01apf| |exponents| |ip4Address| |changeVar| |symmetricPower| |void| + |nextsubResultant2| |purelyAlgebraic?| |number?| |hspace| |pToDmp| + |completeEchelonBasis| |errorKind| |check| |dilog| |birth| |droot| + |gcdprim| |cLog| |infLex?| |infix?| |direction| + |solveLinearPolynomialEquation| |mapdiv| |monicDecomposeIfCan| |sin| + |signatureAst| |mask| |c06fqf| |OMputEndApp| |coerceL| + |upDateBranches| |linearDependenceOverZ| |genericRightNorm| + |changeNameToObjf| |goodnessOfFit| |cos| |region| |minset| |diagonal?| + |gensym| |factorSquareFree| |maxIndex| |categoryFrame| |zeroDimPrime?| + |insert!| |expr| |palgextint0| |tan| |RittWuCompare| + |internalSubPolSet?| |BasicMethod| |mainValue| |endOfFile?| |addmod| + |setelt!| |mainDefiningPolynomial| |s19acf| |cot| |getIdentifier| + |consnewpol| |bipolarCylindrical| |integers| |vertConcat| |cAcoth| + |innerSolve| |coerceImages| |eq?| |sec| GE |pdf2ef| |f04adf| + |algebraicCoefficients?| |double| |coth2tanh| |s17ahf| |space| + |normalForm| |coerceS| |lexGroebner| |csc| |log| GT + |noncommutativeJordanAlgebra?| |irreducibleFactors| |iiatanh| |opeval| + |kovacic| |PollardSmallFactor| |variable| |weighted| |mainVariable| + |integralRepresents| |asin| LE |conical| + |solveLinearPolynomialEquationByRecursion| |c02agf| |setTopPredicate| + |genus| |inverseIntegralMatrixAtInfinity| |possiblyNewVariety?| + |iterators| BY |zeroSetSplitIntoTriangularSystems| |d01gbf| |acos| LT + |extendedint| |removeRedundantFactorsInContents| |s01eaf| |nthRoot| + |deriv| |gradient| |showFortranOutputStack| |minus!| + |bezoutDiscriminant| |atan| |generalizedEigenvector| |totolex| + |monomialIntPoly| |mainContent| |outputBinaryFile| |omError| |const| + |llprop| |makeop| |acot| |diagonalMatrix| |quartic| |cCosh| + |enterPointData| |overlabel| |rotatex| |leftNorm| |taylorQuoByVar| + |nthExponent| |asec| |rationalApproximation| |rightRankPolynomial| + |ord| |reopen!| |iiasinh| |every?| |vspace| |inGroundField?| + |putGraph| |acsc| |environment| |d02cjf| |numberOfChildren| + |asecIfCan| |declare!| |sizeLess?| |characteristicSerie| |returns| + |plenaryPower| |generic?| |sinh| |rdregime| |df2st| |leftFactorIfCan| + |fortranDouble| |addBadValue| |nsqfree| |f01rcf| |writable?| + |branchIfCan| |stopTableInvSet!| |cosh| |exprToGenUPS| + |physicalLength| |LazardQuotient2| |merge| |firstDenom| NOT + |minimumDegree| |Aleph| |symmetricSquare| |baseRDE| |listBranches| + |tanh| |d02ejf| |OMread| |trapezoidalo| |removeSquaresIfCan| OR + |linearPolynomials| |rightFactorIfCan| |f01maf| |postfix| |zero?| + |coth| |e02gaf| |e02zaf| |listYoungTableaus| |defineProperty| AND + |changeWeightLevel| |makeFloatFunction| |f04mcf| |maxRowIndex| + |tableForDiscreteLogarithm| |leftRank| |OMUnknownCD?| |evenlambert| + |ScanArabic| |keys| |monomRDEsys| |distance| |maxPoints| |head| + |depth| |increment| |fortranReal| |usingTable?| |setLength!| |norm| + |factorset| |factors| |tracePowMod| |drawComplexVectorField| |block| + |curryLeft| |quotientByP| |lex| |debug| |rename| |segment| |parents| + |cyclotomic| |OMmakeConn| |inRadical?| |divideIfCan| |hdmpToP| + |iiacos| |integralAtInfinity?| D |integralMatrixAtInfinity| |f07fef| + |reseed| |associates?| |OMbindTCP| |startTableGcd!| |basisOfCentroid| + |combineFeatureCompatibility| |cSech| |innerSolve1| + |fortranLinkerArgs| |removeCoshSq| |setMinPoints| |complexZeros| + |critM| |bandedJacobian| |complexLimit| |trapezoidal| + |squareFreePolynomial| |wrregime| |iiatan| |dflist| |mainKernel| + |cSec| |createPrimitivePoly| |GospersMethod| |belong?| |color| + |create3Space| |normDeriv2| |rarrow| |basisOfLeftAnnihilator| + |lazyIrreducibleFactors| |oddintegers| |quote| |dmp2rfi| |updatF| + |viewDeltaYDefault| |rightUnits| |dark| |insertRoot!| |mpsode| + |polCase| |parts| |symmetricRemainder| |allRootsOf| |setValue!| * + |linearlyDependentOverZ?| |sturmVariationsOf| |SturmHabicht| + |exprHasLogarithmicWeights| |OMopenString| |rationalPower| |cyclic| + |thenBranch| |jokerMode| |exptMod| |basisOfRightNucloid| |flexible?| + |prolateSpheroidal| |universe| |f02xef| |properties| |optimize| + |vconcat| |realSolve| |solveInField| |OMreceive| |adaptive3D?| |curry| + |domainTemplate| |pr2dmp| |setVariableOrder| |translate| |separant| + |setMaxPoints3D| |iicos| |btwFact| |modularGcd| = |eof?| + |setImagSteps| |slash| |polar| |expextendedint| |e01bef| |print| + |rischNormalize| |mainVariables| |se2rfi| |acotIfCan| |getStream| + |intersect| |extractBottom!| |outputMeasure| |normal?| |resolve| + |lexTriangular| |operation| |s21baf| |rightTrace| < |cAcsc| + |lyndonIfCan| |getMatch| |rootSimp| |ramified?| |univariatePolynomial| + |lfextendedint| |firstNumer| |computeBasis| > + |semiDegreeSubResultantEuclidean| |normalDeriv| |OMputBind| |solid?| + |argument| |c05nbf| |generalizedContinuumHypothesisAssumed?| + |outputAsScript| |ramifiedAtInfinity?| <= |screenResolution| + |distdfact| |monic?| |normalize| |divideIfCan!| |minPol| |unitNormal| + |extractClosed| |coefChoose| >= |d01ajf| |removeCosSq| |ldf2vmf| + |explicitlyFinite?| |drawToScale| |completeHensel| |child?| |interval| + |powern| |associatorDependence| |isOpen?| |groebnerFactorize| |recip| + |squareFreeFactors| |genericPosition| |radicalSolve| |OMreadFile| + |scan| |tRange| |contains?| |OMgetEndObject| |atom?| |polygon| + |interpret| |intermediateResultsIF| |refine| |readInt32!| |lazyPquo| + + |pointColorDefault| |e04dgf| |elaboration| |leftFactor| |branchPoint?| + |true| |matrixConcat3D| |triangSolve| |floor| |rur| |any?| - |cn| + |numFunEvals| |cardinality| |UnVectorise| |ScanFloatIgnoreSpacesIfCan| + |chineseRemainder| |linearlyDependent?| |mantissa| + |selectOrPolynomials| / |regime| |trivialIdeal?| |ode2| |reduction| + |d02gbf| |inrootof| |coerceListOfPairs| |identityMatrix| |Frobenius| + |zag| |upperCase| |s15adf| |radicalEigenvalues| |light| |category| + |just| |drawComplex| |roughEqualIdeals?| |cyclotomicFactorization| + |nil| |rewriteIdealWithRemainder| |linearDependence| |removeZeroes| + |transcendentalDecompose| |cross| |factorsOfDegree| |domain| + |expressIdealMember| |SturmHabichtMultiple| |diagonal| |empty| + |atanIfCan| |RemainderList| |OMserve| |package| |exponent| + |splitNodeOf!| |perfectSquare?| |graphs| |OMgetEndAttr| |someBasis| + |inconsistent?| |elseBranch| |red| |shift| |leadingExponent| + |ellipticCylindrical| |polyred| |integral| |changeMeasure| + |approximate| |redmat| |fortranInteger| |s17acf| |varselect| + |mapExpon| |conditionP| |OMgetSymbol| |cosSinInfo| |complex| + |coercePreimagesImages| |listOfLists| |basisOfLeftNucleus| |varList| + |ffactor| |powmod| |deepCopy| |rk4f| |ParCond| |purelyTranscendental?| + |highCommonTerms| |argumentListOf| |pmintegrate| |delta| |overbar| + |show| |mdeg| |irreducible?| |newSubProgram| |setEpilogue!| + |vectorise| |property| |sumOfKthPowerDivisors| |bothWays| |real?| + UP2UTS |radPoly| |quadratic?| |relativeApprox| |padicallyExpand| + |setrest!| |irCtor| |completeSmith| |componentUpperBound| + |exactQuotient!| |trace| |factorial| |normalizedDivide| + |integralLastSubResultant| |midpoint| |remove!| |elementary| + |basisOfRightAnnihilator| |c05adf| |retract| |toseSquareFreePart| + |leader| |cAsin| |intcompBasis| |closeComponent| |bracket| |units| + |semiSubResultantGcdEuclidean2| |capacity| |typeForm| |dAndcExp| + |removeDuplicates!| |extendedSubResultantGcd| |scale| |graphState| + |transcendent?| |LiePoly| |lambert| |simpson| |getZechTable| |surface| + |subResultantChain| |cycleSplit!| |mainExpression| |quickSort| + |sylvesterSequence| |processTemplate| |groebSolve| |mainMonomials| + |getCode| |idealiserMatrix| |formula| |wholePart| |homogeneous?| + |transpose| |listRepresentation| |getGraph| |tablePow| |mulmod| + |expPot| |lambda| |Si| |tanh2trigh| |noValueMode| |sup| |log2| + |charthRoot| |iisinh| |rightRegularRepresentation| + |reducedDiscriminant| |select!| |rootProduct| |monicCompleteDecompose| + |mkIntegral| |OMgetError| |code| |pushup| |radicalSimplify| |c06gcf| + |e02bef| |setright!| |sncndn| |prindINFO| |product| |lowerCase| + |autoReduced?| |perfectNthPower?| |extractIfCan| |xn| |e02baf| + |rightOne| |complement| |newReduc| |leadingIndex| |nrows| + |discreteLog| |alternatingGroup| |datalist| |identification| + |modifyPoint| |s19adf| |axes| |acoshIfCan| |jacobi| |meshPar1Var| + |swapRows!| |ncols| |computeCycleEntry| |yCoord| + |functionIsFracPolynomial?| |lyndon| |degreePartition| |makeSeries| + |inverse| |plus| |isTimes| |hasSolution?| |commaSeparate| |option?| + |createPrimitiveNormalPoly| |createNormalPoly| |OMlistSymbols| + |patternVariable| |rdHack1| |whileLoop| |list?| |returnType!| |tube| + |fTable| |setsubMatrix!| |rootPower| |dom| |makingStats?| + |changeThreshhold| |addPoint| |f02adf| |functionIsOscillatory| |imagk| + |dn| |quadraticForm| |members| |sum| |numberOfHues| |mapMatrixIfCan| + |mix| |prevPrime| |mesh| |polynomial| |socf2socdf| + |removeRedundantFactorsInPols| |pdf2df| |extractProperty| |point| + |concat!| |neglist| |s13acf| |ocf2ocdf| |enqueue!| |getPickedPoints| + |times| |degree| |d01fcf| |resultantEuclidean| |readUInt16!| + |directSum| |alphabetic?| |clearFortranOutputStack| |rubiksGroup| + |countRealRoots| |symbolTable| |leftCharacteristicPolynomial| + |linears| |s13aaf| |high| |truncate| |isConnected?| + |wordsForStrongGenerators| |rightZero| |inHallBasis?| |top| + |rightMult| |aLinear| |nthFactor| |B1solve| |radicalEigenvector| |lp| + |fprindINFO| |systemCommand| |pointSizeDefault| |decomposeFunc| + |antisymmetric?| |squareFreePart| |series| |generalInfiniteProduct| + |pushFortranOutputStack| |prinpolINFO| |connectTo| |laguerreL| + |OMgetAttr| |resultantnaif| |title| |expenseOfEvaluation| |comp| + |numberOfOperations| |splitConstant| |s17dgf| |ode| + |antisymmetricTensors| |setfirst!| |popFortranOutputStack| |makeEq| + |prem| |drawCurves| |fortranLiteral| |c05pbf| |OMputEndObject| |node| + |monom| |normalizeAtInfinity| |options| |find| |argscript| + |deepExpand| |c06fuf| |continue| |firstSubsetGray| |sort| + |incrementKthElement| |FormatArabic| |discriminant| |outputAsFortran| + |subresultantVector| |OMputAttr| |normal| |minColIndex| + |palgintegrate| |subCase?| |f02aaf| |infix| |e| |lazyPseudoQuotient| + |dihedralGroup| |jordanAlgebra?| |f07aef| |pquo| + |nextPrimitiveNormalPoly| |LyndonWordsList| |hMonic| |OMputEndError| + |commutativeEquality| |min| |list| |atanhIfCan| |numberOfVariables| + |rightExtendedGcd| |generalTwoFactor| |readBytes!| |common| + |writeBytes!| |string| |wordInStrongGenerators| |airyBi| |palglimint| + |stoseInternalLastSubResultant| |car| |constantKernel| |d03edf| + |extractPoint| |commonDenominator| |recur| |basisOfLeftNucloid| + |primes| |upperCase!| |e01daf| |enterInCache| |random| |cdr| + |genericLeftTrace| |twoFactor| |binomThmExpt| |nthr| |character?| + |c06gbf| |crushedSet| |terms| |probablyZeroDim?| |symbolTableOf| + |setDifference| |linSolve| |getExplanations| |yCoordinates| + |startTableInvSet!| |complex?| |brillhartTrials| |pade| |addMatch| + |powerSum| |computePowers| |setIntersection| |binary| + |fortranCompilerName| |binaryFunction| |s17dcf| + |squareFreeLexTriangular| |medialSet| |empty?| |laurentIfCan| |d03eef| + |seed| |setUnion| |showTheIFTable| |multiple?| |over| |mirror| + |shallowExpand| FG2F |modTree| |definingEquations| |validExponential| + |cos2sec| |apply| |pomopo!| |resultant| |f2df| |doubleDisc| + |seriesToOutputForm| |forLoop| |eigenvectors| |quotient| + |bivariateSLPEBR| |stopTable!| |goto| |shiftLeft| |leftUnit| |s13adf| + |arrayStack| |zero| |oblateSpheroidal| |binarySearchTree| + |leftExactQuotient| |addMatchRestricted| |cyclicGroup| |size| + |infieldIntegrate| |coefficients| |reverseLex| |back| |collectUpper| + |numeric| |stirling1| |iiacsch| |purelyAlgebraicLeadingMonomial?| + |loopPoints| |width| |tValues| |dimensionOfIrreducibleRepresentation| + |normalDenom| |part?| |sec2cos| |submod| |radical| |And| + |computeCycleLength| |sortConstraints| |leastAffineMultiple| + |ReduceOrder| |figureUnits| |equation| |hexDigit?| |hclf| |precision| + |uniform01| |semiResultantEuclidean1| |vector| |duplicates| |Or| + |normalizeIfCan| |outputSpacing| |invmultisect| + |createLowComplexityNormalBasis| |null?| |makeSketch| |first| |solid| + |complexEigenvectors| |po| |differentiate| + |solveLinearPolynomialEquationByFractions| |Not| + |constantToUnaryFunction| |stopTableGcd!| |userOrdered?| + |doubleComplex?| |complexIntegrate| |rest| |prinb| |iExquo| |optpair| + |rootDirectory| |limitedint| |idealSimplify| |toseLastSubResultant| + |youngGroup| |headReduce| |primeFactor| |lineColorDefault| + |substitute| |doubleFloatFormat| |viewWriteAvailable| |tubePoints| + |f04atf| |infinite?| |halfExtendedSubResultantGcd1| |iiacot| + |factorGroebnerBasis| |seriesSolve| |acothIfCan| |groebner?| |hash| + |removeDuplicates| |readInt16!| |elRow1!| |fi2df| |mapGen| + |pointColorPalette| |principalAncestors| |perfectNthRoot| + |expenseOfEvaluationIF| |showClipRegion| |count| |repeating?| + |nonSingularModel| |s17aff| |queue| |hyperelliptic| |mr| + |rightDiscriminant| |setprevious!| |sequence| |restorePrecision| + |super| |readUInt32!| |perfectSqrt| |name| |optional| + |semiSubResultantGcdEuclidean1| |sinh2csch| |charpol| + |isAbsolutelyIrreducible?| |toroidal| |callForm?| |writeUInt8!| + |LowTriBddDenomInv| |lift| |body| |lazyPremWithDefault| |printInfo!| + |clipWithRanges| |karatsubaOnce| |cap| |lowerPolynomial| |alphabetic| + |inc| |constantOperator| |bindings| |permanent| |LyndonBasis| + |cot2tan| |reduce| |colorDef| |fill!| |semiResultantEuclideannaif| + |divergence| |orbits| |indiceSubResultantEuclidean| |setProperties| + |typeList| |toseInvertibleSet| |taylorIfCan| |getVariableOrder| + |makeViewport3D| |minimize| |airyAi| |f02fjf| |mathieu24| |iiperm| + |d02bhf| |leftPower| |OMreadStr| |vedf2vef| |cAtan| |resetBadValues| + |henselFact| |numberOfComposites| |graphStates| |leadingBasisTerm| + |imagI| |numericalIntegration| |indiceSubResultant| |c02aff| + |principalIdeal| |singular?| |generic| |safeCeiling| |removeZero| + |shiftRoots| |sdf2lst| |safeFloor| |s15aef| |iiGamma| + |supDimElseRittWu?| |f02agf| |typeLists| |movedPoints| |push!| SEGMENT + |error| |nextPartition| |distFact| |coHeight| |viewDeltaXDefault| + |port| |getDatabase| |nextItem| |ratpart| |any| |testModulus| + |topPredicate| |zeroDim?| LODO2FUN |assert| |unvectorise| |tower| + |bag| |makeFR| |antiAssociative?| |definingPolynomial| |zerosOf| + |create| |iomode| |round| |coth2trigh| |prime| |position!| |lexico| + |OMgetEndBVar| |f02aff| |t| |factorials| |quasiMonicPolynomials| + |exprToXXP| |besselJ| |makeCrit| |pdct| |halfExtendedResultant2| + |addPointLast| |identity| |invertible?| |antiCommutator| + |loadNativeModule| |content| |numberOfFactors| |lowerBound| |rotatez| + |gethi| |cup| |weierstrass| |genericRightTrace| |e02ajf| |e02adf| + |cycleEntry| |notelem| |palgint| |sumOfSquares| |e02bbf| |rightRank| + |OMwrite| |f04faf| |square?| |constant| |characteristicPolynomial| + |semicolonSeparate| |weights| |UP2ifCan| |complexNumeric| |irForm| + |palgRDE| |univcase| |rightTraceMatrix| |critMonD1| |att2Result| + |packageCall| |dfRange| |f01rdf| |rangePascalTriangle| |byte| + |recolor| |integralCoordinates| |predicate| |squareTop| + |numberOfCycles| |explogs2trigs| |rotate!| |reduceBasisAtInfinity| + |secIfCan| |headAst| |denomLODE| |sPol| |kernels| |nthExpon| |nthCoef| + |getCurve| |randnum| |midpoints| |subscriptedVariables| |backOldPos| + |element?| |bubbleSort!| |d01akf| |operator| |contract| |cons| |rk4| + |lquo| |internalDecompose| |newTypeLists| |pack!| |compiledFunction| + |OMputEndBVar| |algebraicVariables| |branchPointAtInfinity?| + |partitions| |setColumn!| |iicoth| |rischDE| |step| + |nextIrreduciblePoly| |unparse| |logpart| |errorInfo| |asinIfCan| + |univariate| |positive?| |setnext!| |integralBasis| |palgLODE0| + |OMgetVariable| |setvalue!| |fracPart| |mainVariable?| |comment| + |checkForZero| |qelt| |zeroDimPrimary?| |reflect| |s17akf| |laguerre| + |resultantEuclideannaif| |ipow| |s20acf| |isImplies| |integrate| + |qsetelt| |iiexp| |Lazard| |approximants| |swap!| |readable?| |s14abf| + |linear| |knownInfBasis| |getConstant| |factorList| |OMgetEndBind| + |coerce| |iitan| |xRange| |uncouplingMatrices| |factor| + |skewSFunction| |cubic| |FormatRoman| |sinhcosh| |int| |rootNormalize| + |internal?| |reduced?| |quasiMonic?| |construct| + |differentialVariables| |lintgcd| |yRange| |plus!| |sqrt| + |LyndonCoordinates| |source| |graeffe| |balancedBinaryTree| + |clipBoolean| |anticoord| |sample| |parameters| |zRange| |monomRDE| + |readByte!| |real| |leastPower| |curryRight| |iisech| |symbolIfCan| + |retractable?| |genericRightDiscriminant| + |standardBasisOfCyclicSubmodule| |f01bsf| |poisson| |map!| |bitLength| + |yellow| |imag| |sumSquares| |OMgetType| |pile| |SturmHabichtSequence| + |write!| |extension| |htrigs| |getMeasure| |length| |qsetelt!| |trigs| + |directProduct| |tubePlot| |f02wef| |stoseInvertibleSetsqfreg| + |integralMatrix| |subspace| |makeSin| |fglmIfCan| |rightQuotient| + |unitVector| |scripts| |laplacian| |pleskenSplit| |mainPrimitivePart| + |littleEndian| |mapSolve| |fullDisplay| |plotPolar| |leftAlternative?| + |makeGraphImage| |augment| |numberOfDivisors| |brace| + |subResultantGcdEuclidean| |mathieu22| |target| |ptree| |getlo| + |digits| |simplifyExp| |stronglyReduced?| |powers| |viewPhiDefault| + |fortranTypeOf| |lfinfieldint| |s18def| |destruct| |polyRDE| + |binomial| |coerceP| |remainder| |rootKerSimp| |selectsecond| + |palgextint| |redpps| |scripted?| |repSq| |positiveRemainder| |c06fpf| + |invertibleElseSplit?| |interactiveEnv| |anfactor| |kind| |critpOrder| + |signAround| |iidprod| |compdegd| |meatAxe| |stoseInvertibleSetreg| + |OMputBVar| |headReduced?| |normalise| |expandPower| |op| |countable?| + |primextendedint| |factorsOfCyclicGroupSize| |vark| |showArrayValues| + |rightRecip| |setStatus| |viewport3D| |iflist2Result| |elements| + |qPot| |before?| |composites| |leftOne| |tubeRadiusDefault| + |stronglyReduce| |ravel| |monomial| |triangular?| |paraboloidal| + |duplicates?| |optAttributes| |sin?| |ratDsolve| |OMencodingUnknown| + |stoseSquareFreePart| |weakBiRank| |rangeIsFinite| |iiacoth| |unary?| + |sort!| |polyPart| |setScreenResolution| |minIndex| |reshape| + |arguments| |sayLength| |var1Steps| |rationalPoint?| |setelt| |trunc| + |readLine!| |harmonic| |octon| |getGoodPrime| |double?| |e01baf| + |stopMusserTrials| |moreAlgebraic?| |badNum| |abelianGroup| + |colorFunction| |sequences| |kroneckerDelta| |patternMatchTimes| + |intChoose| |s17dlf| |identitySquareMatrix| |numericalOptimization| + |hue| |digamma| |copy| |tanh2coth| |OMputAtp| |iicsc| |integerIfCan| + |s17ajf| |aQuadratic| |union| |close!| |mapUnivariateIfCan| + |explimitedint| |primextintfrac| |rewriteIdealWithHeadRemainder| + |createPrimitiveElement| |writeLine!| |readUInt8!| |linear?| |rank| + |OMputEndAtp| |e02dcf| |gderiv| |triangulate| |isOr| |uniform| + |cartesian| |singularAtInfinity?| |cAsinh| |blue| |maxrank| |update| + |primaryDecomp| |npcoef| |roman| |primPartElseUnitCanonical!| + |autoCoerce| |maxdeg| |c06ekf| |freeOf?| |float?| |exQuo| |s18acf| + |nonQsign| |laurentRep| |imagJ| |tanAn| + |semiLastSubResultantEuclidean| |outputGeneral| |fortranLogical| + |complexNormalize| |janko2| |deleteRoutine!| |sizePascalTriangle| + |algebraicSort| |stiffnessAndStabilityOfODEIF| |iprint| + |totalGroebner| |crest| |tab1| |makeViewport2D| + |createIrreduciblePoly| |ideal| |hex| |showTheFTable| |top!| + |wronskianMatrix| |Lazard2| |screenResolution3D| |factorOfDegree| + |leftRecip| |asinhIfCan| |showTheSymbolTable| |ptFunc| |dequeue!| + |cscIfCan| |asechIfCan| |digit?| |maximumExponent| |denominators| + |cyclicCopy| |semiIndiceSubResultantEuclidean| |pseudoRemainder| + |exprHasWeightCosWXorSinWX| |position| |subNodeOf?| |ode1| + |makeVariable| |mkPrim| |internalInfRittWu?| |associative?| + |mergeFactors| |gbasis| |c06ebf| |match?| |lists| |torsionIfCan| + |rootRadius| |symmetricTensors| |groebner| |leftGcd| + |antiCommutative?| |monomial?| |binaryTournament| |exportedOperators| + |overlap| |dimensions| |createZechTable| |pastel| |chainSubResultants| + |univariate?| |interpretString| |genericLeftNorm| |alternating| + |coordinate| |isNot| |simplifyLog| |e01sbf| |mathieu11| + |relationsIdeal| |rquo| |bipolar| |associatedSystem| |prime?| + |categoryMode| |OMgetBind| |summation| |declare| |findConstructor| + |simpleBounds?| |linearAssociatedOrder| |f04asf| |ksec| |failed?| + |expt| |curve?| |lSpaceBasis| |univariateSolve| |delete!| + |viewPosDefault| |rootBound| |expIfCan| |ignore?| |printCode| + |conjugates| |multiplyCoefficients| |epilogue| |limitPlus| + |swapColumns!| |clearTheSymbolTable| |f01ref| |atoms| |bernoulliB| + |maxColIndex| |entry?| |numberOfImproperPartitions| |f01qef| + |normalized?| |arg1| |LazardQuotient| |clipSurface| |rk4a| |iFTable| + |setLegalFortranSourceExtensions| |unitsColorDefault| |leadingSupport| + |zeroDimensional?| |euclideanGroebner| |dot| |scopes| |traceMatrix| + |arg2| |factorSquareFreePolynomial| |sech| |mathieu12| |rightGcd| + |aromberg| |indicialEquation| |OMgetFloat| |edf2df| |physicalLength!| + |size?| |hcrf| |generalSqFr| |csch| |composite| + |createNormalPrimitivePoly| |f04axf| |extend| |contractSolve| |close| + |inputBinaryFile| |cAsech| |shanksDiscLogAlgorithm| |quadraticNorm| + |conditions| |expandLog| |nextNormalPoly| |asinh| |exprToUPS| + |outputForm| |createMultiplicationMatrix| |constant?| |sparsityIF| + |extensionDegree| |subtractIfCan| |redPo| |match| + |halfExtendedSubResultantGcd2| |acosh| |closed?| |zeroVector| |stop| + |fibonacci| |linGenPos| |bumprow| |ODESolve| |display| |radix| + |bright| |cylindrical| |clipPointsDefault| |supRittWu?| |atanh| + |leadingCoefficientRicDE| |leadingIdeal| |goodPoint| |algebraicOf| + |largest| |useNagFunctions| |c06gqf| |rootPoly| |li| |rationalIfCan| + |collectQuasiMonic| |genericLeftMinimalPolynomial| |acoth| |s17def| + |compBound| |reindex| |dimension| |complexSolve| |shuffle| |asech| + |arity| |pair?| |diagonals| |sts2stst| |controlPanel| |chvar| + |collectUnder| |subresultantSequence| |ldf2lst| + |initializeGroupForWordProblem| |cCoth| |middle| |rootsOf| |subHeight| + |completeHermite| |OMencodingSGML| |changeName| |rotatey| + |integerBound| |polarCoordinates| |multiple| |OMcloseConn| |presub| + |primitiveElement| |karatsuba| |e02dff| |infinityNorm| |nodeOf?| + |input| |e04gcf| |iisec| |setClosed| |setButtonValue| |rightNorm| + |box| |bat| |applyQuote| |stripCommentsAndBlanks| |simplify| |library| + |is?| |aspFilename| |scanOneDimSubspaces| |cycleElt| |var2Steps| + |deleteProperty!| |nand| |iifact| |HenselLift| |dequeue| + |unrankImproperPartitions0| |sumOfDivisors| |merge!| |frobenius| + |padicFraction| |bfKeys| |multMonom| |critT| |testDim| |pole?| |df2mf| + |leftDiscriminant| |explicitlyEmpty?| |virtualDegree| + |selectNonFiniteRoutines| |extract!| |setLabelValue| + |mainCharacterization| |multiset| |ruleset| |leftZero| + |basisOfMiddleNucleus| |repeatUntilLoop| |updatD| |patternMatch| + |prepareSubResAlgo| |curveColor| |rotate| |s17adf| |Hausdorff| + |f02aef| |pol| |bernoulli| |set| |getMultiplicationTable| |f02axf| + |outputFloating| |axesColorDefault| |imaginary| |setOfMinN| + |basisOfCenter| |expintfldpoly| |test| |countRealRootsMultiple| + |eisensteinIrreducible?| |matrixGcd| |id| |rightMinimalPolynomial| + |ListOfTerms| |decimal| |linearAssociatedExp| |exponential1| + |halfExtendedResultant1| |suchThat| |subTriSet?| |sincos| |split!| + |localIntegralBasis| |putProperties| |unmakeSUP| |latex| |integer?| + |expint| |setCondition!| |leftMinimalPolynomial| + |irreducibleRepresentation| |reify| |shellSort| |table| |inR?| + |linearMatrix| |selectMultiDimensionalRoutines| |constantOpIfCan| + |eulerPhi| |leftUnits| |OMgetString| |subst| |lazy?| |insert| |new| + |sqfree| |split| |setAdaptive| |smith| |calcRanges| |obj| + |OMParseError?| |splitDenominator| |nullSpace| |reducedForm| |isMult| + |moebiusMu| |outlineRender| |solve1| |eq| |palglimint0| |prefix| + |inverseIntegralMatrix| |cache| |makeYoungTableau| |closedCurve| + |f2st| |edf2fi| |iter| |ridHack1| |e04fdf| |adaptive?| |eigenvalues| + |d03faf| |besselK| |sin2csc| |zeroMatrix| |delete| |rowEchelon| |sh| + |signature| |hasTopPredicate?| |clip| |sizeMultiplication| + |radicalRoots| GF2FG |node?| |expintegrate| |order| |localReal?| + |rightPower| |rightFactorCandidate| |logical?| |front| + |var2StepsDefault| |f04jgf| |rightCharacteristicPolynomial| |one?| + |mathieu23| |modularFactor| |parent| |modifyPointData| |specialTrigs| + |scaleRoots| |lazyPseudoRemainder| |entries| |conjunction| |objects| + |useEisensteinCriterion| |exactQuotient| + |rewriteSetByReducingWithParticularGenerators| |oddInfiniteProduct| + |leftMult| |powerAssociative?| |tanhIfCan| |directory| |wholeRadix| + |base| |script| |rightAlternative?| |imports| |lowerCase?| |hasoln| + |pointColor| |pushucoef| |rischDEsys| |parseString| |attributeData| + |module| |s18adf| |rational?| |tryFunctionalDecomposition| + |singleFactorBound| |nor| |cPower| |divide| |retractIfCan| |cExp| + |leftQuotient| |isOp| |monicRightDivide| |selectSumOfSquaresRoutines| + |flatten| |limit| |viewSizeDefault| |exp| |deepestInitial| |shufflein| + |chiSquare1| |trim| |alphanumeric| |complexEigenvalues| |tex| + |cRationalPower| |nil?| |left| |numer| |finiteBound| |reduceLODE| + |cschIfCan| |OMgetEndError| |/\\| |whatInfinity| |s21bbf| + |boundOfCauchy| |chebyshevT| |rspace| |qroot| |right| |outputList| + |denom| |radicalOfLeftTraceForm| |isExpt| |isAnd| |rCoord| + |printingInfo?| |\\/| |e02akf| |e01sef| |coshIfCan| |debug3D| |green| + |subset?| |setPoly| |withPredicates| |denominator| |sorted?| |nil| + |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index ef2d1fc3..4c91cb0c 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,317 +1,317 @@ -(3228209 . 3480528397) -((-4254 (((-112) (-1 (-112) |#2| |#2|) $) 87) (((-112) $) NIL)) (-3239 (($ (-1 (-112) |#2| |#2|) $) 18) (($ 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T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-893 (-384)) |has| |#1| (-893 (-384))) ((-893 (-570)) |has| |#1| (-893 (-570))) ((-891 |#1|) . T) ((-916) -12 (|has| |#1| (-311)) (|has| |#1| (-916))) ((-927) -2740 (|has| |#1| (-354)) (|has| |#1| (-368)) (|has| |#1| (-311))) ((-1011) -12 (|has| |#1| (-1011)) (|has| |#1| (-1212))) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 |#1|) . T) ((-1060 #0#) -2740 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-1060 |#1|) . T) ((-1060 $) . T) ((-1065 #0#) -2740 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-1065 |#1|) . T) ((-1065 $) . T) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1161) |has| |#1| (-354)) ((-1212) |has| |#1| (-1212)) ((-1215) |has| |#1| (-1212)) ((-1227) . 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T) ((-38 |#2|) |has| |#2| (-174)) ((-102) -2740 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-622 #0=(-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-622 (-570)) -2740 (|has| |#2| (-1058)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-622 |#2|) -2740 (|has| |#2| (-1109)) (|has| |#2| (-174))) ((-619 (-868)) -2740 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-619 (-868))) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-619 (-1276 |#2|)) . T) ((-174) |has| |#2| (-174)) ((-233 |#2|) |has| |#2| (-1058)) ((-235) -12 (|has| |#2| (-235)) (|has| |#2| (-1058))) ((-290 #1=(-570) |#2|) . T) ((-292 #1# |#2|) . T) ((-313 |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-373) |has| |#2| (-373)) ((-382 |#2|) |has| |#2| (-1058)) ((-417 |#2|) |has| |#2| (-1109)) ((-495 |#2|) . T) ((-610 #1# |#2|) . T) ((-520 |#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-652 (-570)) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -2740 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -2740 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -2740 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -2740 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -2740 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -2740 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-907 (-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058))) ((-1047 #0#) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-1047 (-570)) -12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) ((-1047 |#2|) |has| |#2| (-1109)) ((-1060 |#2|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -2740 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1226) . 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T) ((-38 |#2|) |has| |#2| (-174)) ((-102) -2740 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-622 #0=(-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-622 (-570)) -2740 (|has| |#2| (-1058)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-622 |#2|) -2740 (|has| |#2| (-1109)) (|has| |#2| (-174))) ((-619 (-868)) -2740 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-619 (-868))) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-619 (-1277 |#2|)) . T) ((-174) |has| |#2| (-174)) ((-233 |#2|) |has| |#2| (-1058)) ((-235) -12 (|has| |#2| (-235)) (|has| |#2| (-1058))) ((-290 #1=(-570) |#2|) . T) ((-292 #1# |#2|) . T) ((-313 |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-373) |has| |#2| (-373)) ((-382 |#2|) |has| |#2| (-1058)) ((-417 |#2|) |has| |#2| (-1109)) ((-495 |#2|) . T) ((-610 #1# |#2|) . T) ((-520 |#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-652 (-570)) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -2740 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -2740 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -2740 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -2740 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -2740 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -2740 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-907 (-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058))) ((-1047 #0#) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-1047 (-570)) -12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) ((-1047 |#2|) |has| |#2| (-1109)) ((-1060 |#2|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -2740 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1227) . T) ((-1284 |#2|) |has| |#2| (-368))) +((-2942 (((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 21)) (-3529 ((|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 23)) (-1352 (((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)) 18))) +(((-241 |#1| |#2| |#3|) (-10 -7 (-15 -2942 ((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -3529 (|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -1352 ((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)))) (-777) (-1227) (-1227)) (T -241)) +((-1352 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *7 (-1227)) (-5 *2 (-242 *5 *7)) (-5 *1 (-241 *5 *6 *7)))) (-3529 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *2 (-1227)) (-5 *1 (-241 *5 *6 *2)))) (-2942 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-242 *6 *7)) (-14 *6 (-777)) (-4 *7 (-1227)) (-4 *5 (-1227)) (-5 *2 (-242 *6 *5)) (-5 *1 (-241 *6 *7 *5))))) +(-10 -7 (-15 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-1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) 34)) (-2761 (((-650 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) $) 31)) (-2599 (($ (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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"))))))) 28)) (-3189 (($ (-650 (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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")))))))) 26)) (-2224 (((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) 38)) (-4348 (((-650 (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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"))))))) $) 36)) (-1740 (((-1282)) 11))) +(((-565) (-10 -8 (-15 -3978 ($)) (-15 -1740 ((-1282))) (-15 -2761 ((-650 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) $)) (-15 -3189 ($ (-650 (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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"))))))))) (-15 -2599 ($ (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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")))))))) (-15 -1626 ((-3 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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")))) "failed") (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-15 -4348 ((-650 (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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"))))))) $)) (-15 -2224 ((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))))) (T -565)) +((-2224 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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 (-565)))) (-4348 (*1 *2 *1) (-12 (-5 *2 (-650 (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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 (-565)))) (-1626 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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 (-565)))) (-2599 (*1 *1 *2) (-12 (-5 *2 (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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 (-565)))) (-3189 (*1 *1 *2) (-12 (-5 *2 (-650 (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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 (-565)))) (-2761 (*1 *2 *1) (-12 (-5 *2 (-650 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-5 *1 (-565)))) (-1740 (*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-565)))) (-3978 (*1 *1) (-5 *1 (-565)))) +(-10 -8 (-15 -3978 ($)) (-15 -1740 ((-1282))) (-15 -2761 ((-650 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) $)) (-15 -3189 ($ (-650 (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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"))))))))) (-15 -2599 ($ (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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")))))))) (-15 -1626 ((-3 (-2 (|:| |endPointContinuity| (-3 (|:| 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T) ((-652 |#1|) . T) ((-652 |#2|) |has| |#1| (-368)) ((-652 $) . T) ((-654 #1#) -2740 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-654 |#1|) . T) ((-654 |#2|) |has| |#1| (-368)) ((-654 $) . T) ((-646 #1#) -2740 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-646 |#1|) |has| |#1| (-174)) ((-646 |#2|) |has| |#1| (-368)) ((-646 $) -2740 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-645 (-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-645 (-570)))) ((-645 |#2|) |has| |#1| (-368)) ((-723 #1#) -2740 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-723 |#1|) |has| |#1| (-174)) ((-723 |#2|) |has| |#1| (-368)) ((-723 $) -2740 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-732) . 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UFD- (NIL T) -8 NIL NIL NIL) (-1228 2950276 2950459 2950675 "UDVO" 2951000 T UDVO (NIL) -7 NIL NIL NIL) (-1227 2948092 2948501 2948972 "UDPO" 2949840 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1226 2948025 2948030 2948060 "TYPE" 2948065 T TYPE (NIL) -9 NIL NIL NIL) (-1225 2947785 2947980 2948011 "TYPEAST" 2948016 T TYPEAST (NIL) -8 NIL NIL NIL) (-1224 2946756 2946958 2947198 "TWOFACT" 2947579 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1223 2945779 2946165 2946400 "TUPLE" 2946556 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1222 2943470 2943989 2944528 "TUBETOOL" 2945262 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1221 2942319 2942524 2942765 "TUBE" 2943263 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1220 2937048 2941291 2941574 "TS" 2942071 NIL TS (NIL T) -8 NIL NIL NIL) (-1219 2925688 2929807 2929904 "TSETCAT" 2935173 NIL TSETCAT (NIL T T T T) -9 NIL 2936704 NIL) (-1218 2920420 2922020 2923911 "TSETCAT-" 2923916 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1217 2915059 2915906 2916835 "TRMANIP" 2919556 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1216 2914500 2914563 2914726 "TRIMAT" 2914991 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1215 2912366 2912603 2912960 "TRIGMNIP" 2914249 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1214 2911886 2911999 2912029 "TRIGCAT" 2912242 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1213 2911555 2911634 2911775 "TRIGCAT-" 2911780 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1212 2908400 2910413 2910694 "TREE" 2911309 NIL TREE (NIL T) -8 NIL NIL NIL) (-1211 2907674 2908202 2908232 "TRANFUN" 2908267 T TRANFUN (NIL) -9 NIL 2908333 NIL) (-1210 2906953 2907144 2907424 "TRANFUN-" 2907429 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1209 2906757 2906789 2906850 "TOPSP" 2906914 T TOPSP (NIL) -7 NIL NIL NIL) (-1208 2906105 2906220 2906374 "TOOLSIGN" 2906638 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1207 2904739 2905282 2905521 "TEXTFILE" 2905888 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1206 2902651 2903192 2903621 "TEX" 2904332 T TEX (NIL) -8 NIL NIL NIL) (-1205 2902432 2902463 2902535 "TEX1" 2902614 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1204 2902080 2902143 2902233 "TEMUTL" 2902364 T TEMUTL (NIL) -7 NIL NIL NIL) (-1203 2900234 2900514 2900839 "TBCMPPK" 2901803 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1202 2892011 2898394 2898450 "TBAGG" 2898850 NIL TBAGG (NIL T T) -9 NIL 2899061 NIL) (-1201 2887081 2888569 2890323 "TBAGG-" 2890328 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1200 2886465 2886572 2886717 "TANEXP" 2886970 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1199 2879855 2886322 2886415 "TABLE" 2886420 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2879267 2879366 2879504 "TABLEAU" 2879752 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2873875 2875095 2876343 "TABLBUMP" 2878053 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2873097 2873244 2873425 "SYSTEM" 2873716 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2869556 2870255 2871038 "SYSSOLP" 2872348 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2869354 2869511 2869542 "SYSPTR" 2869547 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2868398 2868903 2869022 "SYSNNI" 2869208 NIL SYSNNI (NIL NIL) -8 NIL NIL 2869293) (-1192 2867705 2868164 2868243 "SYSINT" 2868303 NIL SYSINT (NIL NIL) -8 NIL NIL 2868348) (-1191 2864037 2864983 2865693 "SYNTAX" 2867017 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2861195 2861797 2862429 "SYMTAB" 2863427 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2856444 2857346 2858329 "SYMS" 2860234 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2853679 2855902 2856132 "SYMPOLY" 2856249 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2853196 2853271 2853394 "SYMFUNC" 2853591 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2849216 2850508 2851321 "SYMBOL" 2852405 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2842755 2844444 2846164 "SWITCH" 2847518 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2835989 2841576 2841879 "SUTS" 2842510 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2828055 2835236 2835509 "SUPXS" 2835774 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2819814 2827673 2827799 "SUP" 2827964 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2818973 2819100 2819317 "SUPFRACF" 2819682 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2818594 2818653 2818766 "SUP2" 2818908 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2817042 2817316 2817672 "SUMRF" 2818293 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2816377 2816443 2816635 "SUMFS" 2816963 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2800344 2815554 2815805 "SULS" 2816184 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2799946 2800166 2800236 "SUCHTAST" 2800296 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2799241 2799471 2799611 "SUCH" 2799854 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2793107 2794147 2795106 "SUBSPACE" 2798329 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2792537 2792627 2792791 "SUBRESP" 2792995 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2785903 2787202 2788513 "STTF" 2791273 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2780076 2781196 2782343 "STTFNC" 2784803 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2771387 2773258 2775052 "STTAYLOR" 2778317 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2764517 2771251 2771334 "STRTBL" 2771339 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2759881 2764472 2764503 "STRING" 2764508 T STRING (NIL) -8 NIL NIL NIL) (-1167 2754742 2759254 2759284 "STRICAT" 2759343 T STRICAT (NIL) -9 NIL 2759405 NIL) (-1166 2747495 2752361 2752972 "STREAM" 2754166 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2747005 2747082 2747226 "STREAM3" 2747412 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2745987 2746170 2746405 "STREAM2" 2746818 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2745675 2745727 2745820 "STREAM1" 2745929 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2744691 2744872 2745103 "STINPROD" 2745491 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2744243 2744453 2744483 "STEP" 2744563 T STEP (NIL) -9 NIL 2744641 NIL) (-1160 2743430 2743732 2743880 "STEPAST" 2744117 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2736862 2743329 2743406 "STBL" 2743411 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2731988 2736083 2736126 "STAGG" 2736279 NIL STAGG (NIL T) -9 NIL 2736368 NIL) (-1157 2729690 2730292 2731164 "STAGG-" 2731169 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2727837 2729460 2729552 "STACK" 2729633 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2720532 2725978 2726434 "SREGSET" 2727467 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2712957 2714326 2715839 "SRDCMPK" 2719138 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2705874 2710397 2710427 "SRAGG" 2711730 T SRAGG (NIL) -9 NIL 2712338 NIL) (-1152 2704891 2705146 2705525 "SRAGG-" 2705530 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2699351 2703838 2704259 "SQMATRIX" 2704517 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2693036 2696069 2696796 "SPLTREE" 2698696 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2688999 2689692 2690338 "SPLNODE" 2692462 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2688046 2688279 2688309 "SPFCAT" 2688753 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2686783 2686993 2687257 "SPECOUT" 2687804 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2677893 2679765 2679795 "SPADXPT" 2684471 T SPADXPT (NIL) -9 NIL 2686635 NIL) (-1145 2677654 2677694 2677763 "SPADPRSR" 2677846 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2675703 2677609 2677640 "SPADAST" 2677645 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2667648 2669421 2669464 "SPACEC" 2673837 NIL SPACEC (NIL T) -9 NIL 2675653 NIL) (-1142 2665778 2667580 2667629 "SPACE3" 2667634 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2664530 2664701 2664992 "SORTPAK" 2665583 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2662622 2662925 2663337 "SOLVETRA" 2664194 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2661672 2661894 2662155 "SOLVESER" 2662395 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2656976 2657864 2658859 "SOLVERAD" 2660724 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2652791 2653400 2654129 "SOLVEFOR" 2656343 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2647061 2652140 2652237 "SNTSCAT" 2652242 NIL SNTSCAT (NIL T T T T) -9 NIL 2652312 NIL) (-1135 2641167 2645384 2645775 "SMTS" 2646751 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2635852 2641055 2641132 "SMP" 2641137 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2634011 2634312 2634710 "SMITH" 2635549 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2626724 2630920 2631023 "SMATCAT" 2632374 NIL SMATCAT (NIL NIL T T T) -9 NIL 2632924 NIL) (-1131 2623664 2624487 2625665 "SMATCAT-" 2625670 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2621330 2622900 2622943 "SKAGG" 2623204 NIL SKAGG (NIL T) -9 NIL 2623339 NIL) (-1129 2617656 2620803 2620987 "SINT" 2621139 T SINT (NIL) -8 NIL NIL 2621301) (-1128 2617428 2617466 2617532 "SIMPAN" 2617612 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2616707 2616963 2617103 "SIG" 2617310 T SIG (NIL) -8 NIL NIL NIL) (-1126 2615545 2615766 2616041 "SIGNRF" 2616466 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2614378 2614529 2614813 "SIGNEF" 2615374 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2613684 2613961 2614085 "SIGAST" 2614276 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2611374 2611828 2612334 "SHP" 2613225 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2605226 2611275 2611351 "SHDP" 2611356 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2604799 2604991 2605021 "SGROUP" 2605114 T SGROUP (NIL) -9 NIL 2605176 NIL) (-1120 2604657 2604683 2604756 "SGROUP-" 2604761 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2601492 2602190 2602913 "SGCF" 2603956 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2595860 2600939 2601036 "SFRTCAT" 2601041 NIL SFRTCAT (NIL T T T T) -9 NIL 2601080 NIL) (-1117 2589281 2590299 2591435 "SFRGCD" 2594843 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2582407 2583480 2584666 "SFQCMPK" 2588214 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2582027 2582116 2582227 "SFORT" 2582348 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2581145 2581867 2581988 "SEXOF" 2581993 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2580252 2581026 2581094 "SEX" 2581099 T SEX (NIL) -8 NIL NIL NIL) (-1112 2575765 2576480 2576575 "SEXCAT" 2579512 NIL SEXCAT (NIL T T T T T) -9 NIL 2580090 NIL) (-1111 2572918 2575699 2575747 "SET" 2575752 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2571142 2571631 2571936 "SETMN" 2572659 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2570638 2570790 2570820 "SETCAT" 2570996 T SETCAT (NIL) -9 NIL 2571106 NIL) (-1108 2570330 2570408 2570538 "SETCAT-" 2570543 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2566691 2568791 2568834 "SETAGG" 2569704 NIL SETAGG (NIL T) -9 NIL 2570044 NIL) (-1106 2566149 2566265 2566502 "SETAGG-" 2566507 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2565592 2565845 2565946 "SEQAST" 2566070 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2564791 2565085 2565146 "SEGXCAT" 2565432 NIL SEGXCAT (NIL T T) -9 NIL 2565552 NIL) (-1103 2563797 2564457 2564639 "SEG" 2564644 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2562776 2562990 2563033 "SEGCAT" 2563555 NIL SEGCAT (NIL T) -9 NIL 2563776 NIL) (-1101 2561708 2562139 2562347 "SEGBIND" 2562603 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2561329 2561388 2561501 "SEGBIND2" 2561643 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560902 2561130 2561207 "SEGAST" 2561274 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2560121 2560247 2560451 "SEG2" 2560746 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2559531 2560056 2560103 "SDVAR" 2560108 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2552058 2559301 2559431 "SDPOL" 2559436 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2550651 2550917 2551236 "SCPKG" 2551773 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2549815 2549987 2550179 "SCOPE" 2550481 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2549035 2549169 2549348 "SCACHE" 2549670 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2548681 2548867 2548897 "SASTCAT" 2548902 T SASTCAT (NIL) -9 NIL 2548915 NIL) (-1091 2548168 2548516 2548592 "SAOS" 2548627 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2547733 2547768 2547941 "SAERFFC" 2548127 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2541672 2547630 2547710 "SAE" 2547715 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2541265 2541300 2541459 "SAEFACT" 2541631 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2539586 2539900 2540301 "RURPK" 2540931 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2538223 2538529 2538834 "RULESET" 2539420 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2535446 2535976 2536434 "RULE" 2537904 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2535058 2535240 2535323 "RULECOLD" 2535398 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2534848 2534876 2534947 "RTVALUE" 2535009 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2534319 2534565 2534659 "RSTRCAST" 2534776 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2529167 2529962 2530882 "RSETGCD" 2533518 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2518397 2523476 2523573 "RSETCAT" 2527692 NIL RSETCAT (NIL T T T T) -9 NIL 2528789 NIL) (-1079 2516324 2516863 2517687 "RSETCAT-" 2517692 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2508710 2510086 2511606 "RSDCMPK" 2514923 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2506689 2507156 2507230 "RRCC" 2508316 NIL RRCC (NIL T T) -9 NIL 2508660 NIL) (-1076 2506040 2506214 2506493 "RRCC-" 2506498 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2505483 2505736 2505837 "RPTAST" 2505961 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2479329 2488688 2488755 "RPOLCAT" 2499421 NIL RPOLCAT (NIL T T T) -9 NIL 2502581 NIL) (-1073 2470827 2473167 2476289 "RPOLCAT-" 2476294 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2461758 2469038 2469520 "ROUTINE" 2470367 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2458556 2461384 2461524 "ROMAN" 2461640 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2456800 2457416 2457676 "ROIRC" 2458361 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2453032 2455316 2455346 "RNS" 2455650 T RNS (NIL) -9 NIL 2455924 NIL) (-1068 2451541 2451924 2452458 "RNS-" 2452533 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450944 2451352 2451382 "RNG" 2451387 T RNG (NIL) -9 NIL 2451408 NIL) (-1066 2449947 2450309 2450511 "RNGBIND" 2450795 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2449346 2449734 2449777 "RMODULE" 2449782 NIL RMODULE (NIL T) -9 NIL 2449809 NIL) (-1064 2448182 2448276 2448612 "RMCAT2" 2449247 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2445032 2447528 2447825 "RMATRIX" 2447944 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2437859 2440119 2440234 "RMATCAT" 2443593 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2444575 NIL) (-1061 2437234 2437381 2437688 "RMATCAT-" 2437693 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2436635 2436856 2436899 "RLINSET" 2437093 NIL RLINSET (NIL T) -9 NIL 2437184 NIL) (-1059 2436202 2436277 2436405 "RINTERP" 2436554 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2435260 2435814 2435844 "RING" 2435900 T RING (NIL) -9 NIL 2435992 NIL) (-1057 2435052 2435096 2435193 "RING-" 2435198 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2433893 2434130 2434388 "RIDIST" 2434816 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2425182 2433361 2433567 "RGCHAIN" 2433741 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2424532 2424938 2424979 "RGBCSPC" 2425037 NIL RGBCSPC (NIL T) -9 NIL 2425089 NIL) (-1053 2423690 2424071 2424112 "RGBCMDL" 2424344 NIL RGBCMDL (NIL T) -9 NIL 2424458 NIL) (-1052 2420684 2421298 2421968 "RF" 2423054 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2420330 2420393 2420496 "RFFACTOR" 2420615 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2420055 2420090 2420187 "RFFACT" 2420289 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2418172 2418536 2418918 "RFDIST" 2419695 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2417625 2417717 2417880 "RETSOL" 2418074 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2417261 2417341 2417384 "RETRACT" 2417517 NIL RETRACT (NIL T) -9 NIL 2417604 NIL) (-1046 2417110 2417135 2417222 "RETRACT-" 2417227 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2416712 2416932 2417002 "RETAST" 2417062 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2409450 2416365 2416492 "RESULT" 2416607 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2408041 2408719 2408918 "RESRING" 2409353 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2407677 2407726 2407824 "RESLATC" 2407978 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2407382 2407417 2407524 "REPSQ" 2407636 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2404804 2405384 2405986 "REP" 2406802 T REP (NIL) -7 NIL NIL NIL) (-1039 2404501 2404536 2404647 "REPDB" 2404763 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2398401 2399790 2401013 "REP2" 2403313 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2394778 2395459 2396267 "REP1" 2397628 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2387474 2392919 2393375 "REGSET" 2394408 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2386239 2386622 2386872 "REF" 2387259 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2385616 2385719 2385886 "REDORDER" 2386123 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2381584 2384829 2385056 "RECLOS" 2385444 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2380636 2380817 2381032 "REALSOLV" 2381391 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2380482 2380523 2380553 "REAL" 2380558 T REAL (NIL) -9 NIL 2380593 NIL) (-1030 2376965 2377767 2378651 "REAL0Q" 2379647 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2372566 2373554 2374615 "REAL0" 2375946 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2372037 2372283 2372377 "RDUCEAST" 2372494 T RDUCEAST (NIL) -8 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"PADEPAC" 2019070 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-873 2017452 2017585 2017791 "PADE" 2018102 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-872 2015839 2016660 2016940 "OWP" 2017256 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-871 2015332 2015545 2015642 "OVERSET" 2015762 T OVERSET (NIL) -8 NIL NIL NIL) (-870 2014378 2014937 2015109 "OVAR" 2015200 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-869 2013642 2013763 2013924 "OUT" 2014237 T OUT (NIL) -7 NIL NIL NIL) (-868 2002514 2004751 2006951 "OUTFORM" 2011462 T OUTFORM (NIL) -8 NIL NIL NIL) (-867 2001850 2002111 2002238 "OUTBFILE" 2002407 T OUTBFILE (NIL) -8 NIL NIL NIL) (-866 2001157 2001322 2001350 "OUTBCON" 2001668 T OUTBCON (NIL) -9 NIL 2001834 NIL) (-865 2000758 2000870 2001027 "OUTBCON-" 2001032 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-864 2000138 2000487 2000576 "OSI" 2000689 T OSI (NIL) -8 NIL NIL NIL) (-863 1999668 2000006 2000034 "OSGROUP" 2000039 T OSGROUP (NIL) -9 NIL 2000061 NIL) (-862 1998413 1998640 1998925 "ORTHPOL" 1999415 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-861 1995964 1998248 1998369 "OREUP" 1998374 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-860 1993367 1995655 1995782 "ORESUP" 1995906 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990895 1991395 1991956 "OREPCTO" 1992856 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984581 1986782 1986823 "OREPCAT" 1989171 NIL OREPCAT (NIL T) -9 NIL 1990275 NIL) (-857 1981728 1982510 1983568 "OREPCAT-" 1983573 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980879 1981177 1981205 "ORDSET" 1981514 T ORDSET (NIL) -9 NIL 1981678 NIL) (-855 1980310 1980458 1980682 "ORDSET-" 1980687 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978875 1979666 1979694 "ORDRING" 1979896 T ORDRING (NIL) -9 NIL 1980021 NIL) (-853 1978520 1978614 1978758 "ORDRING-" 1978763 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977900 1978363 1978391 "ORDMON" 1978396 T ORDMON (NIL) -9 NIL 1978417 NIL) (-851 1977062 1977209 1977404 "ORDFUNS" 1977749 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976400 1976819 1976847 "ORDFIN" 1976912 T ORDFIN (NIL) -9 NIL 1976986 NIL) (-849 1972959 1974986 1975395 "ORDCOMP" 1976024 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1972225 1972352 1972538 "ORDCOMP2" 1972819 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968806 1969716 1970530 "OPTPROB" 1971431 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965608 1966247 1966951 "OPTPACK" 1968122 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1963295 1964061 1964089 "OPTCAT" 1964908 T OPTCAT (NIL) -9 NIL 1965558 NIL) (-844 1962679 1962972 1963077 "OPSIG" 1963210 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962447 1962486 1962552 "OPQUERY" 1962633 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959578 1960758 1961262 "OP" 1961976 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958952 1959178 1959219 "OPERCAT" 1959431 NIL OPERCAT (NIL T) -9 NIL 1959528 NIL) (-840 1958707 1958763 1958880 "OPERCAT-" 1958885 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955520 1957504 1957873 "ONECOMP" 1958371 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954825 1954940 1955114 "ONECOMP2" 1955392 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1954244 1954350 1954480 "OMSERVER" 1954715 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1951106 1953684 1953724 "OMSAGG" 1953785 NIL OMSAGG (NIL T) -9 NIL 1953849 NIL) (-835 1949729 1949992 1950274 "OMPKG" 1950844 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1949159 1949262 1949290 "OM" 1949589 T OM (NIL) -9 NIL NIL NIL) (-833 1947706 1948708 1948877 "OMLO" 1949040 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946666 1946813 1947033 "OMEXPR" 1947532 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945957 1946212 1946348 "OMERR" 1946550 T OMERR (NIL) -8 NIL NIL NIL) (-830 1945108 1945378 1945538 "OMERRK" 1945817 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944559 1944785 1944893 "OMENC" 1945020 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938454 1939639 1940810 "OMDEV" 1943408 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937523 1937694 1937888 "OMCONN" 1938280 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1936044 1937020 1937048 "OINTDOM" 1937053 T OINTDOM (NIL) -9 NIL 1937074 NIL) (-825 1933382 1934732 1935069 "OFMONOID" 1935739 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932793 1933319 1933364 "ODVAR" 1933369 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1930216 1932538 1932693 "ODR" 1932698 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922797 1929992 1930118 "ODPOL" 1930123 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916619 1922669 1922774 "ODP" 1922779 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915385 1915600 1915875 "ODETOOLS" 1916393 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912352 1913010 1913726 "ODESYS" 1914718 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1907234 1908142 1909167 "ODERTRIC" 1911427 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906660 1906742 1906936 "ODERED" 1907146 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903548 1904096 1904773 "ODERAT" 1906083 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900505 1900972 1901569 "ODEPRRIC" 1903077 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898448 1899044 1899530 "ODEPROB" 1900039 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894968 1895453 1896100 "ODEPRIM" 1897927 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1894217 1894319 1894579 "ODEPAL" 1894860 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890379 1891170 1892034 "ODEPACK" 1893373 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889440 1889547 1889769 "ODEINT" 1890268 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883541 1884966 1886413 "ODEIFTBL" 1888013 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878939 1879725 1880677 "ODEEF" 1882700 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1878288 1878377 1878600 "ODECONST" 1878844 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876413 1877074 1877102 "ODECAT" 1877707 T ODECAT (NIL) -9 NIL 1878238 NIL) (-805 1873268 1876118 1876240 "OCT" 1876323 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872906 1872949 1873076 "OCTCT2" 1873219 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867555 1869990 1870030 "OC" 1871127 NIL OC (NIL T) -9 NIL 1871985 NIL) (-802 1864782 1865530 1866520 "OC-" 1866614 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1864134 1864602 1864630 "OCAMON" 1864635 T OCAMON (NIL) -9 NIL 1864656 NIL) (-800 1863665 1864006 1864034 "OASGP" 1864039 T OASGP (NIL) -9 NIL 1864059 NIL) (-799 1862926 1863415 1863443 "OAMONS" 1863483 T OAMONS (NIL) -9 NIL 1863526 NIL) (-798 1862340 1862773 1862801 "OAMON" 1862806 T OAMON (NIL) -9 NIL 1862826 NIL) (-797 1861598 1862116 1862144 "OAGROUP" 1862149 T OAGROUP (NIL) -9 NIL 1862169 NIL) (-796 1861288 1861338 1861426 "NUMTUBE" 1861542 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854861 1856379 1857915 "NUMQUAD" 1859772 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850617 1851605 1852630 "NUMODE" 1853856 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847972 1848852 1848880 "NUMINT" 1849803 T NUMINT (NIL) -9 NIL 1850567 NIL) (-792 1846920 1847117 1847335 "NUMFMT" 1847774 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1833279 1836224 1838756 "NUMERIC" 1844427 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827649 1832728 1832823 "NTSCAT" 1832828 NIL NTSCAT (NIL T T T T) -9 NIL 1832867 NIL) (-789 1826843 1827008 1827201 "NTPOLFN" 1827488 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814920 1823668 1824480 "NSUP" 1826064 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814552 1814609 1814718 "NSUP2" 1814857 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804778 1814326 1814459 "NSMP" 1814464 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1803210 1803511 1803868 "NREP" 1804466 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801801 1802053 1802411 "NPCOEF" 1802953 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800867 1800982 1801198 "NORMRETR" 1801682 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798908 1799198 1799607 "NORMPK" 1800575 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798593 1798621 1798745 "NORMMA" 1798874 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798393 1798550 1798579 "NONE" 1798584 T NONE (NIL) -8 NIL NIL NIL) (-779 1798182 1798211 1798280 "NONE1" 1798357 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797679 1797741 1797920 "NODE1" 1798114 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795964 1796815 1797070 "NNI" 1797417 T NNI (NIL) -8 NIL NIL 1797652) (-776 1794384 1794697 1795061 "NLINSOL" 1795632 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790625 1791620 1792519 "NIPROB" 1793505 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789382 1789616 1789918 "NFINTBAS" 1790387 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788556 1789032 1789073 "NETCLT" 1789245 NIL NETCLT (NIL T) -9 NIL 1789327 NIL) (-772 1787264 1787495 1787776 "NCODIV" 1788324 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1787026 1787063 1787138 "NCNTFRAC" 1787221 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1785206 1785570 1785990 "NCEP" 1786651 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1784057 1784830 1784858 "NASRING" 1784968 T NASRING (NIL) -9 NIL 1785048 NIL) (-768 1783852 1783896 1783990 "NASRING-" 1783995 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782959 1783484 1783512 "NARNG" 1783629 T NARNG (NIL) -9 NIL 1783720 NIL) (-766 1782651 1782718 1782852 "NARNG-" 1782857 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781530 1781737 1781972 "NAGSP" 1782436 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772802 1774486 1776159 "NAGS" 1779877 T NAGS (NIL) -7 NIL NIL NIL) (-763 1771350 1771658 1771989 "NAGF07" 1772491 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765888 1767179 1768486 "NAGF04" 1770063 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758856 1760470 1762103 "NAGF02" 1764275 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1754080 1755180 1756297 "NAGF01" 1757759 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747708 1749274 1750859 "NAGE04" 1752515 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738877 1740998 1743128 "NAGE02" 1745598 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734830 1735777 1736741 "NAGE01" 1737933 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732625 1733159 1733717 "NAGD03" 1734292 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724375 1726303 1728257 "NAGD02" 1730691 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1718186 1719611 1721051 "NAGD01" 1722955 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714395 1715217 1716054 "NAGC06" 1717369 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712860 1713192 1713548 "NAGC05" 1714059 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1712236 1712355 1712499 "NAGC02" 1712736 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1711195 1711778 1711818 "NAALG" 1711897 NIL NAALG (NIL T) -9 NIL 1711958 NIL) (-749 1711030 1711059 1711149 "NAALG-" 1711154 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704980 1706088 1707275 "MULTSQFR" 1709926 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1704299 1704374 1704558 "MULTFACT" 1704892 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1697023 1700936 1700989 "MTSCAT" 1702059 NIL MTSCAT (NIL T T) -9 NIL 1702574 NIL) (-745 1696735 1696789 1696881 "MTHING" 1696963 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696527 1696560 1696620 "MSYSCMD" 1696695 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692609 1695282 1695602 "MSET" 1696240 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689678 1692170 1692211 "MSETAGG" 1692216 NIL MSETAGG (NIL T) -9 NIL 1692250 NIL) (-741 1685519 1687057 1687802 "MRING" 1688978 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1685085 1685152 1685283 "MRF2" 1685446 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684703 1684738 1684882 "MRATFAC" 1685044 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1682315 1682610 1683041 "MPRFF" 1684408 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676612 1682169 1682266 "MPOLY" 1682271 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1676102 1676137 1676345 "MPCPF" 1676571 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675616 1675659 1675843 "MPC3" 1676053 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674811 1674892 1675113 "MPC2" 1675531 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1673112 1673449 1673839 "MONOTOOL" 1674471 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1672337 1672654 1672682 "MONOID" 1672901 T MONOID (NIL) -9 NIL 1673048 NIL) (-731 1671883 1672002 1672183 "MONOID-" 1672188 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1662358 1668309 1668368 "MONOGEN" 1669042 NIL MONOGEN (NIL T T) -9 NIL 1669498 NIL) (-729 1659576 1660311 1661311 "MONOGEN-" 1661430 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658409 1658855 1658883 "MONADWU" 1659275 T MONADWU (NIL) -9 NIL 1659513 NIL) (-727 1657781 1657940 1658188 "MONADWU-" 1658193 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1657140 1657384 1657412 "MONAD" 1657619 T MONAD (NIL) -9 NIL 1657731 NIL) (-725 1656825 1656903 1657035 "MONAD-" 1657040 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1655114 1655738 1656017 "MOEBIUS" 1656578 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654392 1654796 1654836 "MODULE" 1654841 NIL MODULE (NIL T) -9 NIL 1654880 NIL) (-722 1653960 1654056 1654246 "MODULE-" 1654251 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651640 1652324 1652651 "MODRING" 1653784 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648584 1649745 1650266 "MODOP" 1651169 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1647172 1647651 1647928 "MODMONOM" 1648447 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1637214 1645463 1645877 "MODMON" 1646809 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634370 1636058 1636334 "MODFIELD" 1637089 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1633347 1633651 1633841 "MMLFORM" 1634200 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632873 1632916 1633095 "MMAP" 1633298 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630952 1631719 1631760 "MLO" 1632183 NIL MLO (NIL T) -9 NIL 1632425 NIL) (-713 1628318 1628834 1629436 "MLIFT" 1630433 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627709 1627793 1627947 "MKUCFUNC" 1628229 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1627308 1627378 1627501 "MKRECORD" 1627632 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1626355 1626517 1626745 "MKFUNC" 1627119 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625743 1625847 1626003 "MKFLCFN" 1626238 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1625020 1625122 1625307 "MKBCFUNC" 1625636 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621727 1624574 1624710 "MINT" 1624904 T MINT (NIL) -8 NIL NIL NIL) (-706 1620539 1620782 1621059 "MHROWRED" 1621482 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615919 1619074 1619479 "MFLOAT" 1620154 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1615276 1615352 1615523 "MFINFACT" 1615831 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611591 1612439 1613323 "MESH" 1614412 T MESH (NIL) -7 NIL NIL NIL) (-702 1609981 1610293 1610646 "MDDFACT" 1611278 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606776 1609140 1609181 "MDAGG" 1609436 NIL MDAGG (NIL T) -9 NIL 1609579 NIL) (-700 1596516 1606069 1606276 "MCMPLX" 1606589 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595653 1595799 1596000 "MCDEN" 1596365 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593543 1593813 1594193 "MCALCFN" 1595383 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592468 1592708 1592941 "MAYBE" 1593349 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1590080 1590603 1591165 "MATSTOR" 1591939 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1586037 1589452 1589700 "MATRIX" 1589865 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581801 1582510 1583246 "MATLIN" 1585394 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571907 1575093 1575170 "MATCAT" 1580050 NIL MATCAT (NIL T T T) -9 NIL 1581467 NIL) (-692 1568263 1569284 1570640 "MATCAT-" 1570645 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566857 1567010 1567343 "MATCAT2" 1568098 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564969 1565293 1565677 "MAPPKG3" 1566532 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563950 1564123 1564345 "MAPPKG2" 1564793 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562449 1562733 1563060 "MAPPKG1" 1563656 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561528 1561855 1562032 "MAPPAST" 1562292 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1561139 1561197 1561320 "MAPHACK3" 1561464 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560731 1560792 1560906 "MAPHACK2" 1561071 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1560168 1560272 1560414 "MAPHACK1" 1560622 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1558247 1558868 1559172 "MAGMA" 1559896 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557726 1557971 1558062 "MACROAST" 1558176 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1554144 1555965 1556426 "M3D" 1557298 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1548250 1552513 1552554 "LZSTAGG" 1553336 NIL LZSTAGG (NIL T) -9 NIL 1553631 NIL) (-679 1544207 1545381 1546838 "LZSTAGG-" 1546843 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1541294 1542098 1542585 "LWORD" 1543752 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540870 1541098 1541173 "LSTAST" 1541239 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1534036 1540641 1540775 "LSQM" 1540780 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1533260 1533399 1533627 "LSPP" 1533891 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1531072 1531373 1531829 "LSMP" 1532949 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527851 1528525 1529255 "LSMP1" 1530374 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521728 1527018 1527059 "LSAGG" 1527121 NIL LSAGG (NIL T) -9 NIL 1527199 NIL) (-671 1518423 1519347 1520560 "LSAGG-" 1520565 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1516022 1517567 1517816 "LPOLY" 1518218 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515604 1515689 1515812 "LPEFRAC" 1515931 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513925 1514698 1514951 "LO" 1515436 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513577 1513689 1513717 "LOGIC" 1513828 T LOGIC (NIL) -9 NIL 1513909 NIL) (-666 1513439 1513462 1513533 "LOGIC-" 1513538 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512632 1512772 1512965 "LODOOPS" 1513295 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1510055 1512548 1512614 "LODO" 1512619 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508593 1508828 1509181 "LODOF" 1509802 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504811 1507242 1507283 "LODOCAT" 1507721 NIL LODOCAT (NIL T) -9 NIL 1507932 NIL) (-661 1504544 1504602 1504729 "LODOCAT-" 1504734 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501864 1504385 1504503 "LODO2" 1504508 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1499299 1501801 1501846 "LODO1" 1501851 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1498180 1498345 1498650 "LODEEF" 1499122 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493419 1496310 1496351 "LNAGG" 1497298 NIL LNAGG (NIL T) -9 NIL 1497742 NIL) (-656 1492566 1492780 1493122 "LNAGG-" 1493127 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488702 1489491 1490130 "LMOPS" 1491981 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1488105 1488493 1488534 "LMODULE" 1488539 NIL LMODULE (NIL T) -9 NIL 1488565 NIL) (-653 1485303 1487750 1487873 "LMDICT" 1488015 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484709 1484930 1484971 "LLINSET" 1485162 NIL LLINSET (NIL T) -9 NIL 1485253 NIL) (-651 1484408 1484617 1484677 "LITERAL" 1484682 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477571 1483342 1483646 "LIST" 1484137 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1477096 1477170 1477309 "LIST3" 1477491 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1476103 1476281 1476509 "LIST2" 1476914 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1474237 1474549 1474948 "LIST2MAP" 1475750 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473833 1474070 1474111 "LINSET" 1474116 NIL LINSET (NIL T) -9 NIL 1474150 NIL) (-645 1472494 1473164 1473205 "LINEXP" 1473460 NIL LINEXP (NIL T) -9 NIL 1473609 NIL) (-644 1471141 1471401 1471698 "LINDEP" 1472246 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467908 1468627 1469404 "LIMITRF" 1470396 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1466211 1466507 1466916 "LIMITPS" 1467603 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460639 1465722 1465950 "LIE" 1466032 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459587 1460056 1460096 "LIECAT" 1460236 NIL LIECAT (NIL T) -9 NIL 1460387 NIL) (-639 1459428 1459455 1459543 "LIECAT-" 1459548 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451924 1458877 1459042 "LIB" 1459283 T LIB (NIL) -8 NIL NIL NIL) (-637 1447559 1448442 1449377 "LGROBP" 1451041 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445557 1445831 1446181 "LF" 1447280 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444397 1445089 1445117 "LFCAT" 1445324 T LFCAT (NIL) -9 NIL 1445463 NIL) (-634 1441299 1441929 1442617 "LEXTRIPK" 1443761 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1438043 1438869 1439372 "LEXP" 1440879 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437519 1437764 1437856 "LETAST" 1437971 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435917 1436230 1436631 "LEADCDET" 1437201 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1435107 1435181 1435410 "LAZM3PK" 1435838 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1430024 1433184 1433722 "LAUPOL" 1434619 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429603 1429647 1429808 "LAPLACE" 1429974 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427542 1428704 1428955 "LA" 1429436 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426536 1427120 1427161 "LALG" 1427223 NIL LALG (NIL T) -9 NIL 1427282 NIL) (-625 1426250 1426309 1426445 "LALG-" 1426450 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1426085 1426109 1426150 "KVTFROM" 1426212 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1425008 1425452 1425637 "KTVLOGIC" 1425920 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424843 1424867 1424908 "KRCFROM" 1424970 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423747 1423934 1424233 "KOVACIC" 1424643 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423582 1423606 1423647 "KONVERT" 1423709 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423417 1423441 1423482 "KOERCE" 1423544 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1421247 1422010 1422387 "KERNEL" 1423073 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420743 1420824 1420956 "KERNEL2" 1421161 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414513 1419282 1419336 "KDAGG" 1419713 NIL KDAGG (NIL T T) -9 NIL 1419919 NIL) (-615 1414042 1414166 1414371 "KDAGG-" 1414376 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1407190 1413703 1413858 "KAFILE" 1413920 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401618 1406701 1406929 "JORDAN" 1407011 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400997 1401267 1401388 "JOINAST" 1401517 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400843 1400902 1400957 "JAVACODE" 1400962 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1397095 1399048 1399102 "IXAGG" 1400031 NIL IXAGG (NIL T T) -9 NIL 1400490 NIL) (-609 1396014 1396320 1396739 "IXAGG-" 1396744 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391544 1395936 1395995 "IVECTOR" 1396000 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390310 1390547 1390813 "ITUPLE" 1391311 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388812 1388989 1389284 "ITRIGMNP" 1390132 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387557 1387761 1388044 "ITFUN3" 1388588 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1387189 1387246 1387355 "ITFUN2" 1387494 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386348 1386669 1386843 "ITFORM" 1387035 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384309 1385368 1385646 "ITAYLOR" 1386103 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1373254 1378446 1379609 "ISUPS" 1383179 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372358 1372498 1372734 "ISUMP" 1373101 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367733 1372303 1372344 "ISTRING" 1372349 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1367209 1367454 1367546 "ISAST" 1367661 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366418 1366500 1366716 "IRURPK" 1367123 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365354 1365555 1365795 "IRSN" 1366198 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363425 1363780 1364209 "IRRF2F" 1364992 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1363172 1363210 1363286 "IRREDFFX" 1363381 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361787 1362046 1362345 "IROOT" 1362905 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358391 1359471 1360163 "IR" 1361127 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357596 1357884 1358035 "IRFORM" 1358260 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1355209 1355704 1356270 "IR2" 1357074 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354309 1354422 1354636 "IR2F" 1355092 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1354100 1354134 1354194 "IPRNTPK" 1354269 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350681 1353989 1354058 "IPF" 1354063 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1349008 1350606 1350663 "IPADIC" 1350668 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348320 1348568 1348698 "IP4ADDR" 1348898 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347694 1347949 1348081 "IOMODE" 1348208 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346767 1347291 1347418 "IOBFILE" 1347587 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1346255 1346671 1346699 "IOBCON" 1346704 T IOBCON (NIL) -9 NIL 1346725 NIL) (-581 1345766 1345824 1346007 "INVLAPLA" 1346191 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335414 1337768 1340154 "INTTR" 1343430 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331749 1332491 1333356 "INTTOOLS" 1334599 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331335 1331426 1331543 "INTSLPE" 1331652 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329288 1331258 1331317 "INTRVL" 1331322 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326890 1327402 1327977 "INTRF" 1328773 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326301 1326398 1326540 "INTRET" 1326788 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324298 1324687 1325157 "INTRAT" 1325909 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321561 1322144 1322763 "INTPM" 1323783 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318306 1318905 1319643 "INTPAF" 1320947 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313485 1314447 1315498 "INTPACK" 1317275 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310433 1313282 1313391 "INT" 1313396 T INT (NIL) -8 NIL NIL NIL) (-569 1309685 1309837 1310045 "INTHERTR" 1310275 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1309124 1309204 1309392 "INTHERAL" 1309599 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306970 1307413 1307870 "INTHEORY" 1308687 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298376 1299997 1301769 "INTG0" 1305322 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278949 1283739 1288549 "INTFTBL" 1293586 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1278198 1278336 1278509 "INTFACT" 1278808 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275625 1276071 1276628 "INTEF" 1277752 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273992 1274731 1274759 "INTDOM" 1275060 T INTDOM (NIL) -9 NIL 1275267 NIL) (-561 1273361 1273535 1273777 "INTDOM-" 1273782 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269749 1271677 1271731 "INTCAT" 1272530 NIL INTCAT (NIL T) -9 NIL 1272851 NIL) (-559 1269221 1269324 1269452 "INTBIT" 1269641 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267920 1268074 1268381 "INTALG" 1269066 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267403 1267493 1267650 "INTAF" 1267824 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260746 1267213 1267353 "INTABL" 1267358 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1260087 1260553 1260618 "INT8" 1260652 T INT8 (NIL) -8 NIL NIL 1260697) (-554 1259427 1259893 1259958 "INT64" 1259992 T INT64 (NIL) -8 NIL NIL 1260037) (-553 1258767 1259233 1259298 "INT32" 1259332 T INT32 (NIL) -8 NIL NIL 1259377) (-552 1258107 1258573 1258638 "INT16" 1258672 T INT16 (NIL) -8 NIL NIL 1258717) (-551 1253017 1255730 1255758 "INS" 1256692 T INS (NIL) -9 NIL 1257357 NIL) (-550 1250257 1251028 1252002 "INS-" 1252075 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1249032 1249259 1249557 "INPSIGN" 1250010 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1248150 1248267 1248464 "INPRODPF" 1248912 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1247044 1247161 1247398 "INPRODFF" 1248030 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1246044 1246196 1246456 "INNMFACT" 1246880 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1245241 1245338 1245526 "INMODGCD" 1245943 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243749 1243994 1244318 "INFSP" 1244986 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242933 1243050 1243233 "INFPROD0" 1243629 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239788 1240998 1241513 "INFORM" 1242426 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239398 1239458 1239556 "INFORM1" 1239723 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238921 1239010 1239124 "INFINITY" 1239304 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1238097 1238641 1238742 "INETCLTS" 1238840 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236713 1236963 1237284 "INEP" 1237845 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235962 1236610 1236675 "INDE" 1236680 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235526 1235594 1235711 "INCRMAPS" 1235889 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234344 1234795 1235001 "INBFILE" 1235340 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229644 1230580 1231524 "INBFF" 1233432 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228552 1228821 1228849 "INBCON" 1229362 T INBCON (NIL) -9 NIL 1229628 NIL) (-532 1227804 1228027 1228303 "INBCON-" 1228308 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1227283 1227528 1227619 "INAST" 1227733 T INAST (NIL) -8 NIL NIL NIL) (-530 1226710 1226962 1227068 "IMPTAST" 1227197 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1223156 1226554 1226658 "IMATRIX" 1226663 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221864 1221987 1222303 "IMATQF" 1223012 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1220084 1220311 1220648 "IMATLIN" 1221620 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214662 1220008 1220066 "ILIST" 1220071 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212567 1214522 1214635 "IIARRAY2" 1214640 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207965 1212478 1212542 "IFF" 1212547 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207312 1207582 1207698 "IFAST" 1207869 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202307 1206604 1206792 "IFARRAY" 1207169 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201487 1202211 1202284 "IFAMON" 1202289 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1201071 1201136 1201190 "IEVALAB" 1201397 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200746 1200814 1200974 "IEVALAB-" 1200979 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200377 1200660 1200723 "IDPO" 1200728 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199627 1200266 1200341 "IDPOAMS" 1200346 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198934 1199516 1199591 "IDPOAM" 1199596 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197993 1198269 1198322 "IDPC" 1198735 NIL IDPC (NIL T T) -9 NIL 1198884 NIL) (-514 1197462 1197885 1197958 "IDPAM" 1197963 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196838 1197354 1197427 "IDPAG" 1197432 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196483 1196674 1196749 "IDENT" 1196783 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192738 1193586 1194481 "IDECOMP" 1195640 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185576 1186661 1187708 "IDEAL" 1191774 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184736 1184848 1185048 "ICDEN" 1185460 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183807 1184216 1184363 "ICARD" 1184609 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181867 1182180 1182585 "IBPTOOLS" 1183484 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177474 1181487 1181600 "IBITS" 1181786 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1174197 1174773 1175468 "IBATOOL" 1176891 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171976 1172438 1172971 "IBACHIN" 1173732 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169805 1171822 1171925 "IARRAY2" 1171930 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165911 1169731 1169788 "IARRAY1" 1169793 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1160020 1164323 1164804 "IAN" 1165450 T IAN (NIL) -8 NIL NIL NIL) (-500 1159531 1159588 1159761 "IALGFACT" 1159957 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1159059 1159172 1159200 "HYPCAT" 1159407 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158597 1158714 1158900 "HYPCAT-" 1158905 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1158192 1158392 1158475 "HOSTNAME" 1158534 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1158037 1158074 1158115 "HOMOTOP" 1158120 NIL HOMOTOP (NIL T) -9 NIL 1158153 NIL) (-495 1154669 1156047 1156088 "HOAGG" 1157069 NIL HOAGG (NIL T) -9 NIL 1157748 NIL) (-494 1153263 1153662 1154188 "HOAGG-" 1154193 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1147265 1152856 1153006 "HEXADEC" 1153133 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1146013 1146235 1146498 "HEUGCD" 1147042 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1145089 1145850 1145980 "HELLFDIV" 1145985 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1143268 1144866 1144954 "HEAP" 1145033 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142531 1142820 1142954 "HEADAST" 1143154 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136397 1142446 1142508 "HDP" 1142513 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130385 1136032 1136184 "HDMP" 1136298 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129709 1129849 1130013 "HB" 1130241 T HB (NIL) -7 NIL NIL NIL) (-485 1123095 1129555 1129659 "HASHTBL" 1129664 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122571 1122816 1122908 "HASAST" 1123023 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120349 1122193 1122375 "HACKPI" 1122409 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1116017 1120202 1120315 "GTSET" 1120320 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109432 1115895 1115993 "GSTBL" 1115998 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101710 1108463 1108728 "GSERIES" 1109223 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100851 1101268 1101296 "GROUP" 1101499 T GROUP (NIL) -9 NIL 1101633 NIL) (-478 1100217 1100376 1100627 "GROUP-" 1100632 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098584 1098905 1099292 "GROEBSOL" 1099894 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097498 1097786 1097837 "GRMOD" 1098366 NIL GRMOD (NIL T T) -9 NIL 1098534 NIL) (-475 1097266 1097302 1097430 "GRMOD-" 1097435 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092556 1093620 1094620 "GRIMAGE" 1096286 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1091022 1091283 1091607 "GRDEF" 1092252 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090466 1090582 1090723 "GRAY" 1090901 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089653 1090059 1090110 "GRALG" 1090263 NIL GRALG (NIL T T) -9 NIL 1090356 NIL) (-470 1089314 1089387 1089550 "GRALG-" 1089555 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1086091 1088899 1089077 "GPOLSET" 1089221 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085445 1085502 1085760 "GOSPER" 1086028 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1081177 1081883 1082409 "GMODPOL" 1085144 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1080182 1080366 1080604 "GHENSEL" 1080989 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074338 1075181 1076201 "GENUPS" 1079266 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1074035 1074086 1074175 "GENUFACT" 1074281 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073447 1073524 1073689 "GENPGCD" 1073953 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072921 1072956 1073169 "GENMFACT" 1073406 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071487 1071744 1072051 "GENEEZ" 1072664 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065633 1071098 1071260 "GDMP" 1071410 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054975 1059404 1060510 "GCNAALG" 1064616 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053302 1054164 1054192 "GCDDOM" 1054447 T GCDDOM (NIL) -9 NIL 1054604 NIL) (-457 1052772 1052899 1053114 "GCDDOM-" 1053119 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051444 1051629 1051933 "GB" 1052551 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1040060 1042390 1044782 "GBINTERN" 1049135 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037897 1038189 1038610 "GBF" 1039735 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036678 1036843 1037110 "GBEUCLID" 1037713 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1036027 1036152 1036301 "GAUSSFAC" 1036549 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034394 1034696 1035010 "GALUTIL" 1035746 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032702 1032976 1033300 "GALPOLYU" 1034121 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1030067 1030357 1030764 "GALFACTU" 1032399 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021872 1023372 1024980 "GALFACT" 1028499 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1019260 1019918 1019946 "FVFUN" 1021102 T FVFUN (NIL) -9 NIL 1021822 NIL) (-446 1018526 1018708 1018736 "FVC" 1019027 T FVC (NIL) -9 NIL 1019210 NIL) (-445 1018169 1018351 1018419 "FUNDESC" 1018478 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017784 1017966 1018047 "FUNCTION" 1018121 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015528 1016106 1016572 "FT" 1017338 T FT (NIL) -8 NIL NIL NIL) (-442 1014319 1014829 1015032 "FTEM" 1015345 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012610 1012899 1013296 "FSUPFACT" 1014010 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1011007 1011296 1011628 "FST" 1012298 T FST (NIL) -8 NIL NIL NIL) (-439 1010206 1010312 1010500 "FSRED" 1010889 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008905 1009161 1009508 "FSPRMELT" 1009921 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1006211 1006649 1007135 "FSPECF" 1008468 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987849 996180 996221 "FS" 1000105 NIL FS (NIL T) -9 NIL 1002394 NIL) (-435 976492 979485 983542 "FS-" 983842 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 976020 976074 976244 "FSINT" 976433 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974312 975013 975316 "FSERIES" 975799 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973354 973470 973694 "FSCINT" 974192 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969562 972298 972339 "FSAGG" 972709 NIL FSAGG (NIL T) -9 NIL 972968 NIL) (-430 967324 967925 968721 "FSAGG-" 968816 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966366 966509 966736 "FSAGG2" 967177 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 964048 964328 964875 "FS2UPS" 966084 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963682 963725 963854 "FS2" 963999 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962560 962731 963033 "FS2EXPXP" 963507 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961986 962101 962253 "FRUTIL" 962440 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953399 957481 958839 "FR" 960660 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948368 951042 951082 "FRNAALG" 952478 NIL FRNAALG (NIL T) -9 NIL 953085 NIL) (-422 944041 945117 946392 "FRNAALG-" 947142 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943679 943722 943849 "FRNAAF2" 943992 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 942054 942528 942824 "FRMOD" 943491 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939797 940429 940747 "FRIDEAL" 941845 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938988 939075 939366 "FRIDEAL2" 939704 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 938121 938535 938576 "FRETRCT" 938581 NIL FRETRCT (NIL T) -9 NIL 938757 NIL) (-416 937233 937464 937815 "FRETRCT-" 937820 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934321 935531 935590 "FRAMALG" 936472 NIL FRAMALG (NIL T T) -9 NIL 936764 NIL) (-414 932455 932910 933540 "FRAMALG-" 933763 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926374 931928 932205 "FRAC" 932210 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 926010 926067 926174 "FRAC2" 926311 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925646 925703 925810 "FR2" 925947 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 920159 923052 923080 "FPS" 924199 T FPS (NIL) -9 NIL 924756 NIL) (-409 919608 919717 919881 "FPS-" 920027 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916910 918579 918607 "FPC" 918832 T FPC (NIL) -9 NIL 918974 NIL) (-407 916703 916743 916840 "FPC-" 916845 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915493 916191 916232 "FPATMAB" 916237 NIL FPATMAB (NIL T) -9 NIL 916389 NIL) (-405 913166 913669 914095 "FPARFRAC" 915130 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908560 909058 909740 "FORTRAN" 912598 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906276 906776 907315 "FORT" 908041 T FORT (NIL) -7 NIL NIL NIL) (-402 903952 904514 904542 "FORTFN" 905602 T FORTFN (NIL) -9 NIL 906226 NIL) (-401 903716 903766 903794 "FORTCAT" 903853 T FORTCAT (NIL) -9 NIL 903915 NIL) (-400 901822 902332 902722 "FORMULA" 903346 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901610 901640 901709 "FORMULA1" 901786 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 901133 901185 901358 "FORDER" 901552 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 900229 900393 900586 "FOP" 900960 T FOP (NIL) -7 NIL NIL NIL) (-396 898810 899509 899683 "FNLA" 900111 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897539 897954 897982 "FNCAT" 898442 T FNCAT (NIL) -9 NIL 898702 NIL) (-394 897078 897498 897526 "FNAME" 897531 T FNAME (NIL) -8 NIL NIL NIL) (-393 895641 896604 896632 "FMTC" 896637 T FMTC (NIL) -9 NIL 896673 NIL) (-392 894387 895577 895623 "FMONOID" 895628 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 891215 892383 892424 "FMONCAT" 893641 NIL FMONCAT (NIL T) -9 NIL 894246 NIL) (-390 890407 890957 891106 "FM" 891111 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887831 888477 888505 "FMFUN" 889649 T FMFUN (NIL) -9 NIL 890357 NIL) (-388 887100 887281 887309 "FMC" 887599 T FMC (NIL) -9 NIL 887781 NIL) (-387 884179 885039 885093 "FMCAT" 886288 NIL FMCAT (NIL T T) -9 NIL 886783 NIL) (-386 883045 883945 884045 "FM1" 884124 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880819 881235 881729 "FLOATRP" 882596 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874393 878548 879169 "FLOAT" 880218 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871831 872331 872909 "FLOATCP" 873860 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870571 871409 871450 "FLINEXP" 871455 NIL FLINEXP (NIL T) -9 NIL 871548 NIL) (-381 869725 869960 870288 "FLINEXP-" 870293 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868801 868945 869169 "FLASORT" 869577 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865917 866785 866837 "FLALG" 868064 NIL FLALG (NIL T T) -9 NIL 868531 NIL) (-378 859653 863403 863444 "FLAGG" 864706 NIL FLAGG (NIL T) -9 NIL 865358 NIL) (-377 858379 858718 859208 "FLAGG-" 859213 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857421 857564 857791 "FLAGG2" 858232 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854272 855280 855339 "FINRALG" 856467 NIL FINRALG (NIL T T) -9 NIL 856975 NIL) (-374 853432 853661 854000 "FINRALG-" 854005 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852812 853051 853079 "FINITE" 853275 T FINITE (NIL) -9 NIL 853382 NIL) (-372 845169 847356 847396 "FINAALG" 851063 NIL FINAALG (NIL T) -9 NIL 852516 NIL) (-371 840501 841551 842695 "FINAALG-" 844074 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839869 840256 840359 "FILE" 840431 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838527 838865 838919 "FILECAT" 839603 NIL FILECAT (NIL T T) -9 NIL 839819 NIL) (-368 836243 837771 837799 "FIELD" 837839 T FIELD (NIL) -9 NIL 837919 NIL) (-367 834863 835248 835759 "FIELD-" 835764 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832713 833498 833845 "FGROUP" 834549 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831803 831967 832187 "FGLMICPK" 832545 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827635 831728 831785 "FFX" 831790 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 827236 827297 827432 "FFSLPE" 827568 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 823226 824008 824804 "FFPOLY" 826472 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822730 822766 822975 "FFPOLY2" 823184 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818574 822649 822712 "FFP" 822717 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813972 818485 818549 "FF" 818554 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 809098 813315 813505 "FFNBX" 813826 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 804026 808233 808491 "FFNBP" 808952 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798659 803310 803521 "FFNB" 803859 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797491 797689 798004 "FFINTBAS" 798456 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793560 795780 795808 "FFIELDC" 796428 T FFIELDC (NIL) -9 NIL 796804 NIL) (-353 792222 792593 793090 "FFIELDC-" 793095 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791791 791837 791961 "FFHOM" 792164 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789486 789973 790490 "FFF" 791306 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 785104 789228 789329 "FFCGX" 789429 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780726 784836 784943 "FFCGP" 785047 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775909 780453 780561 "FFCG" 780662 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757305 766386 766472 "FFCAT" 771637 NIL FFCAT (NIL T T T) -9 NIL 773088 NIL) (-346 752502 753550 754864 "FFCAT-" 756094 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751913 751956 752191 "FFCAT2" 752453 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 741236 744885 746105 "FEXPR" 750765 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 740236 740671 740712 "FEVALAB" 740796 NIL FEVALAB (NIL T) -9 NIL 741057 NIL) (-342 739395 739605 739943 "FEVALAB-" 739948 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737961 738778 738981 "FDIV" 739294 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734981 735722 735837 "FDIVCAT" 737405 NIL FDIVCAT (NIL T T T T) -9 NIL 737842 NIL) (-339 734743 734770 734940 "FDIVCAT-" 734945 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733963 734050 734327 "FDIV2" 734650 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732937 733258 733460 "FCTRDATA" 733781 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731623 731882 732171 "FCPAK1" 732668 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730722 731123 731264 "FCOMP" 731514 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714427 717872 721410 "FC" 727204 T FC (NIL) -8 NIL NIL NIL) (-333 706790 710818 710858 "FAXF" 712660 NIL FAXF (NIL T) -9 NIL 713352 NIL) (-332 704066 704724 705549 "FAXF-" 706014 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 699118 703442 703618 "FARRAY" 703923 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 694012 696079 696132 "FAMR" 697155 NIL FAMR (NIL T T) -9 NIL 697615 NIL) (-329 692902 693204 693639 "FAMR-" 693644 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 692071 692824 692877 "FAMONOID" 692882 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689857 690567 690620 "FAMONC" 691561 NIL FAMONC (NIL T T) -9 NIL 691947 NIL) (-326 688521 689611 689748 "FAGROUP" 689753 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686316 686635 687038 "FACUTIL" 688202 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685415 685600 685822 "FACTFUNC" 686126 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677837 684718 684917 "EXPUPXS" 685271 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675320 675860 676446 "EXPRTUBE" 677271 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671591 672183 672913 "EXPRODE" 674659 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 657076 670240 670669 "EXPR" 671195 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651630 652217 653023 "EXPR2UPS" 656374 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 651262 651319 651428 "EXPR2" 651567 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642650 650413 650704 "EXPEXPAN" 651098 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642450 642607 642636 "EXIT" 642641 T EXIT (NIL) -8 NIL NIL NIL) (-315 641930 642174 642265 "EXITAST" 642379 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641557 641619 641732 "EVALCYC" 641862 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 641098 641216 641257 "EVALAB" 641427 NIL EVALAB (NIL T) -9 NIL 641531 NIL) (-312 640579 640701 640922 "EVALAB-" 640927 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637947 639249 639277 "EUCDOM" 639832 T EUCDOM (NIL) -9 NIL 640182 NIL) (-310 636352 636794 637384 "EUCDOM-" 637389 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623890 626650 629400 "ESTOOLS" 633622 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623522 623579 623688 "ESTOOLS2" 623827 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 623273 623315 623395 "ESTOOLS1" 623474 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617310 618918 618946 "ES" 621714 T ES (NIL) -9 NIL 623124 NIL) (-305 612257 613544 615361 "ES-" 615525 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608631 609392 610172 "ESCONT" 611497 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608376 608408 608490 "ESCONT1" 608593 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 608051 608101 608201 "ES2" 608320 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607681 607739 607848 "ES1" 607987 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606897 607026 607202 "ERROR" 607525 T ERROR (NIL) -7 NIL NIL NIL) (-299 600289 606756 606847 "EQTBL" 606852 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592792 595603 597052 "EQ" 598873 NIL -2098 (NIL T) -8 NIL NIL NIL) (-297 592424 592481 592590 "EQ2" 592729 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587714 588762 589855 "EP" 591363 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586314 586605 586911 "ENV" 587428 T ENV (NIL) -8 NIL NIL NIL) (-294 585408 585962 585990 "ENTIRER" 585995 T ENTIRER (NIL) -9 NIL 586041 NIL) (-293 581875 583363 583733 "EMR" 585207 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 581019 581204 581258 "ELTAGG" 581638 NIL ELTAGG (NIL T T) -9 NIL 581849 NIL) (-291 580738 580800 580941 "ELTAGG-" 580946 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580527 580556 580610 "ELTAB" 580694 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-289 579653 579799 579998 "ELFUTS" 580378 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579395 579451 579479 "ELEMFUN" 579584 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579265 579286 579354 "ELEMFUN-" 579359 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 574109 577365 577406 "ELAGG" 578346 NIL ELAGG (NIL T) -9 NIL 578809 NIL) (-285 572394 572828 573491 "ELAGG-" 573496 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571706 571843 571999 "ELABOR" 572258 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570367 570646 570940 "ELABEXPR" 571432 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563231 565034 565861 "EFUPXS" 569643 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556681 558482 559292 "EFULS" 562507 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554166 554524 554996 "EFSTRUC" 556313 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543957 545523 547071 "EF" 552681 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 543031 543442 543591 "EAB" 543828 T EAB (NIL) -8 NIL NIL NIL) (-277 542213 542990 543018 "E04UCFA" 543023 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541395 542172 542200 "E04NAFA" 542205 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540577 541354 541382 "E04MBFA" 541387 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539759 540536 540564 "E04JAFA" 540569 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538943 539718 539746 "E04GCFA" 539751 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 538127 538902 538930 "E04FDFA" 538935 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537309 538086 538114 "E04DGFA" 538119 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531482 532834 534198 "E04AGNT" 535965 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530162 530668 530708 "DVARCAT" 531183 NIL DVARCAT (NIL T) -9 NIL 531382 NIL) (-268 529366 529578 529892 "DVARCAT-" 529897 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522503 529165 529294 "DSMP" 529299 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517284 518448 519516 "DROPT" 521455 T DROPT (NIL) -8 NIL NIL NIL) (-265 516949 517008 517106 "DROPT1" 517219 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 512064 513190 514327 "DROPT0" 515832 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510409 510734 511120 "DRAWPT" 511698 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504996 505919 506998 "DRAW" 509383 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504629 504682 504800 "DRAWHACK" 504937 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503360 503629 503920 "DRAWCX" 504358 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502875 502944 503095 "DRAWCURV" 503286 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493343 495305 497420 "DRAWCFUN" 500780 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 490107 492036 492077 "DQAGG" 492706 NIL DQAGG (NIL T) -9 NIL 492980 NIL) (-256 478231 484700 484783 "DPOLCAT" 486635 NIL DPOLCAT (NIL T T T T) -9 NIL 487180 NIL) (-255 473067 474416 476374 "DPOLCAT-" 476379 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466189 472928 473026 "DPMO" 473031 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459214 465969 466136 "DPMM" 466141 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458692 458906 459004 "DOMTMPLT" 459136 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458125 458494 458574 "DOMCTOR" 458632 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457337 457605 457756 "DOMAIN" 457994 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451325 456972 457124 "DMP" 457238 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450925 450981 451125 "DLP" 451263 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444747 450252 450442 "DLIST" 450767 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441544 443600 443641 "DLAGG" 444191 NIL DLAGG (NIL T) -9 NIL 444421 NIL) (-245 440220 440884 440912 "DIVRING" 441004 T DIVRING (NIL) -9 NIL 441087 NIL) (-244 439457 439647 439947 "DIVRING-" 439952 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437559 437916 438322 "DISPLAY" 439071 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431447 437473 437536 "DIRPROD" 437541 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430295 430498 430763 "DIRPROD2" 431240 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419070 425076 425129 "DIRPCAT" 425539 NIL DIRPCAT (NIL NIL T) -9 NIL 426379 NIL) (-239 416396 417038 417919 "DIRPCAT-" 418256 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415683 415843 416029 "DIOSP" 416230 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412338 414595 414636 "DIOPS" 415070 NIL DIOPS (NIL T) -9 NIL 415299 NIL) (-236 411887 412001 412192 "DIOPS-" 412197 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410710 411338 411366 "DIFRING" 411553 T DIFRING (NIL) -9 NIL 411663 NIL) (-234 410356 410433 410585 "DIFRING-" 410590 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408092 409364 409405 "DIFEXT" 409768 NIL DIFEXT (NIL T) -9 NIL 410062 NIL) (-232 406377 406805 407471 "DIFEXT-" 407476 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403652 405909 405950 "DIAGG" 405955 NIL DIAGG (NIL T) -9 NIL 405975 NIL) (-230 403036 403193 403445 "DIAGG-" 403450 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398453 401995 402272 "DHMATRIX" 402805 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394065 394974 395984 "DFSFUN" 397463 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389144 392996 393308 "DFLOAT" 393773 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387407 387688 388077 "DFINTTLS" 388852 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384436 385428 385828 "DERHAM" 387073 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382237 384211 384300 "DEQUEUE" 384380 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381491 381624 381807 "DEGRED" 382099 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377921 378666 379512 "DEFINTRF" 380719 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375476 375945 376537 "DEFINTEF" 377440 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374826 375096 375211 "DEFAST" 375381 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368828 374419 374569 "DECIMAL" 374696 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366340 366798 367304 "DDFACT" 368372 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365936 365979 366130 "DBLRESP" 366291 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363808 364169 364529 "DBASE" 365703 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363050 363288 363434 "DATAARY" 363707 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362156 363009 363037 "D03FAFA" 363042 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361263 362115 362143 "D03EEFA" 362148 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359213 359679 360168 "D03AGNT" 360794 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358502 359172 359200 "D02EJFA" 359205 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357791 358461 358489 "D02CJFA" 358494 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357080 357750 357778 "D02BHFA" 357783 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356369 357039 357067 "D02BBFA" 357072 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349566 351155 352761 "D02AGNT" 354783 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347334 347857 348403 "D01WGTS" 349040 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346401 347293 347321 "D01TRNS" 347326 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345469 346360 346388 "D01GBFA" 346393 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344537 345428 345456 "D01FCFA" 345461 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343605 344496 344524 "D01ASFA" 344529 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342673 343564 343592 "D01AQFA" 343597 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341741 342632 342660 "D01APFA" 342665 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340809 341700 341728 "D01ANFA" 341733 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339877 340768 340796 "D01AMFA" 340801 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338945 339836 339864 "D01ALFA" 339869 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 338013 338904 338932 "D01AKFA" 338937 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337081 337972 338000 "D01AJFA" 338005 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330376 331929 333490 "D01AGNT" 335540 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329713 329841 329993 "CYCLOTOM" 330244 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326448 327161 327888 "CYCLES" 329006 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325760 325894 326065 "CVMP" 326309 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323601 323859 324228 "CTRIGMNP" 325488 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 323037 323395 323468 "CTOR" 323548 T CTOR (NIL) -8 NIL NIL NIL) (-188 322546 322768 322869 "CTORKIND" 322956 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321837 322153 322181 "CTORCAT" 322363 T CTORCAT (NIL) -9 NIL 322476 NIL) (-186 321435 321546 321705 "CTORCAT-" 321710 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320897 321109 321217 "CTORCALL" 321359 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320271 320370 320523 "CSTTOOLS" 320794 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316070 316727 317485 "CRFP" 319583 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315545 315791 315883 "CRCEAST" 315998 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314592 314777 315005 "CRAPACK" 315349 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313976 314077 314281 "CPMATCH" 314468 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313701 313729 313835 "CPIMA" 313942 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310049 310721 311440 "COORDSYS" 313036 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309461 309582 309724 "CONTOUR" 309927 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305352 307464 307956 "CONTFRAC" 309001 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305232 305253 305281 "CONDUIT" 305318 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304320 304874 304902 "COMRING" 304907 T COMRING (NIL) -9 NIL 304959 NIL) (-173 303374 303678 303862 "COMPPROP" 304156 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 303035 303070 303198 "COMPLPAT" 303333 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293326 302844 302953 "COMPLEX" 302958 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292962 293019 293126 "COMPLEX2" 293263 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292301 292422 292582 "COMPILER" 292822 T COMPILER (NIL) -8 NIL NIL NIL) (-168 292019 292054 292152 "COMPFACT" 292260 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276099 286093 286133 "COMPCAT" 287137 NIL COMPCAT (NIL T) -9 NIL 288485 NIL) (-166 265611 268538 272165 "COMPCAT-" 272521 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265340 265368 265471 "COMMUPC" 265577 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265134 265168 265227 "COMMONOP" 265301 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264690 264885 264972 "COMM" 265067 T COMM (NIL) -8 NIL NIL NIL) (-162 264266 264494 264569 "COMMAAST" 264635 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263515 263709 263737 "COMBOPC" 264075 T COMBOPC (NIL) -9 NIL 264250 NIL) (-160 262411 262621 262863 "COMBINAT" 263305 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258868 259442 260069 "COMBF" 261833 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257626 257984 258219 "COLOR" 258653 T COLOR (NIL) -8 NIL NIL NIL) (-157 257102 257347 257439 "COLONAST" 257554 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256742 256789 256914 "CMPLXRT" 257049 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256190 256442 256541 "CLLCTAST" 256663 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251689 252720 253800 "CLIP" 255130 T CLIP (NIL) -7 NIL NIL NIL) (-153 250030 250790 251030 "CLIF" 251516 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246205 248176 248217 "CLAGG" 249146 NIL CLAGG (NIL T) -9 NIL 249682 NIL) (-151 244627 245084 245667 "CLAGG-" 245672 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244171 244256 244396 "CINTSLPE" 244536 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241672 242143 242691 "CHVAR" 243699 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240846 241400 241428 "CHARZ" 241433 T CHARZ (NIL) -9 NIL 241448 NIL) (-147 240600 240640 240718 "CHARPOL" 240800 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239658 240245 240273 "CHARNZ" 240320 T CHARNZ (NIL) -9 NIL 240376 NIL) (-145 237564 238312 238665 "CHAR" 239325 T CHAR (NIL) -8 NIL NIL NIL) (-144 237290 237351 237379 "CFCAT" 237490 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236531 236642 236825 "CDEN" 237174 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232496 235684 235964 "CCLASS" 236271 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231747 231904 232081 "CATEGORY" 232339 T -10 (NIL) -8 NIL NIL NIL) (-140 231320 231666 231714 "CATCTOR" 231719 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230771 231023 231121 "CATAST" 231242 T CATAST (NIL) -8 NIL NIL NIL) (-138 230247 230492 230584 "CASEAST" 230699 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225256 226276 227029 "CARTEN" 229550 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224364 224512 224733 "CARTEN2" 225103 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222680 223514 223771 "CARD" 224127 T CARD (NIL) -8 NIL NIL NIL) (-134 222256 222484 222559 "CAPSLAST" 222625 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221760 221968 221996 "CACHSET" 222128 T CACHSET (NIL) -9 NIL 222206 NIL) (-132 221230 221552 221580 "CABMON" 221630 T CABMON (NIL) -9 NIL 221686 NIL) (-131 220703 220934 221044 "BYTEORD" 221140 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219685 220237 220379 "BYTE" 220542 T BYTE (NIL) -8 NIL NIL 220664) (-129 215035 219190 219362 "BYTEBUF" 219533 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212544 214727 214834 "BTREE" 214961 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 209993 212192 212314 "BTOURN" 212454 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207363 209463 209504 "BTCAT" 209572 NIL BTCAT (NIL T) -9 NIL 209649 NIL) (-125 207030 207110 207259 "BTCAT-" 207264 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202440 206319 206347 "BTAGG" 206461 T BTAGG (NIL) -9 NIL 206571 NIL) (-123 201930 202055 202261 "BTAGG-" 202266 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198925 201208 201423 "BSTREE" 201747 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198063 198189 198373 "BRILL" 198781 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194715 196789 196830 "BRAGG" 197479 NIL BRAGG (NIL T) -9 NIL 197737 NIL) (-119 193244 193650 194205 "BRAGG-" 194210 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186471 192588 192773 "BPADICRT" 193091 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184786 186408 186453 "BPADIC" 186458 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184484 184514 184628 "BOUNDZRO" 184750 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179712 180910 181822 "BOP" 183592 T BOP (NIL) -8 NIL NIL NIL) (-114 177493 177897 178372 "BOP1" 179270 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177194 177255 177283 "BOOLE" 177394 T BOOLE (NIL) -9 NIL 177476 NIL) (-112 176019 176768 176917 "BOOLEAN" 177065 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175298 175702 175756 "BMODULE" 175761 NIL BMODULE (NIL T T) -9 NIL 175826 NIL) (-110 171099 175096 175169 "BITS" 175245 T BITS (NIL) -8 NIL NIL NIL) (-109 170520 170639 170779 "BINDING" 170979 T BINDING (NIL) -8 NIL NIL NIL) (-108 164525 170115 170264 "BINARY" 170391 T BINARY (NIL) -8 NIL NIL NIL) (-107 162305 163780 163821 "BGAGG" 164081 NIL BGAGG (NIL T) -9 NIL 164218 NIL) (-106 162136 162168 162259 "BGAGG-" 162264 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161207 161520 161725 "BFUNCT" 161951 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159897 160075 160363 "BEZOUT" 161031 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156366 158749 159079 "BBTREE" 159600 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156100 156153 156181 "BASTYPE" 156300 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155952 155981 156054 "BASTYPE-" 156059 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155386 155462 155614 "BALFACT" 155863 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154242 154801 154987 "AUTOMOR" 155231 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153968 153973 153999 "ATTREG" 154004 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152220 152665 153017 "ATTRBUT" 153634 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151828 152048 152114 "ATTRAST" 152172 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151364 151477 151503 "ATRIG" 151704 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151173 151214 151301 "ATRIG-" 151306 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150818 151004 151030 "ASTCAT" 151035 T ASTCAT (NIL) -9 NIL 151065 NIL) (-92 150545 150604 150723 "ASTCAT-" 150728 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148694 150321 150409 "ASTACK" 150488 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147199 147496 147861 "ASSOCEQ" 148376 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146231 146858 146982 "ASP9" 147106 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145994 146179 146218 "ASP8" 146223 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144862 145599 145741 "ASP80" 145883 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143760 144497 144629 "ASP7" 144761 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142714 143437 143555 "ASP78" 143673 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141683 142394 142511 "ASP77" 142628 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140595 141321 141452 "ASP74" 141583 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139495 140230 140362 "ASP73" 140494 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138599 139321 139421 "ASP6" 139426 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137544 138276 138394 "ASP55" 138512 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136493 137218 137337 "ASP50" 137456 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135581 136194 136304 "ASP4" 136414 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134669 135282 135392 "ASP49" 135502 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133453 134208 134376 "ASP42" 134558 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132229 132986 133156 "ASP41" 133340 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131179 131906 132024 "ASP35" 132142 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130944 131127 131166 "ASP34" 131171 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130681 130748 130824 "ASP33" 130899 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129574 130316 130448 "ASP31" 130580 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129339 129522 129561 "ASP30" 129566 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129074 129143 129219 "ASP29" 129294 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128839 129022 129061 "ASP28" 129066 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128604 128787 128826 "ASP27" 128831 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127688 128302 128413 "ASP24" 128524 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126764 127490 127602 "ASP20" 127607 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125852 126465 126575 "ASP1" 126685 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124794 125526 125645 "ASP19" 125764 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124531 124598 124674 "ASP12" 124749 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123383 124130 124274 "ASP10" 124418 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121234 123227 123318 "ARRAY2" 123323 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116999 120882 120996 "ARRAY1" 121151 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116031 116204 116425 "ARRAY12" 116822 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110343 112261 112336 "ARR2CAT" 114966 NIL ARR2CAT (NIL T T T) -9 NIL 115724 NIL) (-56 107777 108521 109475 "ARR2CAT-" 109480 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107094 107404 107529 "ARITY" 107670 T ARITY (NIL) -8 NIL NIL NIL) (-54 105870 106022 106321 "APPRULE" 106930 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105521 105569 105688 "APPLYORE" 105816 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104875 105114 105234 "ANY" 105419 T ANY (NIL) -8 NIL NIL NIL) (-51 104153 104276 104433 "ANY1" 104749 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101683 102590 102917 "ANTISYM" 103877 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101175 101390 101486 "ANON" 101605 T ANON (NIL) -8 NIL NIL NIL) (-48 95424 99714 100168 "AN" 100739 T AN (NIL) -8 NIL NIL NIL) (-47 91322 92710 92761 "AMR" 93509 NIL AMR (NIL T T) -9 NIL 94109 NIL) (-46 90434 90655 91018 "AMR-" 91023 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74873 90351 90412 "ALIST" 90417 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71676 74467 74636 "ALGSC" 74791 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68231 68786 69393 "ALGPKG" 71116 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67508 67609 67793 "ALGMFACT" 68117 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63543 64122 64716 "ALGMANIP" 67092 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54913 63169 63319 "ALGFF" 63476 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54109 54240 54419 "ALGFACT" 54771 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53050 53650 53688 "ALGEBRA" 53693 NIL ALGEBRA (NIL T) -9 NIL 53734 NIL) (-37 52768 52827 52959 "ALGEBRA-" 52964 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34861 50770 50822 "ALAGG" 50958 NIL ALAGG (NIL T T) -9 NIL 51119 NIL) (-35 34397 34510 34536 "AHYP" 34737 T AHYP (NIL) -9 NIL NIL NIL) (-34 33328 33576 33602 "AGG" 34101 T AGG (NIL) -9 NIL 34380 NIL) (-33 32762 32924 33138 "AGG-" 33143 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30568 30991 31396 "AF" 32404 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30048 30293 30383 "ADDAST" 30496 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29316 29575 29731 "ACPLOT" 29910 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18639 26443 26481 "ACFS" 27088 NIL ACFS (NIL T) -9 NIL 27327 NIL) (-28 16666 17156 17918 "ACFS-" 17923 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14713 14739 "ACF" 15618 T ACF (NIL) -9 NIL 16031 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3228626 3228631 3228636 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3228611 3228616 3228621 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3228596 3228601 3228606 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3228581 3228586 3228591 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1305 3227724 3228456 3228533 "ZMOD" 3228538 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1304 3226834 3226998 3227207 "ZLINDEP" 3227556 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1303 3216134 3217902 3219874 "ZDSOLVE" 3224964 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1302 3215380 3215521 3215710 "YSTREAM" 3215980 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1301 3213154 3214681 3214885 "XRPOLY" 3215223 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3209707 3211025 3211600 "XPR" 3212626 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1299 3207428 3209038 3209242 "XPOLY" 3209538 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1298 3205081 3206449 3206504 "XPOLYC" 3206792 NIL XPOLYC (NIL T T) -9 NIL 3206905 NIL) (-1297 3201457 3203598 3203986 "XPBWPOLY" 3204739 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3197152 3199447 3199489 "XF" 3200110 NIL XF (NIL T) -9 NIL 3200510 NIL) (-1295 3196773 3196861 3197030 "XF-" 3197035 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1294 3191969 3193258 3193313 "XFALG" 3195485 NIL XFALG (NIL T T) -9 NIL 3196274 NIL) (-1293 3191102 3191206 3191411 "XEXPPKG" 3191861 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1292 3189211 3190952 3191048 "XDPOLY" 3191053 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1291 3188018 3188618 3188661 "XALG" 3188666 NIL XALG (NIL T) -9 NIL 3188777 NIL) (-1290 3181460 3185995 3186489 "WUTSET" 3187610 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1289 3179716 3180512 3180835 "WP" 3181271 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1288 3179318 3179538 3179608 "WHILEAST" 3179668 T WHILEAST (NIL) -8 NIL NIL NIL) (-1287 3178790 3179035 3179129 "WHEREAST" 3179246 T WHEREAST (NIL) -8 NIL NIL NIL) (-1286 3177676 3177874 3178169 "WFFINTBS" 3178587 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1285 3175580 3176007 3176469 "WEIER" 3177248 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1284 3174626 3175076 3175118 "VSPACE" 3175254 NIL VSPACE (NIL T) -9 NIL 3175328 NIL) (-1283 3174464 3174491 3174582 "VSPACE-" 3174587 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1282 3174273 3174315 3174383 "VOID" 3174418 T VOID (NIL) -8 NIL NIL NIL) (-1281 3172409 3172768 3173174 "VIEW" 3173889 T VIEW (NIL) -7 NIL NIL NIL) (-1280 3168833 3169472 3170209 "VIEWDEF" 3171694 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1279 3158137 3160381 3162554 "VIEW3D" 3166682 T VIEW3D (NIL) -8 NIL NIL NIL) (-1278 3150388 3152048 3153627 "VIEW2D" 3156580 T VIEW2D (NIL) -8 NIL NIL NIL) (-1277 3145741 3150158 3150250 "VECTOR" 3150331 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1276 3144318 3144577 3144895 "VECTOR2" 3145471 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1275 3137792 3142099 3142142 "VECTCAT" 3143137 NIL VECTCAT (NIL T) -9 NIL 3143724 NIL) (-1274 3136806 3137060 3137450 "VECTCAT-" 3137455 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1273 3136260 3136457 3136577 "VARIABLE" 3136721 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1272 3136193 3136198 3136228 "UTYPE" 3136233 T UTYPE (NIL) -9 NIL NIL NIL) (-1271 3135023 3135177 3135439 "UTSODETL" 3136019 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1270 3132463 3132923 3133447 "UTSODE" 3134564 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1269 3124300 3130089 3130578 "UTS" 3132032 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1268 3115174 3120541 3120584 "UTSCAT" 3121696 NIL UTSCAT (NIL T) -9 NIL 3122454 NIL) (-1267 3112521 3113244 3114233 "UTSCAT-" 3114238 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1266 3112148 3112191 3112324 "UTS2" 3112472 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1265 3106374 3108986 3109029 "URAGG" 3111099 NIL URAGG (NIL T) -9 NIL 3111822 NIL) (-1264 3103313 3104176 3105299 "URAGG-" 3105304 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1263 3099022 3101948 3102413 "UPXSSING" 3102977 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1262 3091088 3098269 3098542 "UPXS" 3098807 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3084161 3090992 3091064 "UPXSCONS" 3091069 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3073906 3080699 3080761 "UPXSCCA" 3081335 NIL UPXSCCA (NIL T T) -9 NIL 3081568 NIL) (-1259 3073544 3073629 3073803 "UPXSCCA-" 3073808 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1258 3063141 3069707 3069750 "UPXSCAT" 3070398 NIL UPXSCAT (NIL T) -9 NIL 3071007 NIL) (-1257 3062571 3062650 3062829 "UPXS2" 3063056 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3061225 3061478 3061829 "UPSQFREE" 3062314 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1255 3054646 3057703 3057758 "UPSCAT" 3058919 NIL UPSCAT (NIL T T) -9 NIL 3059693 NIL) (-1254 3053850 3054057 3054384 "UPSCAT-" 3054389 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1253 3039505 3047273 3047316 "UPOLYC" 3049417 NIL UPOLYC (NIL T) -9 NIL 3050638 NIL) (-1252 3030833 3033259 3036406 "UPOLYC-" 3036411 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1251 3030460 3030503 3030636 "UPOLYC2" 3030784 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1250 3022271 3030143 3030272 "UP" 3030379 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1249 3021610 3021717 3021881 "UPMP" 3022160 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1248 3021163 3021244 3021383 "UPDIVP" 3021523 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1247 3019731 3019980 3020296 "UPDECOMP" 3020912 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1246 3018962 3019074 3019260 "UPCDEN" 3019615 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1245 3018481 3018550 3018699 "UP2" 3018887 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1244 3016948 3017685 3017962 "UNISEG" 3018239 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1243 3016163 3016290 3016495 "UNISEG2" 3016791 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1242 3015223 3015403 3015629 "UNIFACT" 3015979 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1241 2999155 3014400 3014651 "ULS" 3015030 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1240 2987153 2999059 2999131 "ULSCONS" 2999136 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1239 2969170 2981155 2981217 "ULSCCAT" 2981855 NIL ULSCCAT (NIL T T) -9 NIL 2982144 NIL) (-1238 2968220 2968465 2968853 "ULSCCAT-" 2968858 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1237 2957594 2964074 2964117 "ULSCAT" 2964980 NIL ULSCAT (NIL T) -9 NIL 2965711 NIL) (-1236 2957024 2957103 2957282 "ULS2" 2957509 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1235 2956151 2956661 2956768 "UINT8" 2956879 T UINT8 (NIL) -8 NIL NIL 2956964) (-1234 2955277 2955787 2955894 "UINT64" 2956005 T UINT64 (NIL) -8 NIL NIL 2956090) (-1233 2954403 2954913 2955020 "UINT32" 2955131 T UINT32 (NIL) -8 NIL NIL 2955216) (-1232 2953529 2954039 2954146 "UINT16" 2954257 T UINT16 (NIL) -8 NIL NIL 2954342) (-1231 2951832 2952789 2952819 "UFD" 2953031 T UFD (NIL) -9 NIL 2953145 NIL) (-1230 2951626 2951672 2951767 "UFD-" 2951772 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1229 2950708 2950891 2951107 "UDVO" 2951432 T UDVO (NIL) -7 NIL NIL NIL) (-1228 2948524 2948933 2949404 "UDPO" 2950272 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1227 2948457 2948462 2948492 "TYPE" 2948497 T TYPE (NIL) -9 NIL NIL NIL) (-1226 2948217 2948412 2948443 "TYPEAST" 2948448 T TYPEAST (NIL) -8 NIL NIL NIL) (-1225 2947188 2947390 2947630 "TWOFACT" 2948011 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1224 2946211 2946597 2946832 "TUPLE" 2946988 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1223 2943902 2944421 2944960 "TUBETOOL" 2945694 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1222 2942751 2942956 2943197 "TUBE" 2943695 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1221 2937480 2941723 2942006 "TS" 2942503 NIL TS (NIL T) -8 NIL NIL NIL) (-1220 2926120 2930239 2930336 "TSETCAT" 2935605 NIL TSETCAT (NIL T T T T) -9 NIL 2937136 NIL) (-1219 2920852 2922452 2924343 "TSETCAT-" 2924348 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1218 2915491 2916338 2917267 "TRMANIP" 2919988 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1217 2914932 2914995 2915158 "TRIMAT" 2915423 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1216 2912798 2913035 2913392 "TRIGMNIP" 2914681 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1215 2912318 2912431 2912461 "TRIGCAT" 2912674 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1214 2911987 2912066 2912207 "TRIGCAT-" 2912212 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2908832 2910845 2911126 "TREE" 2911741 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2908106 2908634 2908664 "TRANFUN" 2908699 T TRANFUN (NIL) -9 NIL 2908765 NIL) (-1211 2907385 2907576 2907856 "TRANFUN-" 2907861 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2907189 2907221 2907282 "TOPSP" 2907346 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2906537 2906652 2906806 "TOOLSIGN" 2907070 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2905171 2905714 2905953 "TEXTFILE" 2906320 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2903083 2903624 2904053 "TEX" 2904764 T TEX (NIL) -8 NIL NIL NIL) (-1206 2902864 2902895 2902967 "TEX1" 2903046 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2902512 2902575 2902665 "TEMUTL" 2902796 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2900666 2900946 2901271 "TBCMPPK" 2902235 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2892443 2898826 2898882 "TBAGG" 2899282 NIL TBAGG (NIL T T) -9 NIL 2899493 NIL) (-1202 2887513 2889001 2890755 "TBAGG-" 2890760 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2886897 2887004 2887149 "TANEXP" 2887402 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2886408 2886672 2886762 "TALGOP" 2886842 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2879798 2886265 2886358 "TABLE" 2886363 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2879210 2879309 2879447 "TABLEAU" 2879695 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2873818 2875038 2876286 "TABLBUMP" 2877996 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2873040 2873187 2873368 "SYSTEM" 2873659 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2869499 2870198 2870981 "SYSSOLP" 2872291 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2869297 2869454 2869485 "SYSPTR" 2869490 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2868341 2868846 2868965 "SYSNNI" 2869151 NIL SYSNNI (NIL NIL) -8 NIL NIL 2869236) (-1192 2867648 2868107 2868186 "SYSINT" 2868246 NIL SYSINT (NIL NIL) -8 NIL NIL 2868291) (-1191 2863980 2864926 2865636 "SYNTAX" 2866960 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2861138 2861740 2862372 "SYMTAB" 2863370 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2856387 2857289 2858272 "SYMS" 2860177 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2853622 2855845 2856075 "SYMPOLY" 2856192 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2853139 2853214 2853337 "SYMFUNC" 2853534 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2849159 2850451 2851264 "SYMBOL" 2852348 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2842698 2844387 2846107 "SWITCH" 2847461 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2835932 2841519 2841822 "SUTS" 2842453 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827998 2835179 2835452 "SUPXS" 2835717 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2819757 2827616 2827742 "SUP" 2827907 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2818916 2819043 2819260 "SUPFRACF" 2819625 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2818537 2818596 2818709 "SUP2" 2818851 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816985 2817259 2817615 "SUMRF" 2818236 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2816320 2816386 2816578 "SUMFS" 2816906 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2800287 2815497 2815748 "SULS" 2816127 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2799889 2800109 2800179 "SUCHTAST" 2800239 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2799184 2799414 2799554 "SUCH" 2799797 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2793050 2794090 2795049 "SUBSPACE" 2798272 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2792480 2792570 2792734 "SUBRESP" 2792938 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2785846 2787145 2788456 "STTF" 2791216 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2780019 2781139 2782286 "STTFNC" 2784746 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2771330 2773201 2774995 "STTAYLOR" 2778260 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2764460 2771194 2771277 "STRTBL" 2771282 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2759824 2764415 2764446 "STRING" 2764451 T STRING (NIL) -8 NIL NIL NIL) (-1167 2754685 2759197 2759227 "STRICAT" 2759286 T STRICAT (NIL) -9 NIL 2759348 NIL) (-1166 2747438 2752304 2752915 "STREAM" 2754109 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2746948 2747025 2747169 "STREAM3" 2747355 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2745930 2746113 2746348 "STREAM2" 2746761 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2745618 2745670 2745763 "STREAM1" 2745872 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2744634 2744815 2745046 "STINPROD" 2745434 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2744186 2744396 2744426 "STEP" 2744506 T STEP (NIL) -9 NIL 2744584 NIL) (-1160 2743373 2743675 2743823 "STEPAST" 2744060 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2736805 2743272 2743349 "STBL" 2743354 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2731931 2736026 2736069 "STAGG" 2736222 NIL STAGG (NIL T) -9 NIL 2736311 NIL) (-1157 2729633 2730235 2731107 "STAGG-" 2731112 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2727780 2729403 2729495 "STACK" 2729576 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2720475 2725921 2726377 "SREGSET" 2727410 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2712900 2714269 2715782 "SRDCMPK" 2719081 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2705817 2710340 2710370 "SRAGG" 2711673 T SRAGG (NIL) -9 NIL 2712281 NIL) (-1152 2704834 2705089 2705468 "SRAGG-" 2705473 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2699294 2703781 2704202 "SQMATRIX" 2704460 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2692979 2696012 2696739 "SPLTREE" 2698639 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2688942 2689635 2690281 "SPLNODE" 2692405 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2687989 2688222 2688252 "SPFCAT" 2688696 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2686726 2686936 2687200 "SPECOUT" 2687747 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2677836 2679708 2679738 "SPADXPT" 2684414 T SPADXPT (NIL) -9 NIL 2686578 NIL) (-1145 2677597 2677637 2677706 "SPADPRSR" 2677789 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2675646 2677552 2677583 "SPADAST" 2677588 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2667591 2669364 2669407 "SPACEC" 2673780 NIL SPACEC (NIL T) -9 NIL 2675596 NIL) (-1142 2665721 2667523 2667572 "SPACE3" 2667577 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2664473 2664644 2664935 "SORTPAK" 2665526 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2662565 2662868 2663280 "SOLVETRA" 2664137 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2661615 2661837 2662098 "SOLVESER" 2662338 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2656919 2657807 2658802 "SOLVERAD" 2660667 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2652734 2653343 2654072 "SOLVEFOR" 2656286 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2647004 2652083 2652180 "SNTSCAT" 2652185 NIL SNTSCAT (NIL T T T T) -9 NIL 2652255 NIL) (-1135 2641110 2645327 2645718 "SMTS" 2646694 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2635795 2640998 2641075 "SMP" 2641080 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2633954 2634255 2634653 "SMITH" 2635492 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2626667 2630863 2630966 "SMATCAT" 2632317 NIL SMATCAT (NIL NIL T T T) -9 NIL 2632867 NIL) (-1131 2623607 2624430 2625608 "SMATCAT-" 2625613 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2621273 2622843 2622886 "SKAGG" 2623147 NIL SKAGG (NIL T) -9 NIL 2623282 NIL) (-1129 2617599 2620746 2620930 "SINT" 2621082 T SINT (NIL) -8 NIL NIL 2621244) (-1128 2617371 2617409 2617475 "SIMPAN" 2617555 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2616650 2616906 2617046 "SIG" 2617253 T SIG (NIL) -8 NIL NIL NIL) (-1126 2615488 2615709 2615984 "SIGNRF" 2616409 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2614321 2614472 2614756 "SIGNEF" 2615317 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2613627 2613904 2614028 "SIGAST" 2614219 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2611317 2611771 2612277 "SHP" 2613168 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2605169 2611218 2611294 "SHDP" 2611299 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2604742 2604934 2604964 "SGROUP" 2605057 T SGROUP (NIL) -9 NIL 2605119 NIL) (-1120 2604600 2604626 2604699 "SGROUP-" 2604704 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2601435 2602133 2602856 "SGCF" 2603899 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2595803 2600882 2600979 "SFRTCAT" 2600984 NIL SFRTCAT (NIL T T T T) -9 NIL 2601023 NIL) (-1117 2589224 2590242 2591378 "SFRGCD" 2594786 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2582350 2583423 2584609 "SFQCMPK" 2588157 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2581970 2582059 2582170 "SFORT" 2582291 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2581088 2581810 2581931 "SEXOF" 2581936 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2580195 2580969 2581037 "SEX" 2581042 T SEX (NIL) -8 NIL NIL NIL) (-1112 2575708 2576423 2576518 "SEXCAT" 2579455 NIL SEXCAT (NIL T T T T T) -9 NIL 2580033 NIL) (-1111 2572861 2575642 2575690 "SET" 2575695 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2571085 2571574 2571879 "SETMN" 2572602 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2570581 2570733 2570763 "SETCAT" 2570939 T SETCAT (NIL) -9 NIL 2571049 NIL) (-1108 2570273 2570351 2570481 "SETCAT-" 2570486 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2566634 2568734 2568777 "SETAGG" 2569647 NIL SETAGG (NIL T) -9 NIL 2569987 NIL) (-1106 2566092 2566208 2566445 "SETAGG-" 2566450 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2565535 2565788 2565889 "SEQAST" 2566013 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2564734 2565028 2565089 "SEGXCAT" 2565375 NIL SEGXCAT (NIL T T) -9 NIL 2565495 NIL) (-1103 2563740 2564400 2564582 "SEG" 2564587 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2562719 2562933 2562976 "SEGCAT" 2563498 NIL SEGCAT (NIL T) -9 NIL 2563719 NIL) (-1101 2561651 2562082 2562290 "SEGBIND" 2562546 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2561272 2561331 2561444 "SEGBIND2" 2561586 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560845 2561073 2561150 "SEGAST" 2561217 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2560064 2560190 2560394 "SEG2" 2560689 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2559474 2559999 2560046 "SDVAR" 2560051 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2552001 2559244 2559374 "SDPOL" 2559379 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2550594 2550860 2551179 "SCPKG" 2551716 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2549758 2549930 2550122 "SCOPE" 2550424 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548978 2549112 2549291 "SCACHE" 2549613 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2548624 2548810 2548840 "SASTCAT" 2548845 T SASTCAT (NIL) -9 NIL 2548858 NIL) (-1091 2548111 2548459 2548535 "SAOS" 2548570 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2547676 2547711 2547884 "SAERFFC" 2548070 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2541615 2547573 2547653 "SAE" 2547658 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2541208 2541243 2541402 "SAEFACT" 2541574 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2539529 2539843 2540244 "RURPK" 2540874 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2538166 2538472 2538777 "RULESET" 2539363 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2535389 2535919 2536377 "RULE" 2537847 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2535001 2535183 2535266 "RULECOLD" 2535341 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2534791 2534819 2534890 "RTVALUE" 2534952 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2534262 2534508 2534602 "RSTRCAST" 2534719 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2529110 2529905 2530825 "RSETGCD" 2533461 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2518340 2523419 2523516 "RSETCAT" 2527635 NIL RSETCAT (NIL T T T T) -9 NIL 2528732 NIL) (-1079 2516267 2516806 2517630 "RSETCAT-" 2517635 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2508653 2510029 2511549 "RSDCMPK" 2514866 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2506632 2507099 2507173 "RRCC" 2508259 NIL RRCC (NIL T T) -9 NIL 2508603 NIL) (-1076 2505983 2506157 2506436 "RRCC-" 2506441 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2505426 2505679 2505780 "RPTAST" 2505904 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2479272 2488631 2488698 "RPOLCAT" 2499364 NIL RPOLCAT (NIL T T T) -9 NIL 2502524 NIL) (-1073 2470770 2473110 2476232 "RPOLCAT-" 2476237 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2461701 2468981 2469463 "ROUTINE" 2470310 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2458499 2461327 2461467 "ROMAN" 2461583 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2456743 2457359 2457619 "ROIRC" 2458304 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452975 2455259 2455289 "RNS" 2455593 T RNS (NIL) -9 NIL 2455867 NIL) (-1068 2451484 2451867 2452401 "RNS-" 2452476 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450887 2451295 2451325 "RNG" 2451330 T RNG (NIL) -9 NIL 2451351 NIL) (-1066 2449890 2450252 2450454 "RNGBIND" 2450738 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2449289 2449677 2449720 "RMODULE" 2449725 NIL RMODULE (NIL T) -9 NIL 2449752 NIL) (-1064 2448125 2448219 2448555 "RMCAT2" 2449190 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444975 2447471 2447768 "RMATRIX" 2447887 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2437802 2440062 2440177 "RMATCAT" 2443536 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2444518 NIL) (-1061 2437177 2437324 2437631 "RMATCAT-" 2437636 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2436578 2436799 2436842 "RLINSET" 2437036 NIL RLINSET (NIL T) -9 NIL 2437127 NIL) (-1059 2436145 2436220 2436348 "RINTERP" 2436497 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2435203 2435757 2435787 "RING" 2435843 T RING (NIL) -9 NIL 2435935 NIL) (-1057 2434995 2435039 2435136 "RING-" 2435141 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2433836 2434073 2434331 "RIDIST" 2434759 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2425125 2433304 2433510 "RGCHAIN" 2433684 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2424475 2424881 2424922 "RGBCSPC" 2424980 NIL RGBCSPC (NIL T) -9 NIL 2425032 NIL) (-1053 2423633 2424014 2424055 "RGBCMDL" 2424287 NIL RGBCMDL (NIL T) -9 NIL 2424401 NIL) (-1052 2420627 2421241 2421911 "RF" 2422997 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2420273 2420336 2420439 "RFFACTOR" 2420558 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419998 2420033 2420130 "RFFACT" 2420232 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2418115 2418479 2418861 "RFDIST" 2419638 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2417568 2417660 2417823 "RETSOL" 2418017 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2417204 2417284 2417327 "RETRACT" 2417460 NIL RETRACT (NIL T) -9 NIL 2417547 NIL) (-1046 2417053 2417078 2417165 "RETRACT-" 2417170 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2416655 2416875 2416945 "RETAST" 2417005 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2409393 2416308 2416435 "RESULT" 2416550 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407984 2408662 2408861 "RESRING" 2409296 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2407620 2407669 2407767 "RESLATC" 2407921 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2407325 2407360 2407467 "REPSQ" 2407579 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2404747 2405327 2405929 "REP" 2406745 T REP (NIL) -7 NIL NIL NIL) (-1039 2404444 2404479 2404590 "REPDB" 2404706 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2398344 2399733 2400956 "REP2" 2403256 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2394721 2395402 2396210 "REP1" 2397571 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2387417 2392862 2393318 "REGSET" 2394351 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2386182 2386565 2386815 "REF" 2387202 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2385559 2385662 2385829 "REDORDER" 2386066 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2381527 2384772 2384999 "RECLOS" 2385387 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2380579 2380760 2380975 "REALSOLV" 2381334 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2380425 2380466 2380496 "REAL" 2380501 T REAL (NIL) -9 NIL 2380536 NIL) (-1030 2376908 2377710 2378594 "REAL0Q" 2379590 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2372509 2373497 2374558 "REAL0" 2375889 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371980 2372226 2372320 "RDUCEAST" 2372437 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2371385 2371457 2371664 "RDIV" 2371902 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2370453 2370627 2370840 "RDIST" 2371207 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2369050 2369337 2369709 "RDETRS" 2370161 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366862 2367316 2367854 "RDETR" 2368592 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2365487 2365765 2366162 "RDEEFS" 2366578 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363996 2364302 2364727 "RDEEF" 2365175 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2358057 2360977 2361007 "RCFIELD" 2362302 T RCFIELD (NIL) -9 NIL 2363033 NIL) (-1020 2356121 2356625 2357321 "RCFIELD-" 2357396 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1019 2352390 2354222 2354265 "RCAGG" 2355349 NIL RCAGG (NIL T) -9 NIL 2355814 NIL) (-1018 2352018 2352112 2352275 "RCAGG-" 2352280 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1017 2351353 2351465 2351630 "RATRET" 2351902 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1016 2350906 2350973 2351094 "RATFACT" 2351281 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1015 2350214 2350334 2350486 "RANDSRC" 2350776 T RANDSRC (NIL) -7 NIL NIL NIL) (-1014 2349948 2349992 2350065 "RADUTIL" 2350163 T RADUTIL (NIL) -7 NIL NIL NIL) (-1013 2343062 2348779 2349090 "RADIX" 2349671 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1012 2334681 2342904 2343034 "RADFF" 2343039 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1011 2334328 2334403 2334433 "RADCAT" 2334593 T RADCAT (NIL) -9 NIL NIL NIL) (-1010 2334110 2334158 2334258 "RADCAT-" 2334263 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1009 2332208 2333880 2333972 "QUEUE" 2334053 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1008 2328745 2332141 2332189 "QUAT" 2332194 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1007 2328376 2328419 2328550 "QUATCT2" 2328696 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2321825 2325170 2325212 "QUATCAT" 2326003 NIL QUATCAT (NIL T) -9 NIL 2326769 NIL) (-1005 2317964 2319001 2320391 "QUATCAT-" 2320487 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1004 2315429 2317040 2317083 "QUAGG" 2317464 NIL QUAGG (NIL T) -9 NIL 2317639 NIL) (-1003 2315031 2315251 2315321 "QQUTAST" 2315381 T QQUTAST (NIL) -8 NIL NIL NIL) (-1002 2313924 2314424 2314598 "QFORM" 2314903 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1001 2304917 2310156 2310198 "QFCAT" 2310866 NIL QFCAT (NIL T) -9 NIL 2311867 NIL) (-1000 2300484 2301685 2303279 "QFCAT-" 2303375 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-999 2300118 2300161 2300290 "QFCAT2" 2300435 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-998 2299578 2299688 2299818 "QEQUAT" 2300008 T QEQUAT (NIL) -8 NIL NIL NIL) (-997 2292724 2293797 2294981 "QCMPACK" 2298511 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-996 2290273 2290721 2291149 "QALGSET" 2292379 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-995 2289518 2289692 2289924 "QALGSET2" 2290093 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-994 2288208 2288432 2288749 "PWFFINTB" 2289291 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-993 2286390 2286558 2286912 "PUSHVAR" 2288022 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-992 2282308 2283362 2283403 "PTRANFN" 2285287 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-991 2280710 2281001 2281323 "PTPACK" 2282019 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-990 2280342 2280399 2280508 "PTFUNC2" 2280647 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-989 2274819 2279214 2279255 "PTCAT" 2279551 NIL PTCAT (NIL T) -9 NIL 2279704 NIL) (-988 2274477 2274512 2274636 "PSQFR" 2274778 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-987 2273072 2273370 2273704 "PSEUDLIN" 2274175 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-986 2259835 2262206 2264530 "PSETPK" 2270832 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-985 2252853 2255593 2255689 "PSETCAT" 2258710 NIL PSETCAT (NIL T T T T) -9 NIL 2259524 NIL) (-984 2250689 2251323 2252144 "PSETCAT-" 2252149 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-983 2250038 2250203 2250231 "PSCURVE" 2250499 T PSCURVE (NIL) -9 NIL 2250666 NIL) (-982 2246036 2247552 2247617 "PSCAT" 2248461 NIL PSCAT (NIL T T T) -9 NIL 2248701 NIL) (-981 2245099 2245315 2245715 "PSCAT-" 2245720 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-980 2243835 2244489 2244689 "PRTITION" 2244919 T PRTITION (NIL) -8 NIL NIL NIL) (-979 2243310 2243556 2243648 "PRTDAST" 2243763 T PRTDAST (NIL) -8 NIL NIL NIL) (-978 2232400 2234614 2236802 "PRS" 2241172 NIL PRS (NIL T T) -7 NIL NIL NIL) (-977 2230211 2231750 2231790 "PRQAGG" 2231973 NIL PRQAGG (NIL T) -9 NIL 2232075 NIL) (-976 2229547 2229852 2229880 "PROPLOG" 2230019 T PROPLOG (NIL) -9 NIL 2230134 NIL) (-975 2229151 2229208 2229331 "PROPFUN2" 2229470 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-974 2228466 2228587 2228759 "PROPFUN1" 2229012 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-973 2226647 2227213 2227510 "PROPFRML" 2228202 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-972 2226116 2226223 2226351 "PROPERTY" 2226539 T PROPERTY (NIL) -8 NIL NIL NIL) (-971 2220174 2224282 2225102 "PRODUCT" 2225342 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-970 2217452 2219632 2219866 "PR" 2219985 NIL PR (NIL T T) -8 NIL NIL NIL) (-969 2217248 2217280 2217339 "PRINT" 2217413 T PRINT (NIL) -7 NIL NIL NIL) (-968 2216588 2216705 2216857 "PRIMES" 2217128 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-967 2214653 2215054 2215520 "PRIMELT" 2216167 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-966 2214382 2214431 2214459 "PRIMCAT" 2214583 T PRIMCAT (NIL) -9 NIL NIL NIL) (-965 2210497 2214320 2214365 "PRIMARR" 2214370 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-964 2209504 2209682 2209910 "PRIMARR2" 2210315 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-963 2209147 2209203 2209314 "PREASSOC" 2209442 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-962 2208622 2208755 2208783 "PPCURVE" 2208988 T PPCURVE (NIL) -9 NIL 2209124 NIL) (-961 2208217 2208417 2208500 "PORTNUM" 2208559 T PORTNUM (NIL) -8 NIL NIL NIL) (-960 2205576 2205975 2206567 "POLYROOT" 2207798 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-959 2199758 2205180 2205340 "POLY" 2205449 NIL POLY (NIL T) -8 NIL NIL NIL) (-958 2199141 2199199 2199433 "POLYLIFT" 2199694 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-957 2195416 2195865 2196494 "POLYCATQ" 2198686 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-956 2182128 2187256 2187321 "POLYCAT" 2190835 NIL POLYCAT (NIL T T T) -9 NIL 2192713 NIL) (-955 2175577 2177439 2179823 "POLYCAT-" 2179828 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-954 2175164 2175232 2175352 "POLY2UP" 2175503 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-953 2174796 2174853 2174962 "POLY2" 2175101 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-952 2173481 2173720 2173996 "POLUTIL" 2174570 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-951 2171836 2172113 2172444 "POLTOPOL" 2173203 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-950 2167301 2171772 2171818 "POINT" 2171823 NIL POINT (NIL T) -8 NIL NIL NIL) (-949 2165488 2165845 2166220 "PNTHEORY" 2166946 T PNTHEORY (NIL) -7 NIL NIL NIL) (-948 2163946 2164243 2164642 "PMTOOLS" 2165186 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-947 2163539 2163617 2163734 "PMSYM" 2163862 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-946 2163047 2163116 2163291 "PMQFCAT" 2163464 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-945 2162402 2162512 2162668 "PMPRED" 2162924 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-944 2161795 2161881 2162043 "PMPREDFS" 2162303 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-943 2160459 2160667 2161045 "PMPLCAT" 2161557 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-942 2159991 2160070 2160222 "PMLSAGG" 2160374 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-941 2159464 2159540 2159722 "PMKERNEL" 2159909 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-940 2159081 2159156 2159269 "PMINS" 2159383 NIL PMINS (NIL T) -7 NIL NIL NIL) (-939 2158523 2158592 2158801 "PMFS" 2159006 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-938 2157751 2157869 2158074 "PMDOWN" 2158400 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-937 2156918 2157076 2157257 "PMASS" 2157590 T PMASS (NIL) -7 NIL NIL NIL) (-936 2156191 2156301 2156464 "PMASSFS" 2156805 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-935 2155846 2155914 2156008 "PLOTTOOL" 2156117 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-934 2150453 2151657 2152805 "PLOT" 2154718 T PLOT (NIL) -8 NIL NIL NIL) (-933 2146257 2147301 2148222 "PLOT3D" 2149552 T PLOT3D (NIL) -8 NIL NIL NIL) (-932 2145169 2145346 2145581 "PLOT1" 2146061 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-931 2120558 2125235 2130086 "PLEQN" 2140435 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-930 2119876 2119998 2120178 "PINTERP" 2120423 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-929 2119569 2119616 2119719 "PINTERPA" 2119823 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-928 2118790 2119338 2119425 "PI" 2119465 T PI (NIL) -8 NIL NIL 2119532) (-927 2117087 2118062 2118090 "PID" 2118272 T PID (NIL) -9 NIL 2118406 NIL) (-926 2116838 2116875 2116950 "PICOERCE" 2117044 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-925 2116158 2116297 2116473 "PGROEB" 2116694 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-924 2111745 2112559 2113464 "PGE" 2115273 T PGE (NIL) -7 NIL NIL NIL) (-923 2109868 2110115 2110481 "PGCD" 2111462 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-922 2109206 2109309 2109470 "PFRPAC" 2109752 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-921 2105846 2107754 2108107 "PFR" 2108885 NIL PFR (NIL T) -8 NIL NIL NIL) (-920 2104235 2104479 2104804 "PFOTOOLS" 2105593 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-919 2102768 2103007 2103358 "PFOQ" 2103992 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-918 2101269 2101481 2101837 "PFO" 2102552 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-917 2097822 2101158 2101227 "PF" 2101232 NIL PF (NIL NIL) -8 NIL NIL NIL) (-916 2095156 2096427 2096455 "PFECAT" 2097040 T PFECAT (NIL) -9 NIL 2097424 NIL) (-915 2094601 2094755 2094969 "PFECAT-" 2094974 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-914 2093204 2093456 2093757 "PFBRU" 2094350 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-913 2091070 2091422 2091854 "PFBR" 2092855 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-912 2086952 2088446 2089122 "PERM" 2090427 NIL PERM (NIL T) -8 NIL NIL NIL) (-911 2082186 2083159 2084029 "PERMGRP" 2086115 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-910 2080292 2081249 2081290 "PERMCAT" 2081736 NIL PERMCAT (NIL T) -9 NIL 2082041 NIL) (-909 2079945 2079986 2080110 "PERMAN" 2080245 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-908 2077433 2079610 2079732 "PENDTREE" 2079856 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-907 2075457 2076225 2076266 "PDRING" 2076923 NIL PDRING (NIL T) -9 NIL 2077209 NIL) (-906 2074560 2074778 2075140 "PDRING-" 2075145 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-905 2071775 2072553 2073221 "PDEPROB" 2073912 T PDEPROB (NIL) -8 NIL NIL NIL) (-904 2069320 2069824 2070379 "PDEPACK" 2071240 T PDEPACK (NIL) -7 NIL NIL NIL) (-903 2068232 2068422 2068673 "PDECOMP" 2069119 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-902 2065811 2066654 2066682 "PDECAT" 2067469 T PDECAT (NIL) -9 NIL 2068182 NIL) (-901 2065562 2065595 2065685 "PCOMP" 2065772 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-900 2063740 2064363 2064660 "PBWLB" 2065291 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-899 2056213 2057813 2059151 "PATTERN" 2062423 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-898 2055845 2055902 2056011 "PATTERN2" 2056150 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-897 2053602 2053990 2054447 "PATTERN1" 2055434 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-896 2050970 2051551 2052032 "PATRES" 2053167 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-895 2050534 2050601 2050733 "PATRES2" 2050897 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-894 2048417 2048822 2049229 "PATMATCH" 2050201 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-893 2047927 2048136 2048177 "PATMAB" 2048284 NIL PATMAB (NIL T) -9 NIL 2048367 NIL) (-892 2046445 2046781 2047039 "PATLRES" 2047732 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-891 2045991 2046114 2046155 "PATAB" 2046160 NIL PATAB (NIL T) -9 NIL 2046332 NIL) (-890 2043472 2044004 2044577 "PARTPERM" 2045438 T PARTPERM (NIL) -7 NIL NIL NIL) (-889 2043093 2043156 2043258 "PARSURF" 2043403 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-888 2042725 2042782 2042891 "PARSU2" 2043030 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-887 2042489 2042529 2042596 "PARSER" 2042678 T PARSER (NIL) -7 NIL NIL NIL) (-886 2042110 2042173 2042275 "PARSCURV" 2042420 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-885 2041742 2041799 2041908 "PARSC2" 2042047 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-884 2041381 2041439 2041536 "PARPCURV" 2041678 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-883 2041013 2041070 2041179 "PARPC2" 2041318 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-882 2040074 2040386 2040568 "PARAMAST" 2040851 T PARAMAST (NIL) -8 NIL NIL NIL) (-881 2039594 2039680 2039799 "PAN2EXPR" 2039975 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-880 2038371 2038715 2038943 "PALETTE" 2039386 T PALETTE (NIL) -8 NIL NIL NIL) (-879 2036764 2037376 2037736 "PAIR" 2038057 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-878 2030632 2036021 2036216 "PADICRC" 2036618 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-877 2023859 2029976 2030161 "PADICRAT" 2030479 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-876 2022174 2023796 2023841 "PADIC" 2023846 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-875 2019284 2020848 2020888 "PADICCT" 2021469 NIL PADICCT (NIL NIL) -9 NIL 2021751 NIL) (-874 2018241 2018441 2018709 "PADEPAC" 2019071 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-873 2017453 2017586 2017792 "PADE" 2018103 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-872 2015840 2016661 2016941 "OWP" 2017257 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-871 2015333 2015546 2015643 "OVERSET" 2015763 T OVERSET (NIL) -8 NIL NIL NIL) (-870 2014379 2014938 2015110 "OVAR" 2015201 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-869 2013643 2013764 2013925 "OUT" 2014238 T OUT (NIL) -7 NIL NIL NIL) (-868 2002515 2004752 2006952 "OUTFORM" 2011463 T OUTFORM (NIL) -8 NIL NIL NIL) (-867 2001851 2002112 2002239 "OUTBFILE" 2002408 T OUTBFILE (NIL) -8 NIL NIL NIL) (-866 2001158 2001323 2001351 "OUTBCON" 2001669 T OUTBCON (NIL) -9 NIL 2001835 NIL) (-865 2000759 2000871 2001028 "OUTBCON-" 2001033 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-864 2000139 2000488 2000577 "OSI" 2000690 T OSI (NIL) -8 NIL NIL NIL) (-863 1999669 2000007 2000035 "OSGROUP" 2000040 T OSGROUP (NIL) -9 NIL 2000062 NIL) (-862 1998414 1998641 1998926 "ORTHPOL" 1999416 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-861 1995965 1998249 1998370 "OREUP" 1998375 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-860 1993368 1995656 1995783 "ORESUP" 1995907 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990896 1991396 1991957 "OREPCTO" 1992857 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984582 1986783 1986824 "OREPCAT" 1989172 NIL OREPCAT (NIL T) -9 NIL 1990276 NIL) (-857 1981729 1982511 1983569 "OREPCAT-" 1983574 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980880 1981178 1981206 "ORDSET" 1981515 T ORDSET (NIL) -9 NIL 1981679 NIL) (-855 1980311 1980459 1980683 "ORDSET-" 1980688 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978876 1979667 1979695 "ORDRING" 1979897 T ORDRING (NIL) -9 NIL 1980022 NIL) (-853 1978521 1978615 1978759 "ORDRING-" 1978764 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977901 1978364 1978392 "ORDMON" 1978397 T ORDMON (NIL) -9 NIL 1978418 NIL) (-851 1977063 1977210 1977405 "ORDFUNS" 1977750 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976401 1976820 1976848 "ORDFIN" 1976913 T ORDFIN (NIL) -9 NIL 1976987 NIL) (-849 1972960 1974987 1975396 "ORDCOMP" 1976025 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1972226 1972353 1972539 "ORDCOMP2" 1972820 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968807 1969717 1970531 "OPTPROB" 1971432 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965609 1966248 1966952 "OPTPACK" 1968123 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1963296 1964062 1964090 "OPTCAT" 1964909 T OPTCAT (NIL) -9 NIL 1965559 NIL) (-844 1962680 1962973 1963078 "OPSIG" 1963211 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962448 1962487 1962553 "OPQUERY" 1962634 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959579 1960759 1961263 "OP" 1961977 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958953 1959179 1959220 "OPERCAT" 1959432 NIL OPERCAT (NIL T) -9 NIL 1959529 NIL) (-840 1958708 1958764 1958881 "OPERCAT-" 1958886 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955521 1957505 1957874 "ONECOMP" 1958372 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954826 1954941 1955115 "ONECOMP2" 1955393 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1954245 1954351 1954481 "OMSERVER" 1954716 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1951107 1953685 1953725 "OMSAGG" 1953786 NIL OMSAGG (NIL T) -9 NIL 1953850 NIL) (-835 1949730 1949993 1950275 "OMPKG" 1950845 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1949160 1949263 1949291 "OM" 1949590 T OM (NIL) -9 NIL NIL NIL) (-833 1947707 1948709 1948878 "OMLO" 1949041 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946667 1946814 1947034 "OMEXPR" 1947533 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945958 1946213 1946349 "OMERR" 1946551 T OMERR (NIL) -8 NIL NIL NIL) (-830 1945109 1945379 1945539 "OMERRK" 1945818 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944560 1944786 1944894 "OMENC" 1945021 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938455 1939640 1940811 "OMDEV" 1943409 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937524 1937695 1937889 "OMCONN" 1938281 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1936045 1937021 1937049 "OINTDOM" 1937054 T OINTDOM (NIL) -9 NIL 1937075 NIL) (-825 1933383 1934733 1935070 "OFMONOID" 1935740 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932794 1933320 1933365 "ODVAR" 1933370 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1930217 1932539 1932694 "ODR" 1932699 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922798 1929993 1930119 "ODPOL" 1930124 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916620 1922670 1922775 "ODP" 1922780 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915386 1915601 1915876 "ODETOOLS" 1916394 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912353 1913011 1913727 "ODESYS" 1914719 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1907235 1908143 1909168 "ODERTRIC" 1911428 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906661 1906743 1906937 "ODERED" 1907147 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903549 1904097 1904774 "ODERAT" 1906084 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900506 1900973 1901570 "ODEPRRIC" 1903078 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898449 1899045 1899531 "ODEPROB" 1900040 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894969 1895454 1896101 "ODEPRIM" 1897928 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1894218 1894320 1894580 "ODEPAL" 1894861 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890380 1891171 1892035 "ODEPACK" 1893374 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889441 1889548 1889770 "ODEINT" 1890269 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883542 1884967 1886414 "ODEIFTBL" 1888014 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878940 1879726 1880678 "ODEEF" 1882701 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1878289 1878378 1878601 "ODECONST" 1878845 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876414 1877075 1877103 "ODECAT" 1877708 T ODECAT (NIL) -9 NIL 1878239 NIL) (-805 1873269 1876119 1876241 "OCT" 1876324 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872907 1872950 1873077 "OCTCT2" 1873220 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867556 1869991 1870031 "OC" 1871128 NIL OC (NIL T) -9 NIL 1871986 NIL) (-802 1864783 1865531 1866521 "OC-" 1866615 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1864135 1864603 1864631 "OCAMON" 1864636 T OCAMON (NIL) -9 NIL 1864657 NIL) (-800 1863666 1864007 1864035 "OASGP" 1864040 T OASGP (NIL) -9 NIL 1864060 NIL) (-799 1862927 1863416 1863444 "OAMONS" 1863484 T OAMONS (NIL) -9 NIL 1863527 NIL) (-798 1862341 1862774 1862802 "OAMON" 1862807 T OAMON (NIL) -9 NIL 1862827 NIL) (-797 1861599 1862117 1862145 "OAGROUP" 1862150 T OAGROUP (NIL) -9 NIL 1862170 NIL) (-796 1861289 1861339 1861427 "NUMTUBE" 1861543 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854862 1856380 1857916 "NUMQUAD" 1859773 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850618 1851606 1852631 "NUMODE" 1853857 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847973 1848853 1848881 "NUMINT" 1849804 T NUMINT (NIL) -9 NIL 1850568 NIL) (-792 1846921 1847118 1847336 "NUMFMT" 1847775 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1833280 1836225 1838757 "NUMERIC" 1844428 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827650 1832729 1832824 "NTSCAT" 1832829 NIL NTSCAT (NIL T T T T) -9 NIL 1832868 NIL) (-789 1826844 1827009 1827202 "NTPOLFN" 1827489 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814921 1823669 1824481 "NSUP" 1826065 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814553 1814610 1814719 "NSUP2" 1814858 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804779 1814327 1814460 "NSMP" 1814465 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1803211 1803512 1803869 "NREP" 1804467 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801802 1802054 1802412 "NPCOEF" 1802954 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800868 1800983 1801199 "NORMRETR" 1801683 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798909 1799199 1799608 "NORMPK" 1800576 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798594 1798622 1798746 "NORMMA" 1798875 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798394 1798551 1798580 "NONE" 1798585 T NONE (NIL) -8 NIL NIL NIL) (-779 1798183 1798212 1798281 "NONE1" 1798358 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797680 1797742 1797921 "NODE1" 1798115 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795965 1796816 1797071 "NNI" 1797418 T NNI (NIL) -8 NIL NIL 1797653) (-776 1794385 1794698 1795062 "NLINSOL" 1795633 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790626 1791621 1792520 "NIPROB" 1793506 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789383 1789617 1789919 "NFINTBAS" 1790388 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788557 1789033 1789074 "NETCLT" 1789246 NIL NETCLT (NIL T) -9 NIL 1789328 NIL) (-772 1787265 1787496 1787777 "NCODIV" 1788325 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1787027 1787064 1787139 "NCNTFRAC" 1787222 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1785207 1785571 1785991 "NCEP" 1786652 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1784058 1784831 1784859 "NASRING" 1784969 T NASRING (NIL) -9 NIL 1785049 NIL) (-768 1783853 1783897 1783991 "NASRING-" 1783996 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782960 1783485 1783513 "NARNG" 1783630 T NARNG (NIL) -9 NIL 1783721 NIL) (-766 1782652 1782719 1782853 "NARNG-" 1782858 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781531 1781738 1781973 "NAGSP" 1782437 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772803 1774487 1776160 "NAGS" 1779878 T NAGS (NIL) -7 NIL NIL NIL) (-763 1771351 1771659 1771990 "NAGF07" 1772492 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765889 1767180 1768487 "NAGF04" 1770064 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758857 1760471 1762104 "NAGF02" 1764276 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1754081 1755181 1756298 "NAGF01" 1757760 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747709 1749275 1750860 "NAGE04" 1752516 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738878 1740999 1743129 "NAGE02" 1745599 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734831 1735778 1736742 "NAGE01" 1737934 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732626 1733160 1733718 "NAGD03" 1734293 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724376 1726304 1728258 "NAGD02" 1730692 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1718187 1719612 1721052 "NAGD01" 1722956 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714396 1715218 1716055 "NAGC06" 1717370 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712861 1713193 1713549 "NAGC05" 1714060 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1712237 1712356 1712500 "NAGC02" 1712737 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1711196 1711779 1711819 "NAALG" 1711898 NIL NAALG (NIL T) -9 NIL 1711959 NIL) (-749 1711031 1711060 1711150 "NAALG-" 1711155 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704981 1706089 1707276 "MULTSQFR" 1709927 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1704300 1704375 1704559 "MULTFACT" 1704893 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1697024 1700937 1700990 "MTSCAT" 1702060 NIL MTSCAT (NIL T T) -9 NIL 1702575 NIL) (-745 1696736 1696790 1696882 "MTHING" 1696964 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696528 1696561 1696621 "MSYSCMD" 1696696 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692610 1695283 1695603 "MSET" 1696241 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689679 1692171 1692212 "MSETAGG" 1692217 NIL MSETAGG (NIL T) -9 NIL 1692251 NIL) (-741 1685520 1687058 1687803 "MRING" 1688979 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1685086 1685153 1685284 "MRF2" 1685447 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684704 1684739 1684883 "MRATFAC" 1685045 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1682316 1682611 1683042 "MPRFF" 1684409 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676613 1682170 1682267 "MPOLY" 1682272 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1676103 1676138 1676346 "MPCPF" 1676572 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675617 1675660 1675844 "MPC3" 1676054 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674812 1674893 1675114 "MPC2" 1675532 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1673113 1673450 1673840 "MONOTOOL" 1674472 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1672338 1672655 1672683 "MONOID" 1672902 T MONOID (NIL) -9 NIL 1673049 NIL) (-731 1671884 1672003 1672184 "MONOID-" 1672189 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1662359 1668310 1668369 "MONOGEN" 1669043 NIL MONOGEN (NIL T T) -9 NIL 1669499 NIL) (-729 1659577 1660312 1661312 "MONOGEN-" 1661431 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658410 1658856 1658884 "MONADWU" 1659276 T MONADWU (NIL) -9 NIL 1659514 NIL) (-727 1657782 1657941 1658189 "MONADWU-" 1658194 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1657141 1657385 1657413 "MONAD" 1657620 T MONAD (NIL) -9 NIL 1657732 NIL) (-725 1656826 1656904 1657036 "MONAD-" 1657041 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1655115 1655739 1656018 "MOEBIUS" 1656579 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654393 1654797 1654837 "MODULE" 1654842 NIL MODULE (NIL T) -9 NIL 1654881 NIL) (-722 1653961 1654057 1654247 "MODULE-" 1654252 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651641 1652325 1652652 "MODRING" 1653785 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648585 1649746 1650267 "MODOP" 1651170 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1647173 1647652 1647929 "MODMONOM" 1648448 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1637215 1645464 1645878 "MODMON" 1646810 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634371 1636059 1636335 "MODFIELD" 1637090 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1633348 1633652 1633842 "MMLFORM" 1634201 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632874 1632917 1633096 "MMAP" 1633299 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630953 1631720 1631761 "MLO" 1632184 NIL MLO (NIL T) -9 NIL 1632426 NIL) (-713 1628319 1628835 1629437 "MLIFT" 1630434 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627710 1627794 1627948 "MKUCFUNC" 1628230 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1627309 1627379 1627502 "MKRECORD" 1627633 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1626356 1626518 1626746 "MKFUNC" 1627120 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625744 1625848 1626004 "MKFLCFN" 1626239 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1625021 1625123 1625308 "MKBCFUNC" 1625637 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621728 1624575 1624711 "MINT" 1624905 T MINT (NIL) -8 NIL NIL NIL) (-706 1620540 1620783 1621060 "MHROWRED" 1621483 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615920 1619075 1619480 "MFLOAT" 1620155 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1615277 1615353 1615524 "MFINFACT" 1615832 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611592 1612440 1613324 "MESH" 1614413 T MESH (NIL) -7 NIL NIL NIL) (-702 1609982 1610294 1610647 "MDDFACT" 1611279 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606777 1609141 1609182 "MDAGG" 1609437 NIL MDAGG (NIL T) -9 NIL 1609580 NIL) (-700 1596517 1606070 1606277 "MCMPLX" 1606590 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595654 1595800 1596001 "MCDEN" 1596366 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593544 1593814 1594194 "MCALCFN" 1595384 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592469 1592709 1592942 "MAYBE" 1593350 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1590081 1590604 1591166 "MATSTOR" 1591940 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1586038 1589453 1589701 "MATRIX" 1589866 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581802 1582511 1583247 "MATLIN" 1585395 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571908 1575094 1575171 "MATCAT" 1580051 NIL MATCAT (NIL T T T) -9 NIL 1581468 NIL) (-692 1568264 1569285 1570641 "MATCAT-" 1570646 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566858 1567011 1567344 "MATCAT2" 1568099 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564970 1565294 1565678 "MAPPKG3" 1566533 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563951 1564124 1564346 "MAPPKG2" 1564794 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562450 1562734 1563061 "MAPPKG1" 1563657 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561529 1561856 1562033 "MAPPAST" 1562293 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1561140 1561198 1561321 "MAPHACK3" 1561465 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560732 1560793 1560907 "MAPHACK2" 1561072 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1560169 1560273 1560415 "MAPHACK1" 1560623 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1558248 1558869 1559173 "MAGMA" 1559897 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557727 1557972 1558063 "MACROAST" 1558177 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1554145 1555966 1556427 "M3D" 1557299 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1548251 1552514 1552555 "LZSTAGG" 1553337 NIL LZSTAGG (NIL T) -9 NIL 1553632 NIL) (-679 1544208 1545382 1546839 "LZSTAGG-" 1546844 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1541295 1542099 1542586 "LWORD" 1543753 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540871 1541099 1541174 "LSTAST" 1541240 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1534037 1540642 1540776 "LSQM" 1540781 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1533261 1533400 1533628 "LSPP" 1533892 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1531073 1531374 1531830 "LSMP" 1532950 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527852 1528526 1529256 "LSMP1" 1530375 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521729 1527019 1527060 "LSAGG" 1527122 NIL LSAGG (NIL T) -9 NIL 1527200 NIL) (-671 1518424 1519348 1520561 "LSAGG-" 1520566 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1516023 1517568 1517817 "LPOLY" 1518219 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515605 1515690 1515813 "LPEFRAC" 1515932 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513926 1514699 1514952 "LO" 1515437 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513578 1513690 1513718 "LOGIC" 1513829 T LOGIC (NIL) -9 NIL 1513910 NIL) (-666 1513440 1513463 1513534 "LOGIC-" 1513539 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512633 1512773 1512966 "LODOOPS" 1513296 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1510056 1512549 1512615 "LODO" 1512620 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508594 1508829 1509182 "LODOF" 1509803 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504812 1507243 1507284 "LODOCAT" 1507722 NIL LODOCAT (NIL T) -9 NIL 1507933 NIL) (-661 1504545 1504603 1504730 "LODOCAT-" 1504735 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501865 1504386 1504504 "LODO2" 1504509 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1499300 1501802 1501847 "LODO1" 1501852 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1498181 1498346 1498651 "LODEEF" 1499123 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493420 1496311 1496352 "LNAGG" 1497299 NIL LNAGG (NIL T) -9 NIL 1497743 NIL) (-656 1492567 1492781 1493123 "LNAGG-" 1493128 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488703 1489492 1490131 "LMOPS" 1491982 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1488106 1488494 1488535 "LMODULE" 1488540 NIL LMODULE (NIL T) -9 NIL 1488566 NIL) (-653 1485304 1487751 1487874 "LMDICT" 1488016 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484710 1484931 1484972 "LLINSET" 1485163 NIL LLINSET (NIL T) -9 NIL 1485254 NIL) (-651 1484409 1484618 1484678 "LITERAL" 1484683 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477572 1483343 1483647 "LIST" 1484138 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1477097 1477171 1477310 "LIST3" 1477492 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1476104 1476282 1476510 "LIST2" 1476915 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1474238 1474550 1474949 "LIST2MAP" 1475751 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473834 1474071 1474112 "LINSET" 1474117 NIL LINSET (NIL T) -9 NIL 1474151 NIL) (-645 1472495 1473165 1473206 "LINEXP" 1473461 NIL LINEXP (NIL T) -9 NIL 1473610 NIL) (-644 1471142 1471402 1471699 "LINDEP" 1472247 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467909 1468628 1469405 "LIMITRF" 1470397 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1466212 1466508 1466917 "LIMITPS" 1467604 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460640 1465723 1465951 "LIE" 1466033 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459588 1460057 1460097 "LIECAT" 1460237 NIL LIECAT (NIL T) -9 NIL 1460388 NIL) (-639 1459429 1459456 1459544 "LIECAT-" 1459549 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451925 1458878 1459043 "LIB" 1459284 T LIB (NIL) -8 NIL NIL NIL) (-637 1447560 1448443 1449378 "LGROBP" 1451042 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445558 1445832 1446182 "LF" 1447281 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444398 1445090 1445118 "LFCAT" 1445325 T LFCAT (NIL) -9 NIL 1445464 NIL) (-634 1441300 1441930 1442618 "LEXTRIPK" 1443762 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1438044 1438870 1439373 "LEXP" 1440880 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437520 1437765 1437857 "LETAST" 1437972 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435918 1436231 1436632 "LEADCDET" 1437202 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1435108 1435182 1435411 "LAZM3PK" 1435839 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1430025 1433185 1433723 "LAUPOL" 1434620 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429604 1429648 1429809 "LAPLACE" 1429975 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427543 1428705 1428956 "LA" 1429437 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426537 1427121 1427162 "LALG" 1427224 NIL LALG (NIL T) -9 NIL 1427283 NIL) (-625 1426251 1426310 1426446 "LALG-" 1426451 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1426086 1426110 1426151 "KVTFROM" 1426213 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1425009 1425453 1425638 "KTVLOGIC" 1425921 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424844 1424868 1424909 "KRCFROM" 1424971 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423748 1423935 1424234 "KOVACIC" 1424644 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423583 1423607 1423648 "KONVERT" 1423710 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423418 1423442 1423483 "KOERCE" 1423545 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1421248 1422011 1422388 "KERNEL" 1423074 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420744 1420825 1420957 "KERNEL2" 1421162 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414514 1419283 1419337 "KDAGG" 1419714 NIL KDAGG (NIL T T) -9 NIL 1419920 NIL) (-615 1414043 1414167 1414372 "KDAGG-" 1414377 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1407191 1413704 1413859 "KAFILE" 1413921 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401619 1406702 1406930 "JORDAN" 1407012 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400998 1401268 1401389 "JOINAST" 1401518 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400844 1400903 1400958 "JAVACODE" 1400963 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1397096 1399049 1399103 "IXAGG" 1400032 NIL IXAGG (NIL T T) -9 NIL 1400491 NIL) (-609 1396015 1396321 1396740 "IXAGG-" 1396745 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391545 1395937 1395996 "IVECTOR" 1396001 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390311 1390548 1390814 "ITUPLE" 1391312 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388813 1388990 1389285 "ITRIGMNP" 1390133 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387558 1387762 1388045 "ITFUN3" 1388589 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1387190 1387247 1387356 "ITFUN2" 1387495 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386349 1386670 1386844 "ITFORM" 1387036 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384310 1385369 1385647 "ITAYLOR" 1386104 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1373255 1378447 1379610 "ISUPS" 1383180 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372359 1372499 1372735 "ISUMP" 1373102 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367734 1372304 1372345 "ISTRING" 1372350 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1367210 1367455 1367547 "ISAST" 1367662 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366419 1366501 1366717 "IRURPK" 1367124 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365355 1365556 1365796 "IRSN" 1366199 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363426 1363781 1364210 "IRRF2F" 1364993 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1363173 1363211 1363287 "IRREDFFX" 1363382 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361788 1362047 1362346 "IROOT" 1362906 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358392 1359472 1360164 "IR" 1361128 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357597 1357885 1358036 "IRFORM" 1358261 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1355210 1355705 1356271 "IR2" 1357075 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354310 1354423 1354637 "IR2F" 1355093 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1354101 1354135 1354195 "IPRNTPK" 1354270 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350682 1353990 1354059 "IPF" 1354064 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1349009 1350607 1350664 "IPADIC" 1350669 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348321 1348569 1348699 "IP4ADDR" 1348899 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347695 1347950 1348082 "IOMODE" 1348209 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346768 1347292 1347419 "IOBFILE" 1347588 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1346256 1346672 1346700 "IOBCON" 1346705 T IOBCON (NIL) -9 NIL 1346726 NIL) (-581 1345767 1345825 1346008 "INVLAPLA" 1346192 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335415 1337769 1340155 "INTTR" 1343431 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331750 1332492 1333357 "INTTOOLS" 1334600 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331336 1331427 1331544 "INTSLPE" 1331653 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329289 1331259 1331318 "INTRVL" 1331323 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326891 1327403 1327978 "INTRF" 1328774 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326302 1326399 1326541 "INTRET" 1326789 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324299 1324688 1325158 "INTRAT" 1325910 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321562 1322145 1322764 "INTPM" 1323784 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318307 1318906 1319644 "INTPAF" 1320948 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313486 1314448 1315499 "INTPACK" 1317276 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310434 1313283 1313392 "INT" 1313397 T INT (NIL) -8 NIL NIL NIL) (-569 1309686 1309838 1310046 "INTHERTR" 1310276 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1309125 1309205 1309393 "INTHERAL" 1309600 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306971 1307414 1307871 "INTHEORY" 1308688 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298377 1299998 1301770 "INTG0" 1305323 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278950 1283740 1288550 "INTFTBL" 1293587 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1278199 1278337 1278510 "INTFACT" 1278809 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275626 1276072 1276629 "INTEF" 1277753 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273993 1274732 1274760 "INTDOM" 1275061 T INTDOM (NIL) -9 NIL 1275268 NIL) (-561 1273362 1273536 1273778 "INTDOM-" 1273783 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269750 1271678 1271732 "INTCAT" 1272531 NIL INTCAT (NIL T) -9 NIL 1272852 NIL) (-559 1269222 1269325 1269453 "INTBIT" 1269642 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267921 1268075 1268382 "INTALG" 1269067 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267404 1267494 1267651 "INTAF" 1267825 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260747 1267214 1267354 "INTABL" 1267359 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1260088 1260554 1260619 "INT8" 1260653 T INT8 (NIL) -8 NIL NIL 1260698) (-554 1259428 1259894 1259959 "INT64" 1259993 T INT64 (NIL) -8 NIL NIL 1260038) (-553 1258768 1259234 1259299 "INT32" 1259333 T INT32 (NIL) -8 NIL NIL 1259378) (-552 1258108 1258574 1258639 "INT16" 1258673 T INT16 (NIL) -8 NIL NIL 1258718) (-551 1253018 1255731 1255759 "INS" 1256693 T INS (NIL) -9 NIL 1257358 NIL) (-550 1250258 1251029 1252003 "INS-" 1252076 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1249033 1249260 1249558 "INPSIGN" 1250011 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1248151 1248268 1248465 "INPRODPF" 1248913 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1247045 1247162 1247399 "INPRODFF" 1248031 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1246045 1246197 1246457 "INNMFACT" 1246881 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1245242 1245339 1245527 "INMODGCD" 1245944 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243750 1243995 1244319 "INFSP" 1244987 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242934 1243051 1243234 "INFPROD0" 1243630 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239789 1240999 1241514 "INFORM" 1242427 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239399 1239459 1239557 "INFORM1" 1239724 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238922 1239011 1239125 "INFINITY" 1239305 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1238098 1238642 1238743 "INETCLTS" 1238841 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236714 1236964 1237285 "INEP" 1237846 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235963 1236611 1236676 "INDE" 1236681 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235527 1235595 1235712 "INCRMAPS" 1235890 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234345 1234796 1235002 "INBFILE" 1235341 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229645 1230581 1231525 "INBFF" 1233433 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228553 1228822 1228850 "INBCON" 1229363 T INBCON (NIL) -9 NIL 1229629 NIL) (-532 1227805 1228028 1228304 "INBCON-" 1228309 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1227284 1227529 1227620 "INAST" 1227734 T INAST (NIL) -8 NIL NIL NIL) (-530 1226711 1226963 1227069 "IMPTAST" 1227198 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1223157 1226555 1226659 "IMATRIX" 1226664 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221865 1221988 1222304 "IMATQF" 1223013 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1220085 1220312 1220649 "IMATLIN" 1221621 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214663 1220009 1220067 "ILIST" 1220072 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212568 1214523 1214636 "IIARRAY2" 1214641 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207966 1212479 1212543 "IFF" 1212548 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207313 1207583 1207699 "IFAST" 1207870 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202308 1206605 1206793 "IFARRAY" 1207170 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201488 1202212 1202285 "IFAMON" 1202290 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1201072 1201137 1201191 "IEVALAB" 1201398 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200747 1200815 1200975 "IEVALAB-" 1200980 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200378 1200661 1200724 "IDPO" 1200729 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199628 1200267 1200342 "IDPOAMS" 1200347 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198935 1199517 1199592 "IDPOAM" 1199597 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197994 1198270 1198323 "IDPC" 1198736 NIL IDPC (NIL T T) -9 NIL 1198885 NIL) (-514 1197463 1197886 1197959 "IDPAM" 1197964 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196839 1197355 1197428 "IDPAG" 1197433 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196484 1196675 1196750 "IDENT" 1196784 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192739 1193587 1194482 "IDECOMP" 1195641 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185577 1186662 1187709 "IDEAL" 1191775 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184737 1184849 1185049 "ICDEN" 1185461 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183808 1184217 1184364 "ICARD" 1184610 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181868 1182181 1182586 "IBPTOOLS" 1183485 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177475 1181488 1181601 "IBITS" 1181787 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1174198 1174774 1175469 "IBATOOL" 1176892 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171977 1172439 1172972 "IBACHIN" 1173733 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169806 1171823 1171926 "IARRAY2" 1171931 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165912 1169732 1169789 "IARRAY1" 1169794 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1160021 1164324 1164805 "IAN" 1165451 T IAN (NIL) -8 NIL NIL NIL) (-500 1159532 1159589 1159762 "IALGFACT" 1159958 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1159060 1159173 1159201 "HYPCAT" 1159408 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158598 1158715 1158901 "HYPCAT-" 1158906 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1158193 1158393 1158476 "HOSTNAME" 1158535 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1158038 1158075 1158116 "HOMOTOP" 1158121 NIL HOMOTOP (NIL T) -9 NIL 1158154 NIL) (-495 1154670 1156048 1156089 "HOAGG" 1157070 NIL HOAGG (NIL T) -9 NIL 1157749 NIL) (-494 1153264 1153663 1154189 "HOAGG-" 1154194 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1147266 1152857 1153007 "HEXADEC" 1153134 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1146014 1146236 1146499 "HEUGCD" 1147043 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1145090 1145851 1145981 "HELLFDIV" 1145986 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1143269 1144867 1144955 "HEAP" 1145034 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142532 1142821 1142955 "HEADAST" 1143155 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136398 1142447 1142509 "HDP" 1142514 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130386 1136033 1136185 "HDMP" 1136299 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129710 1129850 1130014 "HB" 1130242 T HB (NIL) -7 NIL NIL NIL) (-485 1123096 1129556 1129660 "HASHTBL" 1129665 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122572 1122817 1122909 "HASAST" 1123024 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120350 1122194 1122376 "HACKPI" 1122410 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1116018 1120203 1120316 "GTSET" 1120321 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109433 1115896 1115994 "GSTBL" 1115999 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101711 1108464 1108729 "GSERIES" 1109224 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100852 1101269 1101297 "GROUP" 1101500 T GROUP (NIL) -9 NIL 1101634 NIL) (-478 1100218 1100377 1100628 "GROUP-" 1100633 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098585 1098906 1099293 "GROEBSOL" 1099895 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097499 1097787 1097838 "GRMOD" 1098367 NIL GRMOD (NIL T T) -9 NIL 1098535 NIL) (-475 1097267 1097303 1097431 "GRMOD-" 1097436 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092557 1093621 1094621 "GRIMAGE" 1096287 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1091023 1091284 1091608 "GRDEF" 1092253 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090467 1090583 1090724 "GRAY" 1090902 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089654 1090060 1090111 "GRALG" 1090264 NIL GRALG (NIL T T) -9 NIL 1090357 NIL) (-470 1089315 1089388 1089551 "GRALG-" 1089556 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1086092 1088900 1089078 "GPOLSET" 1089222 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085446 1085503 1085761 "GOSPER" 1086029 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1081178 1081884 1082410 "GMODPOL" 1085145 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1080183 1080367 1080605 "GHENSEL" 1080990 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074339 1075182 1076202 "GENUPS" 1079267 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1074036 1074087 1074176 "GENUFACT" 1074282 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073448 1073525 1073690 "GENPGCD" 1073954 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072922 1072957 1073170 "GENMFACT" 1073407 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071488 1071745 1072052 "GENEEZ" 1072665 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065634 1071099 1071261 "GDMP" 1071411 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054976 1059405 1060511 "GCNAALG" 1064617 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053303 1054165 1054193 "GCDDOM" 1054448 T GCDDOM (NIL) -9 NIL 1054605 NIL) (-457 1052773 1052900 1053115 "GCDDOM-" 1053120 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051445 1051630 1051934 "GB" 1052552 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1040061 1042391 1044783 "GBINTERN" 1049136 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037898 1038190 1038611 "GBF" 1039736 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036679 1036844 1037111 "GBEUCLID" 1037714 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1036028 1036153 1036302 "GAUSSFAC" 1036550 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034395 1034697 1035011 "GALUTIL" 1035747 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032703 1032977 1033301 "GALPOLYU" 1034122 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1030068 1030358 1030765 "GALFACTU" 1032400 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021873 1023373 1024981 "GALFACT" 1028500 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1019261 1019919 1019947 "FVFUN" 1021103 T FVFUN (NIL) -9 NIL 1021823 NIL) (-446 1018527 1018709 1018737 "FVC" 1019028 T FVC (NIL) -9 NIL 1019211 NIL) (-445 1018170 1018352 1018420 "FUNDESC" 1018479 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017785 1017967 1018048 "FUNCTION" 1018122 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015529 1016107 1016573 "FT" 1017339 T FT (NIL) -8 NIL NIL NIL) (-442 1014320 1014830 1015033 "FTEM" 1015346 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012611 1012900 1013297 "FSUPFACT" 1014011 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1011008 1011297 1011629 "FST" 1012299 T FST (NIL) -8 NIL NIL NIL) (-439 1010207 1010313 1010501 "FSRED" 1010890 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008906 1009162 1009509 "FSPRMELT" 1009922 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1006212 1006650 1007136 "FSPECF" 1008469 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987850 996181 996222 "FS" 1000106 NIL FS (NIL T) -9 NIL 1002395 NIL) (-435 976493 979486 983543 "FS-" 983843 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 976021 976075 976245 "FSINT" 976434 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974313 975014 975317 "FSERIES" 975800 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973355 973471 973695 "FSCINT" 974193 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969563 972299 972340 "FSAGG" 972710 NIL FSAGG (NIL T) -9 NIL 972969 NIL) (-430 967325 967926 968722 "FSAGG-" 968817 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966367 966510 966737 "FSAGG2" 967178 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 964049 964329 964876 "FS2UPS" 966085 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963683 963726 963855 "FS2" 964000 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962561 962732 963034 "FS2EXPXP" 963508 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961987 962102 962254 "FRUTIL" 962441 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953400 957482 958840 "FR" 960661 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948369 951043 951083 "FRNAALG" 952479 NIL FRNAALG (NIL T) -9 NIL 953086 NIL) (-422 944042 945118 946393 "FRNAALG-" 947143 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943680 943723 943850 "FRNAAF2" 943993 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 942055 942529 942825 "FRMOD" 943492 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939798 940430 940748 "FRIDEAL" 941846 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938989 939076 939367 "FRIDEAL2" 939705 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 938122 938536 938577 "FRETRCT" 938582 NIL FRETRCT (NIL T) -9 NIL 938758 NIL) (-416 937234 937465 937816 "FRETRCT-" 937821 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934322 935532 935591 "FRAMALG" 936473 NIL FRAMALG (NIL T T) -9 NIL 936765 NIL) (-414 932456 932911 933541 "FRAMALG-" 933764 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926375 931929 932206 "FRAC" 932211 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 926011 926068 926175 "FRAC2" 926312 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925647 925704 925811 "FR2" 925948 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 920160 923053 923081 "FPS" 924200 T FPS (NIL) -9 NIL 924757 NIL) (-409 919609 919718 919882 "FPS-" 920028 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916911 918580 918608 "FPC" 918833 T FPC (NIL) -9 NIL 918975 NIL) (-407 916704 916744 916841 "FPC-" 916846 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915494 916192 916233 "FPATMAB" 916238 NIL FPATMAB (NIL T) -9 NIL 916390 NIL) (-405 913167 913670 914096 "FPARFRAC" 915131 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908561 909059 909741 "FORTRAN" 912599 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906277 906777 907316 "FORT" 908042 T FORT (NIL) -7 NIL NIL NIL) (-402 903953 904515 904543 "FORTFN" 905603 T FORTFN (NIL) -9 NIL 906227 NIL) (-401 903717 903767 903795 "FORTCAT" 903854 T FORTCAT (NIL) -9 NIL 903916 NIL) (-400 901823 902333 902723 "FORMULA" 903347 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901611 901641 901710 "FORMULA1" 901787 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 901134 901186 901359 "FORDER" 901553 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 900230 900394 900587 "FOP" 900961 T FOP (NIL) -7 NIL NIL NIL) (-396 898811 899510 899684 "FNLA" 900112 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897540 897955 897983 "FNCAT" 898443 T FNCAT (NIL) -9 NIL 898703 NIL) (-394 897079 897499 897527 "FNAME" 897532 T FNAME (NIL) -8 NIL NIL NIL) (-393 895642 896605 896633 "FMTC" 896638 T FMTC (NIL) -9 NIL 896674 NIL) (-392 894388 895578 895624 "FMONOID" 895629 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 891216 892384 892425 "FMONCAT" 893642 NIL FMONCAT (NIL T) -9 NIL 894247 NIL) (-390 890408 890958 891107 "FM" 891112 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887832 888478 888506 "FMFUN" 889650 T FMFUN (NIL) -9 NIL 890358 NIL) (-388 887101 887282 887310 "FMC" 887600 T FMC (NIL) -9 NIL 887782 NIL) (-387 884180 885040 885094 "FMCAT" 886289 NIL FMCAT (NIL T T) -9 NIL 886784 NIL) (-386 883046 883946 884046 "FM1" 884125 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880820 881236 881730 "FLOATRP" 882597 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874394 878549 879170 "FLOAT" 880219 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871832 872332 872910 "FLOATCP" 873861 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870572 871410 871451 "FLINEXP" 871456 NIL FLINEXP (NIL T) -9 NIL 871549 NIL) (-381 869726 869961 870289 "FLINEXP-" 870294 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868802 868946 869170 "FLASORT" 869578 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865918 866786 866838 "FLALG" 868065 NIL FLALG (NIL T T) -9 NIL 868532 NIL) (-378 859654 863404 863445 "FLAGG" 864707 NIL FLAGG (NIL T) -9 NIL 865359 NIL) (-377 858380 858719 859209 "FLAGG-" 859214 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857422 857565 857792 "FLAGG2" 858233 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854273 855281 855340 "FINRALG" 856468 NIL FINRALG (NIL T T) -9 NIL 856976 NIL) (-374 853433 853662 854001 "FINRALG-" 854006 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852813 853052 853080 "FINITE" 853276 T FINITE (NIL) -9 NIL 853383 NIL) (-372 845170 847357 847397 "FINAALG" 851064 NIL FINAALG (NIL T) -9 NIL 852517 NIL) (-371 840502 841552 842696 "FINAALG-" 844075 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839870 840257 840360 "FILE" 840432 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838528 838866 838920 "FILECAT" 839604 NIL FILECAT (NIL T T) -9 NIL 839820 NIL) (-368 836244 837772 837800 "FIELD" 837840 T FIELD (NIL) -9 NIL 837920 NIL) (-367 834864 835249 835760 "FIELD-" 835765 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832714 833499 833846 "FGROUP" 834550 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831804 831968 832188 "FGLMICPK" 832546 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827636 831729 831786 "FFX" 831791 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 827237 827298 827433 "FFSLPE" 827569 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 823227 824009 824805 "FFPOLY" 826473 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822731 822767 822976 "FFPOLY2" 823185 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818575 822650 822713 "FFP" 822718 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813973 818486 818550 "FF" 818555 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 809099 813316 813506 "FFNBX" 813827 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 804027 808234 808492 "FFNBP" 808953 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798660 803311 803522 "FFNB" 803860 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797492 797690 798005 "FFINTBAS" 798457 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793561 795781 795809 "FFIELDC" 796429 T FFIELDC (NIL) -9 NIL 796805 NIL) (-353 792223 792594 793091 "FFIELDC-" 793096 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791792 791838 791962 "FFHOM" 792165 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789487 789974 790491 "FFF" 791307 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 785105 789229 789330 "FFCGX" 789430 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780727 784837 784944 "FFCGP" 785048 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775910 780454 780562 "FFCG" 780663 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757306 766387 766473 "FFCAT" 771638 NIL FFCAT (NIL T T T) -9 NIL 773089 NIL) (-346 752503 753551 754865 "FFCAT-" 756095 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751914 751957 752192 "FFCAT2" 752454 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 741237 744886 746106 "FEXPR" 750766 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 740237 740672 740713 "FEVALAB" 740797 NIL FEVALAB (NIL T) -9 NIL 741058 NIL) (-342 739396 739606 739944 "FEVALAB-" 739949 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737962 738779 738982 "FDIV" 739295 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734982 735723 735838 "FDIVCAT" 737406 NIL FDIVCAT (NIL T T T T) -9 NIL 737843 NIL) (-339 734744 734771 734941 "FDIVCAT-" 734946 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733964 734051 734328 "FDIV2" 734651 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732938 733259 733461 "FCTRDATA" 733782 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731624 731883 732172 "FCPAK1" 732669 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730723 731124 731265 "FCOMP" 731515 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714428 717873 721411 "FC" 727205 T FC (NIL) -8 NIL NIL NIL) (-333 706791 710819 710859 "FAXF" 712661 NIL FAXF (NIL T) -9 NIL 713353 NIL) (-332 704067 704725 705550 "FAXF-" 706015 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 699119 703443 703619 "FARRAY" 703924 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 694013 696080 696133 "FAMR" 697156 NIL FAMR (NIL T T) -9 NIL 697616 NIL) (-329 692903 693205 693640 "FAMR-" 693645 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 692072 692825 692878 "FAMONOID" 692883 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689858 690568 690621 "FAMONC" 691562 NIL FAMONC (NIL T T) -9 NIL 691948 NIL) (-326 688522 689612 689749 "FAGROUP" 689754 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686317 686636 687039 "FACUTIL" 688203 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685416 685601 685823 "FACTFUNC" 686127 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677838 684719 684918 "EXPUPXS" 685272 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675321 675861 676447 "EXPRTUBE" 677272 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671592 672184 672914 "EXPRODE" 674660 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 657077 670241 670670 "EXPR" 671196 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651631 652218 653024 "EXPR2UPS" 656375 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 651263 651320 651429 "EXPR2" 651568 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642651 650414 650705 "EXPEXPAN" 651099 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642451 642608 642637 "EXIT" 642642 T EXIT (NIL) -8 NIL NIL NIL) (-315 641931 642175 642266 "EXITAST" 642380 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641558 641620 641733 "EVALCYC" 641863 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 641099 641217 641258 "EVALAB" 641428 NIL EVALAB (NIL T) -9 NIL 641532 NIL) (-312 640580 640702 640923 "EVALAB-" 640928 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637948 639250 639278 "EUCDOM" 639833 T EUCDOM (NIL) -9 NIL 640183 NIL) (-310 636353 636795 637385 "EUCDOM-" 637390 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623891 626651 629401 "ESTOOLS" 633623 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623523 623580 623689 "ESTOOLS2" 623828 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 623274 623316 623396 "ESTOOLS1" 623475 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617311 618919 618947 "ES" 621715 T ES (NIL) -9 NIL 623125 NIL) (-305 612258 613545 615362 "ES-" 615526 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608632 609393 610173 "ESCONT" 611498 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608377 608409 608491 "ESCONT1" 608594 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 608052 608102 608202 "ES2" 608321 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607682 607740 607849 "ES1" 607988 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606898 607027 607203 "ERROR" 607526 T ERROR (NIL) -7 NIL NIL NIL) (-299 600290 606757 606848 "EQTBL" 606853 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592793 595604 597053 "EQ" 598874 NIL -2099 (NIL T) -8 NIL NIL NIL) (-297 592425 592482 592591 "EQ2" 592730 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587715 588763 589856 "EP" 591364 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586315 586606 586912 "ENV" 587429 T ENV (NIL) -8 NIL NIL NIL) (-294 585409 585963 585991 "ENTIRER" 585996 T ENTIRER (NIL) -9 NIL 586042 NIL) (-293 581876 583364 583734 "EMR" 585208 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 581020 581205 581259 "ELTAGG" 581639 NIL ELTAGG (NIL T T) -9 NIL 581850 NIL) (-291 580739 580801 580942 "ELTAGG-" 580947 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580528 580557 580611 "ELTAB" 580695 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-289 579654 579800 579999 "ELFUTS" 580379 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579396 579452 579480 "ELEMFUN" 579585 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579266 579287 579355 "ELEMFUN-" 579360 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 574110 577366 577407 "ELAGG" 578347 NIL ELAGG (NIL T) -9 NIL 578810 NIL) (-285 572395 572829 573492 "ELAGG-" 573497 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571707 571844 572000 "ELABOR" 572259 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570368 570647 570941 "ELABEXPR" 571433 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563232 565035 565862 "EFUPXS" 569644 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556682 558483 559293 "EFULS" 562508 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554167 554525 554997 "EFSTRUC" 556314 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543958 545524 547072 "EF" 552682 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 543032 543443 543592 "EAB" 543829 T EAB (NIL) -8 NIL NIL NIL) (-277 542214 542991 543019 "E04UCFA" 543024 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541396 542173 542201 "E04NAFA" 542206 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540578 541355 541383 "E04MBFA" 541388 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539760 540537 540565 "E04JAFA" 540570 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538944 539719 539747 "E04GCFA" 539752 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 538128 538903 538931 "E04FDFA" 538936 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537310 538087 538115 "E04DGFA" 538120 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531483 532835 534199 "E04AGNT" 535966 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530163 530669 530709 "DVARCAT" 531184 NIL DVARCAT (NIL T) -9 NIL 531383 NIL) (-268 529367 529579 529893 "DVARCAT-" 529898 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522504 529166 529295 "DSMP" 529300 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517285 518449 519517 "DROPT" 521456 T DROPT (NIL) -8 NIL NIL NIL) (-265 516950 517009 517107 "DROPT1" 517220 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 512065 513191 514328 "DROPT0" 515833 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510410 510735 511121 "DRAWPT" 511699 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504997 505920 506999 "DRAW" 509384 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504630 504683 504801 "DRAWHACK" 504938 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503361 503630 503921 "DRAWCX" 504359 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502876 502945 503096 "DRAWCURV" 503287 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493344 495306 497421 "DRAWCFUN" 500781 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 490108 492037 492078 "DQAGG" 492707 NIL DQAGG (NIL T) -9 NIL 492981 NIL) (-256 478232 484701 484784 "DPOLCAT" 486636 NIL DPOLCAT (NIL T T T T) -9 NIL 487181 NIL) (-255 473068 474417 476375 "DPOLCAT-" 476380 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466190 472929 473027 "DPMO" 473032 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459215 465970 466137 "DPMM" 466142 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458693 458907 459005 "DOMTMPLT" 459137 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458126 458495 458575 "DOMCTOR" 458633 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457338 457606 457757 "DOMAIN" 457995 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451326 456973 457125 "DMP" 457239 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450926 450982 451126 "DLP" 451264 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444748 450253 450443 "DLIST" 450768 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441545 443601 443642 "DLAGG" 444192 NIL DLAGG (NIL T) -9 NIL 444422 NIL) (-245 440221 440885 440913 "DIVRING" 441005 T DIVRING (NIL) -9 NIL 441088 NIL) (-244 439458 439648 439948 "DIVRING-" 439953 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437560 437917 438323 "DISPLAY" 439072 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431448 437474 437537 "DIRPROD" 437542 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430296 430499 430764 "DIRPROD2" 431241 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419071 425077 425130 "DIRPCAT" 425540 NIL DIRPCAT (NIL NIL T) -9 NIL 426380 NIL) (-239 416397 417039 417920 "DIRPCAT-" 418257 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415684 415844 416030 "DIOSP" 416231 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412339 414596 414637 "DIOPS" 415071 NIL DIOPS (NIL T) -9 NIL 415300 NIL) (-236 411888 412002 412193 "DIOPS-" 412198 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410711 411339 411367 "DIFRING" 411554 T DIFRING (NIL) -9 NIL 411664 NIL) (-234 410357 410434 410586 "DIFRING-" 410591 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408093 409365 409406 "DIFEXT" 409769 NIL DIFEXT (NIL T) -9 NIL 410063 NIL) (-232 406378 406806 407472 "DIFEXT-" 407477 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403653 405910 405951 "DIAGG" 405956 NIL DIAGG (NIL T) -9 NIL 405976 NIL) (-230 403037 403194 403446 "DIAGG-" 403451 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398454 401996 402273 "DHMATRIX" 402806 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394066 394975 395985 "DFSFUN" 397464 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389145 392997 393309 "DFLOAT" 393774 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387408 387689 388078 "DFINTTLS" 388853 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384437 385429 385829 "DERHAM" 387074 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382238 384212 384301 "DEQUEUE" 384381 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381492 381625 381808 "DEGRED" 382100 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377922 378667 379513 "DEFINTRF" 380720 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375477 375946 376538 "DEFINTEF" 377441 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374827 375097 375212 "DEFAST" 375382 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368829 374420 374570 "DECIMAL" 374697 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366341 366799 367305 "DDFACT" 368373 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365937 365980 366131 "DBLRESP" 366292 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363809 364170 364530 "DBASE" 365704 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363051 363289 363435 "DATAARY" 363708 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362157 363010 363038 "D03FAFA" 363043 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361264 362116 362144 "D03EEFA" 362149 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359214 359680 360169 "D03AGNT" 360795 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358503 359173 359201 "D02EJFA" 359206 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357792 358462 358490 "D02CJFA" 358495 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357081 357751 357779 "D02BHFA" 357784 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356370 357040 357068 "D02BBFA" 357073 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349567 351156 352762 "D02AGNT" 354784 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347335 347858 348404 "D01WGTS" 349041 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346402 347294 347322 "D01TRNS" 347327 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345470 346361 346389 "D01GBFA" 346394 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344538 345429 345457 "D01FCFA" 345462 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343606 344497 344525 "D01ASFA" 344530 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342674 343565 343593 "D01AQFA" 343598 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341742 342633 342661 "D01APFA" 342666 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340810 341701 341729 "D01ANFA" 341734 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339878 340769 340797 "D01AMFA" 340802 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338946 339837 339865 "D01ALFA" 339870 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 338014 338905 338933 "D01AKFA" 338938 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337082 337973 338001 "D01AJFA" 338006 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330377 331930 333491 "D01AGNT" 335541 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329714 329842 329994 "CYCLOTOM" 330245 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326448 327162 327889 "CYCLES" 329007 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325760 325894 326065 "CVMP" 326309 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323601 323859 324228 "CTRIGMNP" 325488 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 323037 323395 323468 "CTOR" 323548 T CTOR (NIL) -8 NIL NIL NIL) (-188 322546 322768 322869 "CTORKIND" 322956 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321837 322153 322181 "CTORCAT" 322363 T CTORCAT (NIL) -9 NIL 322476 NIL) (-186 321435 321546 321705 "CTORCAT-" 321710 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320897 321109 321217 "CTORCALL" 321359 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320271 320370 320523 "CSTTOOLS" 320794 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316070 316727 317485 "CRFP" 319583 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315545 315791 315883 "CRCEAST" 315998 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314592 314777 315005 "CRAPACK" 315349 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313976 314077 314281 "CPMATCH" 314468 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313701 313729 313835 "CPIMA" 313942 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310049 310721 311440 "COORDSYS" 313036 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309461 309582 309724 "CONTOUR" 309927 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305352 307464 307956 "CONTFRAC" 309001 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305232 305253 305281 "CONDUIT" 305318 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304320 304874 304902 "COMRING" 304907 T COMRING (NIL) -9 NIL 304959 NIL) (-173 303374 303678 303862 "COMPPROP" 304156 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 303035 303070 303198 "COMPLPAT" 303333 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293326 302844 302953 "COMPLEX" 302958 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292962 293019 293126 "COMPLEX2" 293263 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292301 292422 292582 "COMPILER" 292822 T COMPILER (NIL) -8 NIL NIL NIL) (-168 292019 292054 292152 "COMPFACT" 292260 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276099 286093 286133 "COMPCAT" 287137 NIL COMPCAT (NIL T) -9 NIL 288485 NIL) (-166 265611 268538 272165 "COMPCAT-" 272521 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265340 265368 265471 "COMMUPC" 265577 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265134 265168 265227 "COMMONOP" 265301 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264690 264885 264972 "COMM" 265067 T COMM (NIL) -8 NIL NIL NIL) (-162 264266 264494 264569 "COMMAAST" 264635 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263515 263709 263737 "COMBOPC" 264075 T COMBOPC (NIL) -9 NIL 264250 NIL) (-160 262411 262621 262863 "COMBINAT" 263305 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258868 259442 260069 "COMBF" 261833 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257626 257984 258219 "COLOR" 258653 T COLOR (NIL) -8 NIL NIL NIL) (-157 257102 257347 257439 "COLONAST" 257554 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256742 256789 256914 "CMPLXRT" 257049 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256190 256442 256541 "CLLCTAST" 256663 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251689 252720 253800 "CLIP" 255130 T CLIP (NIL) -7 NIL NIL NIL) (-153 250030 250790 251030 "CLIF" 251516 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246205 248176 248217 "CLAGG" 249146 NIL CLAGG (NIL T) -9 NIL 249682 NIL) (-151 244627 245084 245667 "CLAGG-" 245672 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244171 244256 244396 "CINTSLPE" 244536 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241672 242143 242691 "CHVAR" 243699 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240846 241400 241428 "CHARZ" 241433 T CHARZ (NIL) -9 NIL 241448 NIL) (-147 240600 240640 240718 "CHARPOL" 240800 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239658 240245 240273 "CHARNZ" 240320 T CHARNZ (NIL) -9 NIL 240376 NIL) (-145 237564 238312 238665 "CHAR" 239325 T CHAR (NIL) -8 NIL NIL NIL) (-144 237290 237351 237379 "CFCAT" 237490 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236531 236642 236825 "CDEN" 237174 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232496 235684 235964 "CCLASS" 236271 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231747 231904 232081 "CATEGORY" 232339 T -10 (NIL) -8 NIL NIL NIL) (-140 231320 231666 231714 "CATCTOR" 231719 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230771 231023 231121 "CATAST" 231242 T CATAST (NIL) -8 NIL NIL NIL) (-138 230247 230492 230584 "CASEAST" 230699 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225256 226276 227029 "CARTEN" 229550 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224364 224512 224733 "CARTEN2" 225103 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222680 223514 223771 "CARD" 224127 T CARD (NIL) -8 NIL NIL NIL) (-134 222256 222484 222559 "CAPSLAST" 222625 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221760 221968 221996 "CACHSET" 222128 T CACHSET (NIL) -9 NIL 222206 NIL) (-132 221230 221552 221580 "CABMON" 221630 T CABMON (NIL) -9 NIL 221686 NIL) (-131 220703 220934 221044 "BYTEORD" 221140 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219685 220237 220379 "BYTE" 220542 T BYTE (NIL) -8 NIL NIL 220664) (-129 215035 219190 219362 "BYTEBUF" 219533 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212544 214727 214834 "BTREE" 214961 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 209993 212192 212314 "BTOURN" 212454 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207363 209463 209504 "BTCAT" 209572 NIL BTCAT (NIL T) -9 NIL 209649 NIL) (-125 207030 207110 207259 "BTCAT-" 207264 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202440 206319 206347 "BTAGG" 206461 T BTAGG (NIL) -9 NIL 206571 NIL) (-123 201930 202055 202261 "BTAGG-" 202266 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198925 201208 201423 "BSTREE" 201747 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198063 198189 198373 "BRILL" 198781 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194715 196789 196830 "BRAGG" 197479 NIL BRAGG (NIL T) -9 NIL 197737 NIL) (-119 193244 193650 194205 "BRAGG-" 194210 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186471 192588 192773 "BPADICRT" 193091 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184786 186408 186453 "BPADIC" 186458 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184484 184514 184628 "BOUNDZRO" 184750 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179712 180910 181822 "BOP" 183592 T BOP (NIL) -8 NIL NIL NIL) (-114 177493 177897 178372 "BOP1" 179270 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177194 177255 177283 "BOOLE" 177394 T BOOLE (NIL) -9 NIL 177476 NIL) (-112 176019 176768 176917 "BOOLEAN" 177065 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175298 175702 175756 "BMODULE" 175761 NIL BMODULE (NIL T T) -9 NIL 175826 NIL) (-110 171099 175096 175169 "BITS" 175245 T BITS (NIL) -8 NIL NIL NIL) (-109 170520 170639 170779 "BINDING" 170979 T BINDING (NIL) -8 NIL NIL NIL) (-108 164525 170115 170264 "BINARY" 170391 T BINARY (NIL) -8 NIL NIL NIL) (-107 162305 163780 163821 "BGAGG" 164081 NIL BGAGG (NIL T) -9 NIL 164218 NIL) (-106 162136 162168 162259 "BGAGG-" 162264 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161207 161520 161725 "BFUNCT" 161951 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159897 160075 160363 "BEZOUT" 161031 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156366 158749 159079 "BBTREE" 159600 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156100 156153 156181 "BASTYPE" 156300 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155952 155981 156054 "BASTYPE-" 156059 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155386 155462 155614 "BALFACT" 155863 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154242 154801 154987 "AUTOMOR" 155231 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153968 153973 153999 "ATTREG" 154004 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152220 152665 153017 "ATTRBUT" 153634 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151828 152048 152114 "ATTRAST" 152172 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151364 151477 151503 "ATRIG" 151704 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151173 151214 151301 "ATRIG-" 151306 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150818 151004 151030 "ASTCAT" 151035 T ASTCAT (NIL) -9 NIL 151065 NIL) (-92 150545 150604 150723 "ASTCAT-" 150728 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148694 150321 150409 "ASTACK" 150488 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147199 147496 147861 "ASSOCEQ" 148376 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146231 146858 146982 "ASP9" 147106 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145994 146179 146218 "ASP8" 146223 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144862 145599 145741 "ASP80" 145883 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143760 144497 144629 "ASP7" 144761 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142714 143437 143555 "ASP78" 143673 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141683 142394 142511 "ASP77" 142628 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140595 141321 141452 "ASP74" 141583 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139495 140230 140362 "ASP73" 140494 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138599 139321 139421 "ASP6" 139426 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137544 138276 138394 "ASP55" 138512 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136493 137218 137337 "ASP50" 137456 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135581 136194 136304 "ASP4" 136414 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134669 135282 135392 "ASP49" 135502 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133453 134208 134376 "ASP42" 134558 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132229 132986 133156 "ASP41" 133340 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131179 131906 132024 "ASP35" 132142 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130944 131127 131166 "ASP34" 131171 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130681 130748 130824 "ASP33" 130899 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129574 130316 130448 "ASP31" 130580 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129339 129522 129561 "ASP30" 129566 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129074 129143 129219 "ASP29" 129294 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128839 129022 129061 "ASP28" 129066 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128604 128787 128826 "ASP27" 128831 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127688 128302 128413 "ASP24" 128524 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126764 127490 127602 "ASP20" 127607 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125852 126465 126575 "ASP1" 126685 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124794 125526 125645 "ASP19" 125764 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124531 124598 124674 "ASP12" 124749 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123383 124130 124274 "ASP10" 124418 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121234 123227 123318 "ARRAY2" 123323 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116999 120882 120996 "ARRAY1" 121151 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116031 116204 116425 "ARRAY12" 116822 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110343 112261 112336 "ARR2CAT" 114966 NIL ARR2CAT (NIL T T T) -9 NIL 115724 NIL) (-56 107777 108521 109475 "ARR2CAT-" 109480 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107094 107404 107529 "ARITY" 107670 T ARITY (NIL) -8 NIL NIL NIL) (-54 105870 106022 106321 "APPRULE" 106930 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105521 105569 105688 "APPLYORE" 105816 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104875 105114 105234 "ANY" 105419 T ANY (NIL) -8 NIL NIL NIL) (-51 104153 104276 104433 "ANY1" 104749 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101683 102590 102917 "ANTISYM" 103877 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101175 101390 101486 "ANON" 101605 T ANON (NIL) -8 NIL NIL NIL) (-48 95424 99714 100168 "AN" 100739 T AN (NIL) -8 NIL NIL NIL) (-47 91322 92710 92761 "AMR" 93509 NIL AMR (NIL T T) -9 NIL 94109 NIL) (-46 90434 90655 91018 "AMR-" 91023 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74873 90351 90412 "ALIST" 90417 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71676 74467 74636 "ALGSC" 74791 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68231 68786 69393 "ALGPKG" 71116 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67508 67609 67793 "ALGMFACT" 68117 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63543 64122 64716 "ALGMANIP" 67092 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54913 63169 63319 "ALGFF" 63476 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54109 54240 54419 "ALGFACT" 54771 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53050 53650 53688 "ALGEBRA" 53693 NIL ALGEBRA (NIL T) -9 NIL 53734 NIL) (-37 52768 52827 52959 "ALGEBRA-" 52964 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34861 50770 50822 "ALAGG" 50958 NIL ALAGG (NIL T T) -9 NIL 51119 NIL) (-35 34397 34510 34536 "AHYP" 34737 T AHYP (NIL) -9 NIL NIL NIL) (-34 33328 33576 33602 "AGG" 34101 T AGG (NIL) -9 NIL 34380 NIL) (-33 32762 32924 33138 "AGG-" 33143 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30568 30991 31396 "AF" 32404 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30048 30293 30383 "ADDAST" 30496 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29316 29575 29731 "ACPLOT" 29910 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18639 26443 26481 "ACFS" 27088 NIL ACFS (NIL T) -9 NIL 27327 NIL) (-28 16666 17156 17918 "ACFS-" 17923 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14713 14739 "ACF" 15618 T ACF (NIL) -9 NIL 16031 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 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 6b307f17..16f49c90 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,65 +1,69 @@ -(733502 . 3480528376) -(((*1 *1 *2) - (-12 (-5 *2 (-650 *3)) (-4 *3 (-1226)) (-5 *1 (-1166 *3))))) -(((*1 *2 *1 *1) - (-12 - (-5 *2 - (-2 (|:| -1939 *3) (|:| |coef1| (-788 *3)) (|:| |coef2| (-788 *3)))) - (-5 *1 (-788 *3)) (-4 *3 (-562)) (-4 *3 (-1058))))) -(((*1 *2 *1) (-12 (-4 *1 (-803 *2)) (-4 *2 (-174))))) +(733547 . 3480551178) +(((*1 *2 *1) + (-12 (-4 *1 (-378 *3)) (-4 *3 (-1227)) (-4 *3 (-856)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *1 (-378 *4)) (-4 *4 (-1227)) + (-5 *2 (-112))))) +(((*1 *1 *1) (-12 (-4 *1 (-436 *2)) (-4 *2 (-1109)) (-4 *2 (-562)))) + ((*1 *1 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-562))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-650 (-52))) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) +(((*1 *2 *2) + (-12 (-4 *3 (-1058)) (-5 *1 (-718 *3 *2)) (-4 *2 (-1253 *3))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-650 (-788 *3))) (-5 *1 (-788 *3)) (-4 *3 (-562)) - (-4 *3 (-1058))))) -(((*1 *2 *1 *2) (-12 (-5 *1 (-1035 *2)) (-4 *2 (-1226))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-650 (-650 (-650 *4)))) (-5 *3 (-650 *4)) (-4 *4 (-856)) - (-5 *1 (-1197 *4))))) -(((*1 *1 *1 *2 *2) - (|partial| -12 (-5 *2 (-928)) (-5 *1 (-1110 *3 *4)) (-14 *3 *2) - (-14 *4 *2)))) + (-12 (-4 *1 (-1107 *3)) (-4 *3 (-1109)) (-5 *2 (-112))))) +(((*1 *1) (-5 *1 (-158))) + ((*1 *2 *1) (-12 (-4 *1 (-1053 *2)) (-4 *2 (-23))))) +(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-933))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) +(((*1 *2 *3 *4 *4 *4 *3 *3 *5 *5 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *5 (-227)) + (-5 *2 (-1044)) (-5 *1 (-757))))) +(((*1 *2 *3 *4 *4 *5 *3 *3 *4 *3) + (-12 (-5 *3 (-570)) (-5 *5 (-695 (-227))) (-5 *4 (-227)) + (-5 *2 (-1044)) (-5 *1 (-758))))) (((*1 *1 *1 *1) (-4 *1 (-667)))) (((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-448 *3)) (-4 *3 (-1252 (-570)))))) + (-12 (-5 *2 (-112)) (-5 *1 (-1204 *3 *4)) (-4 *3 (-1109)) + (-4 *4 (-1109))))) +(((*1 *2 *3) (-12 (-5 *3 (-950 *2)) (-5 *1 (-991 *2)) (-4 *2 (-1058))))) +(((*1 *2 *1) + (-12 (-5 *2 (-697 (-879 (-973 *3) (-973 *3)))) (-5 *1 (-973 *3)) + (-4 *3 (-1109))))) +(((*1 *2 *1 *3) + (|partial| -12 (-5 *3 (-1186)) (-4 *4 (-1058)) (-4 *4 (-1109)) + (-5 *2 (-2 (|:| |var| (-618 *1)) (|:| -3011 (-570)))) + (-4 *1 (-436 *4)))) + ((*1 *2 *1 *3) + (|partial| -12 (-5 *3 (-115)) (-4 *4 (-1058)) (-4 *4 (-1109)) + (-5 *2 (-2 (|:| |var| (-618 *1)) (|:| -3011 (-570)))) + (-4 *1 (-436 *4)))) + ((*1 *2 *1) + (|partial| -12 (-4 *3 (-1121)) (-4 *3 (-1109)) + (-5 *2 (-2 (|:| |var| (-618 *1)) (|:| -3011 (-570)))) + (-4 *1 (-436 *3)))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-2 (|:| |val| (-899 *3)) (|:| -3011 (-777)))) + (-5 *1 (-899 *3)) (-4 *3 (-1109)))) + ((*1 *2 *1) + (|partial| -12 (-4 *1 (-956 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-799)) + (-4 *5 (-856)) (-5 *2 (-2 (|:| |var| *5) (|:| -3011 (-777)))))) + ((*1 *2 *3) + (|partial| -12 (-4 *4 (-799)) (-4 *5 (-856)) (-4 *6 (-1058)) + (-4 *7 (-956 *6 *4 *5)) + (-5 *2 (-2 (|:| |var| *5) (|:| -3011 (-570)))) + (-5 *1 (-957 *4 *5 *6 *7 *3)) + (-4 *3 + (-13 (-368) + (-10 -8 (-15 -3735 ($ *7)) (-15 -4399 (*7 $)) + (-15 -4413 (*7 $)))))))) (((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-448 *3)) (-4 *3 (-1252 (-570)))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1 (-950 *3) (-950 *3))) (-5 *1 (-178 *3)) - (-4 *3 (-13 (-368) (-1211) (-1011))))) - ((*1 *2) - (|partial| -12 (-4 *4 (-1230)) (-4 *5 (-1252 (-413 *2))) - (-4 *2 (-1252 *4)) (-5 *1 (-346 *3 *4 *2 *5)) - (-4 *3 (-347 *4 *2 *5)))) - ((*1 *2) - (|partial| -12 (-4 *1 (-347 *3 *2 *4)) (-4 *3 (-1230)) - (-4 *4 (-1252 (-413 *2))) (-4 *2 (-1252 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-650 *2)) (-4 *2 (-436 *4)) (-5 *1 (-159 *4 *2)) - (-4 *4 (-562))))) -(((*1 *2 *3) - (-12 (-5 *3 (-928)) (-5 *2 (-1182 *4)) (-5 *1 (-594 *4)) - (-4 *4 (-354))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-562) (-148))) (-5 *1 (-543 *3 *2)) - (-4 *2 (-1267 *3)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-368) (-373) (-620 (-570)))) (-4 *4 (-1252 *3)) - (-4 *5 (-730 *3 *4)) (-5 *1 (-547 *3 *4 *5 *2)) (-4 *2 (-1267 *5)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-368) (-373) (-620 (-570)))) (-5 *1 (-548 *3 *2)) - (-4 *2 (-1267 *3)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1166 *3)) (-4 *3 (-13 (-562) (-148))) - (-5 *1 (-1162 *3))))) -(((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-330 *3 *4)) (-4 *3 (-1058)) - (-4 *4 (-798))))) -(((*1 *2 *3) - (-12 (-5 *3 (-650 *2)) (-4 *2 (-1252 *4)) (-5 *1 (-545 *4 *2 *5 *6)) - (-4 *4 (-311)) (-14 *5 *4) (-14 *6 (-1 *4 *4 (-777)))))) + (-12 (-4 *3 (-562)) (-5 *2 (-650 *4)) (-5 *1 (-43 *3 *4)) + (-4 *4 (-423 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-1134 (-570) (-618 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) - (-12 (-4 *3 (-1001 *2)) (-4 *4 (-1252 *3)) (-4 *2 (-311)) + (-12 (-4 *3 (-1001 *2)) (-4 *4 (-1253 *3)) (-4 *2 (-311)) (-5 *1 (-419 *2 *3 *4 *5)) (-4 *5 (-13 (-415 *3 *4) (-1047 *3))))) ((*1 *2 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1109)) (-5 *2 (-1134 *3 (-618 *1))) @@ -72,53 +76,47 @@ (-12 (-4 *4 (-174)) (-4 *2 (|SubsetCategory| (-732) *4)) (-5 *1 (-668 *3 *4 *2)) (-4 *3 (-723 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-562))))) -(((*1 *2 *3) (-12 (-5 *3 (-650 (-52))) (-5 *2 (-1281)) (-5 *1 (-869))))) -(((*1 *1 *1) (-12 (-4 *1 (-120 *2)) (-4 *2 (-1226)))) +(((*1 *2 *3) (-12 (-5 *3 (-650 (-52))) (-5 *2 (-1282)) (-5 *1 (-869))))) +(((*1 *1 *1) (-12 (-4 *1 (-120 *2)) (-4 *2 (-1227)))) ((*1 *1 *1) (-12 (-5 *1 (-678 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-683 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-5 *1 (-868))) ((*1 *1 *1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-868)))) ((*1 *2 *1) (-12 (-4 *2 (-13 (-854) (-368))) (-5 *1 (-1070 *2 *3)) - (-4 *3 (-1252 *2))))) -(((*1 *2 *1 *2 *3) - (|partial| -12 (-5 *2 (-1168)) (-5 *3 (-570)) (-5 *1 (-1072))))) + (-4 *3 (-1253 *2))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-413 (-570))) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-562)) (-4 *8 (-956 *7 *5 *6)) + (-5 *2 (-2 (|:| -3011 (-777)) (|:| -1442 *9) (|:| |radicand| *9))) + (-5 *1 (-960 *5 *6 *7 *8 *9)) (-5 *4 (-777)) + (-4 *9 + (-13 (-368) + (-10 -8 (-15 -3735 ($ *8)) (-15 -4399 (*8 $)) (-15 -4413 (*8 $)))))))) +(((*1 *1 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-868))))) +(((*1 *2 *3 *2) (-12 (-5 *3 (-777)) (-5 *1 (-862 *2)) (-4 *2 (-174)))) + ((*1 *2 *3) + (-12 (-5 *2 (-1182 (-570))) (-5 *1 (-949)) (-5 *3 (-570))))) (((*1 *2 *3) - (-12 (-4 *4 (-799)) - (-4 *5 (-13 (-856) (-10 -8 (-15 -1416 ((-1186) $))))) (-4 *6 (-562)) - (-5 *2 (-2 (|:| -3947 (-959 *6)) (|:| -1718 (-959 *6)))) - (-5 *1 (-738 *4 *5 *6 *3)) (-4 *3 (-956 (-413 (-959 *6)) *4 *5))))) + (-12 (-4 *2 (-368)) (-4 *2 (-854)) (-5 *1 (-952 *2 *3)) + (-4 *3 (-1253 *2))))) +(((*1 *2 *3 *3 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) +(((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-849 *3)) (-4 *3 (-1109))))) (((*1 *1 *1 *1) (-4 *1 (-667)))) -(((*1 *1 *1) (-5 *1 (-1072)))) -(((*1 *2 *3) - (-12 (-5 *3 (-650 (-618 *5))) (-4 *4 (-1109)) (-5 *2 (-618 *5)) - (-5 *1 (-579 *4 *5)) (-4 *5 (-436 *4))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-512)) (-5 *2 (-650 (-972))) (-5 *1 (-295))))) -(((*1 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1011)))))) -(((*1 *2 *3) - (-12 (-4 *4 (-916)) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *7 (-956 *4 *5 *6)) (-5 *2 (-424 (-1182 *7))) - (-5 *1 (-913 *4 *5 *6 *7)) (-5 *3 (-1182 *7)))) - ((*1 *2 *3) - (-12 (-4 *4 (-916)) (-4 *5 (-1252 *4)) (-5 *2 (-424 (-1182 *5))) - (-5 *1 (-914 *4 *5)) (-5 *3 (-1182 *5))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-950 *4)) (-4 *4 (-1058)) (-5 *1 (-1174 *3 *4)) - (-14 *3 (-928))))) -(((*1 *2 *2) - (-12 (-5 *2 (-950 *3)) (-4 *3 (-13 (-368) (-1211) (-1011))) - (-5 *1 (-178 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1276 *1)) (-5 *4 (-1 *5 *5)) (-4 *5 (-368)) - (-4 *1 (-730 *5 *6)) (-4 *5 (-174)) (-4 *6 (-1252 *5)) - (-5 *2 (-695 *5))))) + (-12 (-4 *5 (-368)) (-4 *7 (-1253 *5)) (-4 *4 (-730 *5 *7)) + (-5 *2 (-2 (|:| -2042 (-695 *6)) (|:| |vec| (-1277 *5)))) + (-5 *1 (-817 *5 *6 *7 *4 *3)) (-4 *6 (-662 *5)) (-4 *3 (-662 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-650 (-849 (-227)))) (-5 *4 (-227)) (-5 *2 (-650 *4)) + (-5 *1 (-270))))) (((*1 *2 *1) (-12 (-5 *2 (-1134 (-570) (-618 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) - (-12 (-4 *3 (-311)) (-4 *4 (-1001 *3)) (-4 *5 (-1252 *4)) - (-5 *2 (-1276 *6)) (-5 *1 (-419 *3 *4 *5 *6)) + (-12 (-4 *3 (-311)) (-4 *4 (-1001 *3)) (-4 *5 (-1253 *4)) + (-5 *2 (-1277 *6)) (-5 *1 (-419 *3 *4 *5 *6)) (-4 *6 (-13 (-415 *4 *5) (-1047 *4))))) ((*1 *2 *1) (-12 (-4 *3 (-1058)) (-4 *3 (-1109)) (-5 *2 (-1134 *3 (-618 *1))) @@ -131,31 +129,32 @@ (-12 (-4 *3 (-174)) (-4 *2 (-723 *3)) (-5 *1 (-668 *2 *3 *4)) (-4 *4 (|SubsetCategory| (-732) *3)))) ((*1 *2 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-562))))) -(((*1 *1 *1) (-12 (-4 *1 (-120 *2)) (-4 *2 (-1226)))) +(((*1 *1 *1) (-12 (-4 *1 (-120 *2)) (-4 *2 (-1227)))) ((*1 *1 *1) (-12 (-5 *1 (-678 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-683 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-5 *1 (-868))) ((*1 *1 *1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-868)))) ((*1 *2 *1) (-12 (-4 *2 (-13 (-854) (-368))) (-5 *1 (-1070 *2 *3)) - (-4 *3 (-1252 *2))))) -(((*1 *1 *1) (-12 (-4 *1 (-1267 *2)) (-4 *2 (-1058))))) -(((*1 *2 *1) (-12 (-4 *1 (-372 *2)) (-4 *2 (-174))))) -(((*1 *2 *1) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1206))))) -(((*1 *2 *2 *3 *2) - (-12 (-5 *2 (-695 *3)) (-4 *3 (-1058)) (-5 *1 (-696 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-825 *4)) (-4 *4 (-856)) (-5 *2 (-112)) - (-5 *1 (-678 *4))))) -(((*1 *1 *2 *3) - (-12 (-5 *1 (-655 *2 *3 *4)) (-4 *2 (-1109)) (-4 *3 (-23)) - (-14 *4 *3)))) -(((*1 *1 *1 *1) (-4 *1 (-144))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-159 *3 *2)) (-4 *2 (-436 *3)))) - ((*1 *2 *2 *2) (-12 (-5 *1 (-160 *2)) (-4 *2 (-551))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-486))))) + (-4 *3 (-1253 *2))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1191))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-413 (-570))) (-5 *1 (-601 *3)) (-4 *3 (-38 *2)) + (-4 *3 (-1058))))) +(((*1 *2 *1) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1207))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-695 (-171 (-413 (-570))))) (-5 *2 (-650 (-171 *4))) + (-5 *1 (-770 *4)) (-4 *4 (-13 (-368) (-854)))))) +(((*1 *1) (-5 *1 (-142)))) +(((*1 *1 *1 *2) (-12 (-4 *1 (-1153)) (-5 *2 (-142)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-1153)) (-5 *2 (-145))))) +(((*1 *2 *3) (-12 (-5 *3 (-777)) (-5 *2 (-384)) (-5 *1 (-1049))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-1166 (-650 (-570)))) (-5 *3 (-650 (-570))) + (-5 *1 (-890))))) +(((*1 *1 *1) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856))))) (((*1 *1 *2) (-12 (-5 *2 (-650 (-570))) (-5 *1 (-50 *3 *4)) (-4 *3 (-1058)) (-14 *4 (-650 (-1186))))) @@ -163,11 +162,11 @@ (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) ((*1 *2 *2) - (-12 (-4 *3 (-38 (-413 (-570)))) (-4 *4 (-1267 *3)) - (-5 *1 (-281 *3 *4 *2)) (-4 *2 (-1238 *3 *4)))) + (-12 (-4 *3 (-38 (-413 (-570)))) (-4 *4 (-1268 *3)) + (-5 *1 (-281 *3 *4 *2)) (-4 *2 (-1239 *3 *4)))) ((*1 *2 *2) - (-12 (-4 *3 (-38 (-413 (-570)))) (-4 *4 (-1236 *3)) - (-5 *1 (-282 *3 *4 *2 *5)) (-4 *2 (-1259 *3 *4)) (-4 *5 (-992 *4)))) + (-12 (-4 *3 (-38 (-413 (-570)))) (-4 *4 (-1237 *3)) + (-5 *1 (-282 *3 *4 *2 *5)) (-4 *2 (-1260 *3 *4)) (-4 *5 (-992 *4)))) ((*1 *1 *1) (-4 *1 (-288))) ((*1 *1 *1) (-12 (-5 *1 (-344 *2 *3 *4)) (-14 *2 (-650 (-1186))) @@ -184,32 +183,70 @@ (-5 *1 (-1172 *3)))) ((*1 *2 *2 *3) (-12 (-5 *3 (-777)) (-4 *4 (-13 (-1058) (-723 (-413 (-570))))) - (-4 *5 (-856)) (-5 *1 (-1292 *4 *5 *2)) (-4 *2 (-1297 *5 *4)))) + (-4 *5 (-856)) (-5 *1 (-1293 *4 *5 *2)) (-4 *2 (-1298 *5 *4)))) ((*1 *1 *1 *2) - (-12 (-5 *2 (-777)) (-5 *1 (-1296 *3 *4)) + (-12 (-5 *2 (-777)) (-5 *1 (-1297 *3 *4)) (-4 *4 (-723 (-413 (-570)))) (-4 *3 (-856)) (-4 *4 (-174))))) -(((*1 *2 *2) - (-12 (-4 *3 (-458)) (-5 *1 (-1217 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1211)))))) +(((*1 *2) (-12 (-5 *2 (-650 (-928))) (-5 *1 (-1280)))) + ((*1 *2 *2) (-12 (-5 *2 (-650 (-928))) (-5 *1 (-1280))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-298 (-849 *3))) (-4 *3 (-13 (-27) (-1212) (-436 *5))) + (-4 *5 (-13 (-458) (-1047 (-570)) (-645 (-570)))) + (-5 *2 + (-3 (-849 *3) + (-2 (|:| |leftHandLimit| (-3 (-849 *3) "failed")) + (|:| |rightHandLimit| (-3 (-849 *3) "failed"))) + "failed")) + (-5 *1 (-642 *5 *3)))) + ((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *4 (-298 *3)) (-5 *5 (-1168)) + (-4 *3 (-13 (-27) (-1212) (-436 *6))) + (-4 *6 (-13 (-458) (-1047 (-570)) (-645 (-570)))) + (-5 *2 (-849 *3)) (-5 *1 (-642 *6 *3)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-298 (-849 (-959 *5)))) (-4 *5 (-458)) + (-5 *2 + (-3 (-849 (-413 (-959 *5))) + (-2 (|:| |leftHandLimit| (-3 (-849 (-413 (-959 *5))) "failed")) + (|:| |rightHandLimit| (-3 (-849 (-413 (-959 *5))) "failed"))) + "failed")) + (-5 *1 (-643 *5)) (-5 *3 (-413 (-959 *5))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-298 (-413 (-959 *5)))) (-5 *3 (-413 (-959 *5))) + (-4 *5 (-458)) + (-5 *2 + (-3 (-849 *3) + (-2 (|:| |leftHandLimit| (-3 (-849 *3) "failed")) + (|:| |rightHandLimit| (-3 (-849 *3) "failed"))) + "failed")) + (-5 *1 (-643 *5)))) + ((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *4 (-298 (-413 (-959 *6)))) (-5 *5 (-1168)) + (-5 *3 (-413 (-959 *6))) (-4 *6 (-458)) (-5 *2 (-849 *3)) + (-5 *1 (-643 *6))))) (((*1 *1 *1) (-5 *1 (-542)))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-570)) (-5 *1 (-424 *2)) (-4 *2 (-562))))) +(((*1 *1 *1) (-5 *1 (-1072)))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-562)) (-4 *3 (-1058)) + (-5 *2 (-2 (|:| -3389 *1) (|:| -3831 *1))) (-4 *1 (-858 *3)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-99 *5)) (-4 *5 (-562)) (-4 *5 (-1058)) + (-5 *2 (-2 (|:| -3389 *3) (|:| -3831 *3))) (-5 *1 (-859 *5 *3)) + (-4 *3 (-858 *5))))) (((*1 *2 *1) - (-12 (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *2 (-650 *1)) - (-4 *1 (-1074 *3 *4 *5))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-384) (-384))) (-5 *4 (-384)) - (-5 *2 - (-2 (|:| -2195 *4) (|:| -3578 *4) (|:| |totalpts| (-570)) - (|:| |success| (-112)))) - (-5 *1 (-795)) (-5 *5 (-570))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -1874 *3))) - (-5 *1 (-978 *4 *3)) (-4 *3 (-1252 *4))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1188 (-413 (-570)))) (-5 *1 (-192)) (-5 *3 (-570))))) -(((*1 *1 *2 *3) (-12 (-5 *2 (-512)) (-5 *3 (-603)) (-5 *1 (-591))))) + (|partial| -12 + (-5 *2 (-2 (|:| -3854 (-115)) (|:| |arg| (-650 (-899 *3))))) + (-5 *1 (-899 *3)) (-4 *3 (-1109)))) + ((*1 *2 *1 *3) + (|partial| -12 (-5 *3 (-115)) (-5 *2 (-650 (-899 *4))) + (-5 *1 (-899 *4)) (-4 *4 (-1109))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-368)) (-5 *1 (-772 *2 *3)) (-4 *2 (-714 *3)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-858 *2)) (-4 *2 (-1058)) (-4 *2 (-368))))) +(((*1 *1 *1) + (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) (((*1 *2 *3) - (|partial| -12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1226)))) + (|partial| -12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) (|partial| -12 (-5 *2 (-959 (-384))) (-5 *1 (-344 *3 *4 *5)) (-4 *5 (-1047 (-384))) (-14 *3 (-650 (-1186))) @@ -262,47 +299,47 @@ ((*1 *1 *2) (|partial| -12 (-5 *2 (-320 (-570))) (-4 *1 (-402)))) ((*1 *1 *2) (|partial| -12 (-5 *2 (-320 (-384))) (-4 *1 (-402)))) ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1276 (-413 (-959 (-570))))) (-4 *1 (-447)))) + (|partial| -12 (-5 *2 (-1277 (-413 (-959 (-570))))) (-4 *1 (-447)))) ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1276 (-413 (-959 (-384))))) (-4 *1 (-447)))) + (|partial| -12 (-5 *2 (-1277 (-413 (-959 (-384))))) (-4 *1 (-447)))) ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1276 (-959 (-570)))) (-4 *1 (-447)))) + (|partial| -12 (-5 *2 (-1277 (-959 (-570)))) (-4 *1 (-447)))) ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1276 (-959 (-384)))) (-4 *1 (-447)))) + (|partial| -12 (-5 *2 (-1277 (-959 (-384)))) (-4 *1 (-447)))) ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1276 (-320 (-570)))) (-4 *1 (-447)))) + (|partial| -12 (-5 *2 (-1277 (-320 (-570)))) (-4 *1 (-447)))) ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1276 (-320 (-384)))) (-4 *1 (-447)))) + (|partial| -12 (-5 *2 (-1277 (-320 (-384)))) (-4 *1 (-447)))) ((*1 *2 *3) - (|partial| -12 (-4 *4 (-354)) (-4 *5 (-333 *4)) (-4 *6 (-1252 *5)) + (|partial| -12 (-4 *4 (-354)) (-4 *5 (-333 *4)) (-4 *6 (-1253 *5)) (-5 *2 (-1182 (-1182 *4))) (-5 *1 (-783 *4 *5 *6 *3 *7)) - (-4 *3 (-1252 *6)) (-14 *7 (-928)))) + (-4 *3 (-1253 *6)) (-14 *7 (-928)))) ((*1 *1 *2) (|partial| -12 (-5 *2 (-650 *6)) (-4 *6 (-1074 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) (-4 *1 (-985 *3 *4 *5 *6)))) - ((*1 *2 *1) (|partial| -12 (-4 *1 (-1047 *2)) (-4 *2 (-1226)))) + ((*1 *2 *1) (|partial| -12 (-4 *1 (-1047 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) (|partial| -2740 (-12 (-5 *2 (-959 *3)) - (-12 (-1754 (-4 *3 (-38 (-413 (-570))))) - (-1754 (-4 *3 (-38 (-570)))) (-4 *5 (-620 (-1186)))) + (-12 (-1753 (-4 *3 (-38 (-413 (-570))))) + (-1753 (-4 *3 (-38 (-570)))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 *3)) - (-12 (-1754 (-4 *3 (-551))) (-1754 (-4 *3 (-38 (-413 (-570))))) + (-12 (-1753 (-4 *3 (-551))) (-1753 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 *3)) - (-12 (-1754 (-4 *3 (-1001 (-570)))) (-4 *3 (-38 (-413 (-570)))) + (-12 (-1753 (-4 *3 (-1001 (-570)))) (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))))) ((*1 *1 *2) (|partial| -2740 (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) - (-12 (-1754 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) + (-12 (-1753 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 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(-4 *1 (-1146)) (-5 *2 (-531)))) - ((*1 *2 *1) (-12 (-4 *1 (-1146)) (-5 *2 (-1287)))) + ((*1 *2 *1) (-12 (-4 *1 (-1146)) (-5 *2 (-1288)))) ((*1 *2 *1) (-12 (-4 *1 (-1146)) (-5 *2 (-1075)))) ((*1 *2 *1) (-12 (-4 *1 (-1146)) (-5 *2 (-523)))) ((*1 *2 *1) (-12 (-4 *1 (-1146)) (-5 *2 (-687)))) @@ -2349,7 +2503,7 @@ ((*1 *2 *1) (-12 (-4 *1 (-1146)) (-5 *2 (-134)))) ((*1 *2 *1) (-12 (-4 *1 (-1146)) (-5 *2 (-612)))) ((*1 *2 *1) (-12 (-4 *1 (-1146)) (-5 *2 (-139)))) - ((*1 *2 *1) (-12 (-4 *1 (-1146)) (-5 *2 (-1286)))) + ((*1 *2 *1) (-12 (-4 *1 (-1146)) (-5 *2 (-1287)))) ((*1 *2 *1) (-12 (-4 *1 (-1146)) (-5 *2 (-682)))) ((*1 *2 *1) (-12 (-4 *1 (-1146)) (-5 *2 (-220)))) ((*1 *2 *1) (-12 (-4 *1 (-1146)) (-5 *2 (-530)))) @@ -2357,71 +2511,87 @@ ((*1 *2 *1) (-12 (-5 *2 (-512)) (-5 *1 (-1191)))) ((*1 *2 *1) (-12 (-5 *2 (-227)) (-5 *1 (-1191)))) ((*1 *2 *1) (-12 (-5 *2 (-570)) (-5 *1 (-1191))))) -(((*1 *1) (-5 *1 (-142))) ((*1 *1 *1) (-5 *1 (-145))) - ((*1 *1 *1) (-4 *1 (-1153)))) -(((*1 *2 *1) (-12 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|vec| (-1277 *5)))) + (-5 *1 (-819 *5 *6)) (-5 *3 (-695 *6)) (-5 *4 (-1277 *5))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-1166 *4)) (-5 *3 (-1 *4 (-570))) (-4 *4 (-1058)) + (-5 *1 (-1170 *4))))) +(((*1 *2 *3 *4 *5 *4 *5 *5 *6 *4 *4 *4 *4 *4 *5 *4 *5 *5 *7 *4) + (-12 (-5 *3 (-1168)) (-5 *5 (-695 (-227))) (-5 *6 (-227)) + (-5 *7 (-695 (-570))) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-758))))) +(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) (((*1 *2 *1) (-12 (-5 *2 (-777)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 (-570)) (-14 *4 *2) (-4 *5 (-174)))) @@ -2430,17 +2600,17 @@ (-4 *3 (-167 *4)))) ((*1 *2) (-12 (-4 *1 (-372 *3)) (-4 *3 (-174)) (-5 *2 (-928)))) ((*1 *2) - (-12 (-4 *1 (-375 *3 *4)) (-4 *3 (-174)) (-4 *4 (-1252 *3)) + (-12 (-4 *1 (-375 *3 *4)) (-4 *3 (-174)) (-4 *4 (-1253 *3)) (-5 *2 (-928)))) ((*1 *2 *3) (-12 (-4 *4 (-368)) (-4 *5 (-378 *4)) (-4 *6 (-378 *4)) (-5 *2 (-777)) (-5 *1 (-527 *4 *5 *6 *3)) (-4 *3 (-693 *4 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-695 *5)) (-5 *4 (-1276 *5)) (-4 *5 (-368)) + (-12 (-5 *3 (-695 *5)) (-5 *4 (-1277 *5)) (-4 *5 (-368)) (-5 *2 (-777)) (-5 *1 (-673 *5)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-368)) (-4 *6 (-13 (-378 *5) (-10 -7 (-6 -4449)))) - (-4 *4 (-13 (-378 *5) (-10 -7 (-6 -4449)))) (-5 *2 (-777)) + (-12 (-4 *5 (-368)) (-4 *6 (-13 (-378 *5) (-10 -7 (-6 -4450)))) + (-4 *4 (-13 (-378 *5) (-10 -7 (-6 -4450)))) (-5 *2 (-777)) (-5 *1 (-674 *5 *6 *4 *3)) (-4 *3 (-693 *5 *6 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-693 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-378 *3)) @@ -2453,43 +2623,46 @@ (-12 (-4 *1 (-1062 *3 *4 *5 *6 *7)) (-4 *5 (-1058)) (-4 *6 (-240 *4 *5)) (-4 *7 (-240 *3 *5)) (-4 *5 (-562)) (-5 *2 (-777))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1182 *5)) (-4 *5 (-368)) (-5 *2 (-650 *6)) - (-5 *1 (-538 *5 *6 *4)) (-4 *6 (-368)) (-4 *4 (-13 (-368) (-854)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-311)) (-4 *4 (-378 *3)) (-4 *5 (-378 *3)) - (-5 *1 (-1133 *3 *4 *5 *2)) (-4 *2 (-693 *3 *4 *5))))) -(((*1 *1 *1) (-5 *1 (-1072)))) -(((*1 *1 *2) - (-12 (-5 *2 (-1182 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(-4 *4 (-393)))) @@ -3299,34 +3481,21 @@ ((*1 *1 *2) (-12 (-5 *2 (-413 (-570))) (-4 *1 (-1021)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1021)) (-5 *2 (-928)))) ((*1 *1 *1) (-4 *1 (-1021)))) +(((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-695 *3)) (-4 *3 (-1058)) (-5 *1 (-696 *3))))) (((*1 *2 *1) (-12 (-4 *1 (-962)) (-5 *2 (-1103 (-227))))) ((*1 *2 *1) (-12 (-4 *1 (-983)) (-5 *2 (-1103 (-227)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-650 (-570))) (-5 *2 (-570)) (-5 *1 (-492 *4)) + (-4 *4 (-1253 *2))))) (((*1 *2 *1) - (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1109)) (-5 *2 (-650 *1)) - (-4 *1 (-436 *3)))) - ((*1 *2 *1) - (|partial| -12 (-5 *2 (-650 (-899 *3))) (-5 *1 (-899 *3)) - (-4 *3 (-1109)))) - ((*1 *2 *1) - (|partial| -12 (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) - (-5 *2 (-650 *1)) (-4 *1 (-956 *3 *4 *5)))) - ((*1 *2 *3) - (|partial| -12 (-4 *4 (-799)) (-4 *5 (-856)) (-4 *6 (-1058)) - (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-650 *3)) - (-5 *1 (-957 *4 *5 *6 *7 *3)) - (-4 *3 - (-13 (-368) - (-10 -8 (-15 -3735 ($ *7)) (-15 -4398 (*7 $)) - (-15 -4412 (*7 $)))))))) -(((*1 *2 *2) - (-12 (-5 *2 (-950 *3)) (-4 *3 (-13 (-368) (-1211) (-1011))) - (-5 *1 (-178 *3))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-1281)) (-5 *1 (-1278))))) -(((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1226)) (-4 *1 (-152 *3)))) + (-12 (-4 *1 (-256 *3 *4 *5 *6)) (-4 *3 (-1058)) (-4 *4 (-856)) + (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-650 *4))))) +(((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1227)) (-4 *1 (-152 *3)))) ((*1 *1 *2) (-12 - (-5 *2 (-650 (-2 (|:| -1907 (-777)) (|:| -2177 *4) (|:| |num| *4)))) - (-4 *4 (-1252 *3)) (-4 *3 (-13 (-368) (-148))) (-5 *1 (-405 *3 *4)))) + (-5 *2 (-650 (-2 (|:| -3011 (-777)) (|:| -2178 *4) (|:| |num| *4)))) + (-4 *4 (-1253 *3)) (-4 *3 (-13 (-368) (-148))) (-5 *1 (-405 *3 *4)))) ((*1 *1 *2 *3 *4) (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2559 "void"))) (-5 *3 (-650 (-959 (-570)))) (-5 *4 (-112)) (-5 *1 (-443)))) @@ -3334,7 +3503,7 @@ (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2559 "void"))) (-5 *3 (-650 (-1186))) (-5 *4 (-112)) (-5 *1 (-443)))) ((*1 *2 *1) - (-12 (-5 *2 (-1166 *3)) (-5 *1 (-607 *3)) (-4 *3 (-1226)))) + (-12 (-5 *2 (-1166 *3)) (-5 *1 (-607 *3)) (-4 *3 (-1227)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-640 *2)) (-4 *2 (-174)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-678 *3)) (-4 *3 (-856)) (-5 *1 (-670 *3 *4)) @@ -3351,13 +3520,13 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-719 *2 *3 *4)) (-4 *2 (-856)) (-4 *3 (-1109)) (-14 *4 - (-1 (-112) (-2 (|:| -2159 *2) (|:| -1907 *3)) - (-2 (|:| -2159 *2) (|:| -1907 *3)))))) + (-1 (-112) (-2 (|:| -2160 *2) (|:| -3011 *3)) + (-2 (|:| -2160 *2) (|:| -3011 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-512)) (-5 *3 (-1127)) (-5 *1 (-844)))) ((*1 *1 *2 *3) - (-12 (-5 *1 (-879 *2 *3)) (-4 *2 (-1226)) (-4 *3 (-1226)))) + (-12 (-5 *1 (-879 *2 *3)) (-4 *2 (-1227)) (-4 *3 (-1227)))) ((*1 *1 *2) - (-12 (-5 *2 (-650 (-2 (|:| -2013 (-1186)) (|:| -2223 *4)))) + (-12 (-5 *2 (-650 (-2 (|:| -2013 (-1186)) (|:| -2224 *4)))) (-4 *4 (-1109)) (-5 *1 (-896 *3 *4)) (-4 *3 (-1109)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-650 *5)) (-4 *5 (-13 (-1109) (-34))) @@ -3392,68 +3561,52 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-1175 *2 *3)) (-4 *2 (-1109)) (-4 *3 (-1109))))) (((*1 *2 *1) - (-12 (-4 *1 (-693 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-378 *3)) - (-4 *5 (-378 *3)) (-5 *2 (-650 (-650 *3))))) - ((*1 *2 *1) - (-12 (-4 *1 (-1062 *3 *4 *5 *6 *7)) (-4 *5 (-1058)) - (-4 *6 (-240 *4 *5)) (-4 *7 (-240 *3 *5)) (-5 *2 (-650 (-650 *5))))) - ((*1 *2 *1) - (-12 (-5 *2 (-650 (-650 *3))) (-5 *1 (-1198 *3)) (-4 *3 (-1109))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-1186)) (-5 *3 (-384)) (-5 *1 (-1072))))) -(((*1 *2 *3) (-12 (-5 *2 (-112)) (-5 *1 (-593 *3)) (-4 *3 (-551))))) + (-12 (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-799)) + (-4 *5 (-856)) (-5 *2 (-112))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-650 *1)) (-4 *1 (-1074 *4 *5 *6)) (-4 *4 (-1058)) + (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)))) + ((*1 *2 *1 *1) + (-12 (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-799)) + (-4 *5 (-856)) 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*1 (-1137 *3 *4)) (-4 *3 (-1253 *4)))) + ((*1 *2 *3 *3 *3 *3) + (-12 (-4 *3 (-13 (-368) (-10 -8 (-15 ** ($ $ (-413 (-570))))))) + (-5 *2 (-650 *3)) (-5 *1 (-1137 *4 *3)) (-4 *4 (-1253 *3))))) (((*1 *2 *3 *3) - (-12 (-5 *3 (-650 *2)) (-5 *1 (-181 *2)) (-4 *2 (-311)))) - ((*1 *2 *3 *2) - (-12 (-5 *3 (-650 (-650 *4))) (-5 *2 (-650 *4)) (-4 *4 (-311)) - (-5 *1 (-181 *4)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-650 *8)) - (-5 *4 - (-650 - (-2 (|:| -2331 (-695 *7)) (|:| |basisDen| *7) - (|:| |basisInv| (-695 *7))))) - (-5 *5 (-777)) (-4 *8 (-1252 *7)) (-4 *7 (-1252 *6)) (-4 *6 (-354)) - (-5 *2 - (-2 (|:| -2331 (-695 *7)) (|:| |basisDen| *7) - (|:| |basisInv| (-695 *7)))) - (-5 *1 (-504 *6 *7 *8)))) - ((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-567))))) -(((*1 *2 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-562)) (-4 *2 (-551)))) - ((*1 *1 *1) (-4 *1 (-1069)))) + (-12 (-5 *3 (-650 (-570))) (-5 *2 (-1188 (-413 (-570)))) + (-5 *1 (-192))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-650 (-48))) (-5 *2 (-424 *3)) (-5 *1 (-39 *3)) - (-4 *3 (-1252 (-48))))) + (-4 *3 (-1253 (-48))))) ((*1 *2 *3) - (-12 (-5 *2 (-424 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1252 (-48))))) + (-12 (-5 *2 (-424 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1253 (-48))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-650 (-48))) (-4 *5 (-856)) (-4 *6 (-799)) (-5 *2 (-424 *3)) (-5 *1 (-42 *5 *6 *3)) (-4 *3 (-956 (-48) *6 *5)))) @@ -3463,33 +3616,33 @@ (-5 *1 (-42 *5 *6 *7)) (-5 *3 (-1182 *7)))) ((*1 *2 *3) (-12 (-4 *4 (-311)) (-5 *2 (-424 *3)) (-5 *1 (-168 *4 *3)) - (-4 *3 (-1252 (-171 *4))))) + (-4 *3 (-1253 (-171 *4))))) ((*1 *2 *3 *4 *5) (-12 (-5 *5 (-112)) (-4 *4 (-13 (-368) (-854))) (-5 *2 (-424 *3)) - (-5 *1 (-183 *4 *3)) (-4 *3 (-1252 (-171 *4))))) + (-5 *1 (-183 *4 *3)) (-4 *3 (-1253 (-171 *4))))) ((*1 *2 *3 *4) (-12 (-4 *4 (-13 (-368) (-854))) (-5 *2 (-424 *3)) - (-5 *1 (-183 *4 *3)) (-4 *3 (-1252 (-171 *4))))) + (-5 *1 (-183 *4 *3)) (-4 *3 (-1253 (-171 *4))))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-368) (-854))) (-5 *2 (-424 *3)) - (-5 *1 (-183 *4 *3)) (-4 *3 (-1252 (-171 *4))))) + (-5 *1 (-183 *4 *3)) (-4 *3 (-1253 (-171 *4))))) ((*1 *2 *3) (-12 (-4 *4 (-354)) (-5 *2 (-424 *3)) (-5 *1 (-218 *4 *3)) - (-4 *3 (-1252 *4)))) + (-4 *3 (-1253 *4)))) ((*1 *2 *3) - (-12 (-5 *2 (-424 *3)) (-5 *1 (-448 *3)) (-4 *3 (-1252 (-570))))) + (-12 (-5 *2 (-424 *3)) (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-777)) (-5 *2 (-424 *3)) (-5 *1 (-448 *3)) - (-4 *3 (-1252 (-570))))) + (-4 *3 (-1253 (-570))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-650 (-777))) (-5 *2 (-424 *3)) (-5 *1 (-448 *3)) - (-4 *3 (-1252 (-570))))) + (-4 *3 (-1253 (-570))))) ((*1 *2 *3 *4 *5) (-12 (-5 *4 (-650 (-777))) (-5 *5 (-777)) (-5 *2 (-424 *3)) - (-5 *1 (-448 *3)) (-4 *3 (-1252 (-570))))) + (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570))))) ((*1 *2 *3 *4 *4) (-12 (-5 *4 (-777)) (-5 *2 (-424 *3)) (-5 *1 (-448 *3)) - (-4 *3 (-1252 (-570))))) + (-4 *3 (-1253 (-570))))) ((*1 *2 *3) (-12 (-5 *2 (-424 (-171 (-570)))) (-5 *1 (-452)) (-5 *3 (-171 (-570))))) @@ -3497,7 +3650,7 @@ (-12 (-4 *4 (-13 (-856) - (-10 -8 (-15 -1416 ((-1186) $)) + (-10 -8 (-15 -1417 ((-1186) $)) (-15 -2643 ((-3 $ "failed") (-1186)))))) (-4 *5 (-799)) (-4 *7 (-562)) (-5 *2 (-424 *3)) (-5 *1 (-462 *4 *5 *6 *7 *3)) (-4 *6 (-562)) @@ -3506,9 +3659,9 @@ (-12 (-4 *4 (-311)) (-5 *2 (-424 (-1182 *4))) (-5 *1 (-464 *4)) (-5 *3 (-1182 *4)))) ((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-424 *6) *6)) (-4 *6 (-1252 *5)) (-4 *5 (-368)) + (-12 (-5 *4 (-1 (-424 *6) *6)) (-4 *6 (-1253 *5)) (-4 *5 (-368)) (-4 *7 (-13 (-368) (-148) (-730 *5 *6))) (-5 *2 (-424 *3)) - (-5 *1 (-500 *5 *6 *7 *3)) (-4 *3 (-1252 *7)))) + (-5 *1 (-500 *5 *6 *7 *3)) (-4 *3 (-1253 *7)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-424 (-1182 *7)) (-1182 *7))) (-4 *7 (-13 (-311) (-148))) (-4 *5 (-856)) (-4 *6 (-799)) @@ -3523,19 +3676,19 @@ ((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-650 *5) *6)) (-4 *5 (-13 (-368) (-148) (-1047 (-570)) (-1047 (-413 (-570))))) - (-4 *6 (-1252 *5)) (-5 *2 (-650 (-659 (-413 *6)))) + (-4 *6 (-1253 *5)) (-5 *2 (-650 (-659 (-413 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(-3748) (-705)))) + (-12 (-5 *2 (-1277 (-344 (-3749 'X) (-3749) (-705)))) (-5 *1 (-85 *3)) (-14 *3 (-1186)))) ((*1 *1 *2) - (-12 (-5 *2 (-1276 (-344 (-3748 'X) (-3748 '-1547) (-705)))) + (-12 (-5 *2 (-1277 (-344 (-3749 'X) (-3749 '-1548) (-705)))) (-5 *1 (-86 *3)) (-14 *3 (-1186)))) ((*1 *1 *2) - (-12 (-5 *2 (-695 (-344 (-3748 'XL 'XR 'ELAM) (-3748) (-705)))) + (-12 (-5 *2 (-695 (-344 (-3749 'XL 'XR 'ELAM) (-3749) (-705)))) (-5 *1 (-87 *3)) (-14 *3 (-1186)))) ((*1 *1 *2) - (-12 (-5 *2 (-344 (-3748 'X) (-3748 '-1547) (-705))) (-5 *1 (-89 *3)) + (-12 (-5 *2 (-344 (-3749 'X) (-3749 '-1548) (-705))) (-5 *1 (-89 *3)) (-14 *3 (-1186)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-137 *3 *4 *5))) (-5 *1 (-137 *3 *4 *5)) @@ -3669,8 +3827,8 @@ (-12 (-5 *2 (-242 *4 *5)) (-14 *4 (-777)) (-4 *5 (-174)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 (-570)))) ((*1 *2 *3) - (-12 (-5 *3 (-1276 (-695 *4))) (-4 *4 (-174)) - (-5 *2 (-1276 (-695 (-413 (-959 *4))))) (-5 *1 (-191 *4)))) + (-12 (-5 *3 (-1277 (-695 *4))) (-4 *4 (-174)) + (-5 *2 (-1277 (-695 (-413 (-959 *4))))) (-5 *1 (-191 *4)))) ((*1 *2 *3) (-12 (-5 *3 (-1101 (-320 *4))) (-4 *4 (-13 (-856) (-562) (-620 (-384)))) (-5 *2 (-1101 (-384))) @@ -3678,12 +3836,12 @@ ((*1 *1 *2) (-12 (-4 *1 (-269 *2)) (-4 *2 (-856)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-570))) (-5 *1 (-278)))) ((*1 *2 *1) - (-12 (-4 *2 (-1252 *3)) (-5 *1 (-293 *3 *2 *4 *5 *6 *7)) + (-12 (-4 *2 (-1253 *3)) (-5 *1 (-293 *3 *2 *4 *5 *6 *7)) (-4 *3 (-174)) (-4 *4 (-23)) (-14 *5 (-1 *2 *2 *4)) (-14 *6 (-1 (-3 *4 "failed") *4 *4)) (-14 *7 (-1 (-3 *2 "failed") *2 *2 *4)))) ((*1 *1 *2) - (-12 (-5 *2 (-1261 *4 *5 *6)) (-4 *4 (-13 (-27) (-1211) (-436 *3))) + (-12 (-5 *2 (-1262 *4 *5 *6)) (-4 *4 (-13 (-27) (-1212) (-436 *3))) (-14 *5 (-1186)) (-14 *6 *4) (-4 *3 (-13 (-1047 (-570)) (-645 (-570)) (-458))) (-5 *1 (-317 *3 *4 *5 *6)))) @@ -3698,10 +3856,10 @@ (-4 *3 (-333 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-379 *3 *4)) (-4 *3 (-856)) (-4 *4 (-174)) - (-5 *2 (-1300 *3 *4)))) + (-5 *2 (-1301 *3 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-379 *3 *4)) (-4 *3 (-856)) (-4 *4 (-174)) - (-5 *2 (-1291 *3 *4)))) + (-5 *2 (-1292 *3 *4)))) ((*1 *1 *2) (-12 (-4 *1 (-379 *2 *3)) (-4 *2 (-856)) (-4 *3 (-174)))) ((*1 *1 *2) (-12 @@ -3814,7 +3972,7 @@ (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-334)) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-334))) (-4 *1 (-446)))) - ((*1 *1 *2) (-12 (-5 *2 (-1276 (-705))) (-4 *1 (-446)))) + ((*1 *1 *2) (-12 (-5 *2 (-1277 (-705))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3136 (-650 (-334))))) @@ -3822,34 +3980,34 @@ ((*1 *1 *2) (-12 (-5 *2 (-334)) (-4 *1 (-447)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-334))) (-4 *1 (-447)))) ((*1 *1 *2) - (-12 (-5 *2 (-1276 (-413 (-959 *3)))) (-4 *3 (-174)) - (-14 *6 (-1276 (-695 *3))) (-5 *1 (-459 *3 *4 *5 *6)) + (-12 (-5 *2 (-1277 (-413 (-959 *3)))) (-4 *3 (-174)) + (-14 *6 (-1277 (-695 *3))) (-5 *1 (-459 *3 *4 *5 *6)) (-14 *4 (-928)) (-14 *5 (-650 (-1186))))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-650 (-950 (-227))))) (-5 *1 (-474)))) ((*1 *2 *1) (-12 (-5 *2 (-868)) (-5 *1 (-474)))) ((*1 *1 *2) - (-12 (-5 *2 (-1261 *3 *4 *5)) (-4 *3 (-1058)) (-14 *4 (-1186)) + (-12 (-5 *2 (-1262 *3 *4 *5)) (-4 *3 (-1058)) (-14 *4 (-1186)) (-14 *5 *3) (-5 *1 (-480 *3 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 *4)) (-14 *4 (-1186)) (-5 *1 (-480 *3 *4 *5)) + (-12 (-5 *2 (-1273 *4)) (-14 *4 (-1186)) (-5 *1 (-480 *3 *4 *5)) (-4 *3 (-1058)) (-14 *5 *3))) ((*1 *1 *2) (-12 (-5 *2 (-1134 (-570) (-618 (-501)))) (-5 *1 (-501)))) ((*1 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-508)))) ((*1 *1 *2) (-12 (-5 *2 (-650 *6)) (-4 *6 (-956 *3 *4 *5)) (-4 *3 (-368)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-510 *3 *4 *5 *6)))) - ((*1 *1 *2) (-12 (-5 *2 (-650 (-1225))) (-5 *1 (-530)))) - ((*1 *1 *2) (-12 (-5 *2 (-650 (-1225))) (-5 *1 (-612)))) + ((*1 *1 *2) (-12 (-5 *2 (-650 (-1226))) (-5 *1 (-530)))) + ((*1 *1 *2) (-12 (-5 *2 (-650 (-1226))) (-5 *1 (-612)))) ((*1 *1 *2) (-12 (-4 *3 (-174)) (-5 *1 (-613 *3 *2)) (-4 *2 (-750 *3)))) - ((*1 *2 *1) (-12 (-4 *1 (-619 *2)) (-4 *2 (-1226)))) - ((*1 *1 *2) (-12 (-4 *1 (-622 *2)) (-4 *2 (-1226)))) + ((*1 *2 *1) (-12 (-4 *1 (-619 *2)) (-4 *2 (-1227)))) + ((*1 *1 *2) (-12 (-4 *1 (-622 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) (-12 (-4 *1 (-626 *2)) (-4 *2 (-1058)))) ((*1 *2 *1) - (-12 (-5 *2 (-1296 *3 *4)) (-5 *1 (-633 *3 *4 *5)) (-4 *3 (-856)) + (-12 (-5 *2 (-1297 *3 *4)) (-5 *1 (-633 *3 *4 *5)) (-4 *3 (-856)) (-4 *4 (-13 (-174) (-723 (-413 (-570))))) (-14 *5 (-928)))) ((*1 *2 *1) - (-12 (-5 *2 (-1291 *3 *4)) (-5 *1 (-633 *3 *4 *5)) (-4 *3 (-856)) + (-12 (-5 *2 (-1292 *3 *4)) (-5 *1 (-633 *3 *4 *5)) (-4 *3 (-856)) (-4 *4 (-13 (-174) (-723 (-413 (-570))))) (-14 *5 (-928)))) ((*1 *1 *2) (-12 (-4 *3 (-174)) (-5 *1 (-641 *3 *2)) (-4 *2 (-750 *3)))) @@ -3886,7 +4044,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-650 (-2 (|:| -1441 *3) (|:| -3278 *4)))) + (-12 (-5 *2 (-650 (-2 (|:| -1442 *3) (|:| -3278 *4)))) (-4 *3 (-1058)) (-4 *4 (-732)) (-5 *1 (-741 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-570)) (-4 *1 (-769)))) ((*1 *1 *2) @@ -3895,33 +4053,33 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -3758 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-320 (-227))) - (|:| -3758 (-650 (-1103 (-849 (-227))))) + (|:| -1990 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-775)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-320 (-227))) - (|:| -3758 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) + (|:| -1990 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-775)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -3758 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-775)))) - ((*1 *2 *3) (-12 (-5 *2 (-780)) (-5 *1 (-779 *3)) (-4 *3 (-1226)))) + ((*1 *2 *3) (-12 (-5 *2 (-780)) (-5 *1 (-779 *3)) (-4 *3 (-1227)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) - (|:| |fn| (-1276 (-320 (-227)))) (|:| |yinit| (-650 (-227))) + (|:| |fn| (-1277 (-320 (-227)))) (|:| |yinit| (-650 (-227))) (|:| |intvals| (-650 (-227))) (|:| |g| (-320 (-227))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-814)))) @@ -3931,23 +4089,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-320 (-227))) (|:| -2314 (-650 (-227))) + (-2 (|:| |fn| (-320 (-227))) (|:| -2315 (-650 (-227))) (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) (|:| |ub| (-650 (-849 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-650 (-320 (-227)))) - (|:| -2314 (-650 (-227))))))) + (|:| -2315 (-650 (-227))))))) (-5 *1 (-847)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -2314 (-650 (-227))))) + (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -2315 (-650 (-227))))) (-5 *1 (-847)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-320 (-227))) (|:| -2314 (-650 (-227))) + (-2 (|:| |fn| (-320 (-227))) (|:| -2315 (-650 (-227))) (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) (|:| |ub| (-650 (-849 (-227)))))) (-5 *1 (-847)))) @@ -3985,8 +4143,8 @@ ((*1 *2 *3) (-12 (-5 *3 (-483)) (-5 *2 (-320 *4)) (-5 *1 (-926 *4)) (-4 *4 (-562)))) - ((*1 *2 *3) (-12 (-5 *2 (-1281)) (-5 *1 (-1042 *3)) (-4 *3 (-1226)))) - ((*1 *2 *3) (-12 (-5 *3 (-316)) (-5 *1 (-1042 *2)) (-4 *2 (-1226)))) + ((*1 *2 *3) (-12 (-5 *2 (-1282)) (-5 *1 (-1042 *3)) (-4 *3 (-1227)))) + ((*1 *2 *3) (-12 (-5 *3 (-316)) (-5 *1 (-1042 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) (-12 (-4 *3 (-368)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-1043 *3 *4 *5 *2 *6)) (-4 *2 (-956 *3 *4 *5)) @@ -4004,13 +4162,13 @@ ((*1 *2 *3) (-12 (-5 *2 (-1166 *3)) (-5 *1 (-1170 *3)) (-4 *3 (-1058)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 *4)) (-14 *4 (-1186)) (-5 *1 (-1177 *3 *4 *5)) + (-12 (-5 *2 (-1273 *4)) (-14 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*5 (-13 (-458) (-1047 (-570)) (-645 (-570)))) - (-5 *2 - (-3 (|:| |%expansion| (-317 *5 *3 *6 *7)) - (|:| |%problem| (-2 (|:| |func| (-1168)) (|:| |prob| (-1168)))))) - (-5 *1 (-426 *5 *3 *6 *7)) (-4 *3 (-13 (-27) (-1211) (-436 *5))) - (-14 *6 (-1186)) (-14 *7 *3)))) -(((*1 *1 *1) (-4 *1 (-1069)))) -(((*1 *2 *1) (-12 (-5 *2 (-650 (-618 *1))) (-4 *1 (-306))))) -(((*1 *2 *1) - (-12 (-4 *3 (-368)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *2 (-112)) - (-5 *1 (-510 *3 *4 *5 *6)) (-4 *6 (-956 *3 *4 *5)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-650 *6)) (-4 *6 (-856)) (-4 *4 (-368)) (-4 *5 (-799)) - (-5 *2 (-112)) (-5 *1 (-510 *4 *5 *6 *7)) (-4 *7 (-956 *4 *5 *6))))) -(((*1 *2 *1) - (-12 (-5 *2 (-1111 *3)) (-5 *1 (-911 *3)) (-4 *3 (-1109)))) - ((*1 *2 *1) - (-12 (-5 *2 (-1111 *3)) (-5 *1 (-912 *3)) (-4 *3 (-1109))))) +(((*1 *2 *2) (-12 (-5 *2 (-1103 (-849 (-227)))) (-5 *1 (-309))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1186)) (-5 *2 (-542)) (-5 *1 (-541 *4)) + (-4 *4 (-1227))))) (((*1 *2 *3) - (-12 (-5 *2 (-570)) (-5 *1 (-451 *3)) (-4 *3 (-410)) (-4 *3 (-1058))))) -(((*1 *2 *1) + (-12 + (-5 *3 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1166 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1990 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *2 (-1044)) (-5 *1 (-309))))) +(((*1 *2 *3 *2) (-12 (-5 *2 - (-1276 - (-2 (|:| |scaleX| (-227)) (|:| 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- (-12 (-5 *2 (-950 (-227))) (-5 *1 (-1222)) (-5 *3 (-227))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) - (-4 *8 (-1074 *5 *6 *7)) - (-5 *2 - (-2 (|:| |val| (-650 *8)) - (|:| |towers| (-650 (-1036 *5 *6 *7 *8))))) - (-5 *1 (-1036 *5 *6 *7 *8)) (-5 *3 (-650 *8)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) - (-4 *8 (-1074 *5 *6 *7)) - (-5 *2 - (-2 (|:| |val| (-650 *8)) - (|:| |towers| (-650 (-1155 *5 *6 *7 *8))))) - (-5 *1 (-1155 *5 *6 *7 *8)) (-5 *3 (-650 *8))))) + (-12 (-5 *2 (-950 (-227))) (-5 *1 (-1223)) (-5 *3 (-227))))) (((*1 *2 *1) - (-12 (-5 *2 (-650 (-570))) (-5 *1 (-1013 *3)) (-14 *3 (-570))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) - (-4 *4 (-856))))) -(((*1 *1 *1) (-12 (-4 *1 (-680 *2)) (-4 *2 (-1226))))) -(((*1 *1 *2) - (-12 (-5 *2 (-413 *4)) (-4 *4 (-1252 *3)) (-4 *3 (-13 (-368) (-148))) - (-5 *1 (-405 *3 *4))))) + (-12 (-5 *2 (-173)) (-5 *1 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*4) + (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *8)) + (-5 *4 (-695 (-1182 *8))) (-4 *5 (-1058)) (-4 *8 (-1058)) + (-4 *6 (-1253 *5)) (-5 *2 (-695 *6)) (-5 *1 (-507 *5 *6 *7 *8)) + (-4 *7 (-1253 *6))))) +(((*1 *2) (-12 (-5 *2 (-928)) (-5 *1 (-158))))) (((*1 *2 *3 *4 *5) (-12 (-5 *5 (-1103 *3)) (-4 *3 (-956 *7 *6 *4)) (-4 *6 (-799)) (-4 *4 (-856)) (-4 *7 (-562)) @@ -6830,9 +7006,9 @@ ((*1 *2 *2 *3) (-12 (-5 *3 (-1186)) (-4 *4 (-13 (-562) (-1047 (-570)) (-645 (-570)))) - (-5 *1 (-1178 *4 *2)) (-4 *2 (-13 (-436 *4) (-161) (-27) (-1211))))) + (-5 *1 (-1178 *4 *2)) (-4 *2 (-13 (-436 *4) (-161) (-27) (-1212))))) ((*1 *2 *2 *3) - (-12 (-5 *3 (-1101 *2)) (-4 *2 (-13 (-436 *4) (-161) (-27) (-1211))) + (-12 (-5 *3 (-1101 *2)) (-4 *2 (-13 (-436 *4) (-161) (-27) (-1212))) (-4 *4 (-13 (-562) (-1047 (-570)) (-645 (-570)))) (-5 *1 (-1178 *4 *2)))) ((*1 *2 *3 *4) @@ -6850,67 +7026,152 @@ (-12 (-5 *4 (-1101 (-413 (-959 *5)))) (-5 *3 (-413 (-959 *5))) (-4 *5 (-13 (-562) (-1047 (-570)))) (-5 *2 (-3 *3 (-320 *5))) (-5 *1 (-1179 *5))))) -(((*1 *2 *3 *3 *3) - (-12 (-5 *2 (-650 (-570))) (-5 *1 (-1119)) (-5 *3 (-570))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-567)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1182 (-413 (-570)))) (-5 *1 (-949)) (-5 *3 (-570))))) -(((*1 *1 *1) (-12 (-5 *1 (-921 *2)) (-4 *2 (-311))))) -(((*1 *2 *3) - (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-570)) - (-5 *1 (-455 *4 *5 *6 *3)) (-4 *3 (-956 *4 *5 *6))))) +(((*1 *2 *1) + (-12 (|has| *1 (-6 -4449)) (-4 *1 (-495 *3)) (-4 *3 (-1227)) + (-5 *2 (-650 *3)))) + ((*1 *2 *1) (-12 (-5 *2 (-650 *3)) (-5 *1 (-743 *3)) (-4 *3 (-1109)))) + ((*1 *2 *1) (-12 (-5 *2 (-650 (-445))) (-5 *1 (-871))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1151 *3 *4)) (-14 *3 (-928)) (-4 *4 (-368)) + (-5 *1 (-1002 *3 *4))))) (((*1 *2 *2 *3) - (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1226)) (-5 *1 (-1141 *4 *2)) - (-4 *2 (-13 (-610 (-570) *4) (-10 -7 (-6 -4448) (-6 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(-384)) (-5 *1 (-194))))) +(((*1 *2 *3 *3 *3 *4 *4 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) + (-5 *1 (-761))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-950 *5)) (-4 *5 (-1058)) (-5 *2 (-777)) + (-5 *1 (-1174 *4 *5)) (-14 *4 (-928)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-650 (-777))) (-5 *3 (-777)) (-5 *1 (-1174 *4 *5)) + (-14 *4 (-928)) (-4 *5 (-1058)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-650 (-777))) (-5 *3 (-950 *5)) (-4 *5 (-1058)) + (-5 *1 (-1174 *4 *5)) (-14 *4 (-928))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-1186)) (-5 *3 (-384)) (-5 *1 (-1072))))) +(((*1 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-1204 *3 *4)) (-4 *3 (-1109)) + (-4 *4 (-1109))))) (((*1 *2 *1) (-12 (-5 *2 (-1113)) (-5 *1 (-52))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-777)) (-5 *2 (-1281)) (-5 *1 (-1277)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-777)) (-5 *2 (-1281)) (-5 *1 (-1278))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1252 *3)) (-4 *3 (-1058)) (-5 *2 (-1182 *3))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-458) (-1047 (-570)))) (-4 *3 (-562)) + (-5 *1 (-41 *3 *2)) (-4 *2 (-436 *3)) + (-4 *2 + (-13 (-368) (-306) + (-10 -8 (-15 -4399 ((-1134 *3 (-618 $)) $)) + (-15 -4413 ((-1134 *3 (-618 $)) $)) + (-15 -3735 ($ (-1134 *3 (-618 $)))))))))) +(((*1 *1 *1 *2 *2 *1) + (-12 (-5 *2 (-570)) (-4 *1 (-693 *3 *4 *5)) (-4 *3 (-1058)) + (-4 *4 (-378 *3)) (-4 *5 (-378 *3))))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-650 + (-2 + (|:| -2013 + (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) + (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -2224 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1166 (-227))) + (|:| 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(-732)))) ((*1 *1 *2 *1) - (-12 (-5 *1 (-298 *2)) (-4 *2 (-1121)) (-4 *2 (-1226)))) + (-12 (-5 *1 (-298 *2)) (-4 *2 (-1121)) (-4 *2 (-1227)))) ((*1 *1 *1 *2) - (-12 (-5 *1 (-298 *2)) (-4 *2 (-1121)) (-4 *2 (-1226)))) + (-12 (-5 *1 (-298 *2)) (-4 *2 (-1121)) (-4 *2 (-1227)))) ((*1 *1 *2 *3) (-12 (-4 *1 (-327 *3 *2)) (-4 *3 (-1109)) (-4 *2 (-132)))) ((*1 *1 *1 *2) (-12 (-5 *1 (-366 *2)) (-4 *2 (-1109)))) @@ -8726,8 +8970,8 @@ (-12 (-14 *3 (-650 (-1186))) (-4 *4 (-174)) (-4 *6 (-240 (-2426 *3) (-777))) (-14 *7 - (-1 (-112) (-2 (|:| -2159 *5) (|:| -1907 *6)) - (-2 (|:| -2159 *5) (|:| -1907 *6)))) + (-1 (-112) (-2 (|:| -2160 *5) (|:| -3011 *6)) + (-2 (|:| -2160 *5) (|:| -3011 *6)))) (-5 *1 (-467 *3 *4 *5 *6 *7 *2)) (-4 *5 (-856)) (-4 *2 (-956 *4 *6 (-870 *3))))) ((*1 *1 *1 *2) @@ -8738,7 +8982,7 @@ (-12 (-4 *2 (-368)) (-4 *3 (-799)) (-4 *4 (-856)) (-5 *1 (-510 *2 *3 *4 *5)) (-4 *5 (-956 *2 *3 *4)))) ((*1 *2 *2 *2) - (-12 (-5 *2 (-1276 *3)) (-4 *3 (-354)) (-5 *1 (-534 *3)))) + (-12 (-5 *2 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(-1058)) (-4 *2 (-368))))) +(((*1 *1 *2) (-12 (-5 *2 (-777)) (-5 *1 (-135))))) +(((*1 *2 *1) (-12 (-4 *1 (-330 *3 *2)) (-4 *3 (-1058)) (-4 *2 (-798)))) + ((*1 *2 *1) (-12 (-4 *1 (-714 *3)) (-4 *3 (-1058)) (-5 *2 (-777)))) + ((*1 *2 *1) (-12 (-4 *1 (-858 *3)) (-4 *3 (-1058)) (-5 *2 (-777)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-650 *6)) (-4 *1 (-956 *4 *5 *6)) (-4 *4 (-1058)) + (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-650 (-777))))) + ((*1 *2 *1 *3) + (-12 (-4 *1 (-956 *4 *5 *3)) (-4 *4 (-1058)) (-4 *5 (-799)) + (-4 *3 (-856)) (-5 *2 (-777))))) (((*1 *1 *1) (-5 *1 (-1185))) ((*1 *1 *2) (-12 @@ -9428,127 +9587,47 @@ (-3 (|:| I (-320 (-570))) (|:| -1674 (-320 (-384))) (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) (-5 *1 (-1185))))) -(((*1 *2 *3 *4 *5 *6 *2 *7 *8) - (|partial| -12 (-5 *2 (-650 (-1182 *11))) (-5 *3 (-1182 *11)) - (-5 *4 (-650 *10)) (-5 *5 (-650 *8)) (-5 *6 (-650 (-777))) - (-5 *7 (-1276 (-650 (-1182 *8)))) (-4 *10 (-856)) - (-4 *8 (-311)) (-4 *11 (-956 *8 *9 *10)) (-4 *9 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"There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1166 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1990 + (-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 (-565)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-777)) (-4 *1 (-701 *2)) (-4 *2 (-1109)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -2013 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1277 (-320 (-227)))) (|:| |yinit| (-650 (-227))) + (|:| |intvals| (-650 (-227))) (|:| |g| (-320 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (|:| -2224 + (-2 (|:| |stiffness| (-384)) (|:| |stability| (-384)) + (|:| |expense| (-384)) (|:| 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*1 (-281 *3 *4 *2)) (-4 *2 (-1238 *3 *4)))) + (-12 (-4 *3 (-38 (-413 (-570)))) (-4 *4 (-1268 *3)) + (-5 *1 (-281 *3 *4 *2)) (-4 *2 (-1239 *3 *4)))) ((*1 *2 *2) - (-12 (-4 *3 (-38 (-413 (-570)))) (-4 *4 (-1236 *3)) - (-5 *1 (-282 *3 *4 *2 *5)) (-4 *2 (-1259 *3 *4)) (-4 *5 (-992 *4)))) + (-12 (-4 *3 (-38 (-413 (-570)))) (-4 *4 (-1237 *3)) + (-5 *1 (-282 *3 *4 *2 *5)) (-4 *2 (-1260 *3 *4)) (-4 *5 (-992 *4)))) + ((*1 *1 *2) (-12 (-5 *1 (-335 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-344 *2 *3 *4)) (-14 *2 (-650 (-1186))) (-14 *3 (-650 (-1186))) (-4 *4 (-393)))) @@ -10259,35 +10424,19 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) - ((*1 *1 *1) (-4 *1 (-1214)))) -(((*1 *1 *1) - (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) + ((*1 *1 *1) (-4 *1 (-1215)))) +(((*1 *2 *3) (-12 (-5 *3 (-847)) (-5 *2 (-1044)) (-5 *1 (-846)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-650 (-320 (-384)))) (-5 *4 (-650 (-384))) + (-5 *2 (-1044)) (-5 *1 (-846))))) +(((*1 *2 *3 *2) (-12 (-5 *2 (-1044)) (-5 *3 (-1186)) (-5 *1 (-270))))) (((*1 *2 *1) - (-12 (-4 *1 (-1112 *3 *4 *5 *6 *2)) (-4 *3 (-1109)) (-4 *4 (-1109)) - (-4 *5 (-1109)) (-4 *6 (-1109)) (-4 *2 (-1109))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) - (-4 *4 (-856)) (-4 *2 (-458))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-424 *5)) (-4 *5 (-562)) - (-5 *2 - (-2 (|:| -1907 (-777)) (|:| -1441 *5) (|:| |radicand| (-650 *5)))) - (-5 *1 (-324 *5)) (-5 *4 (-777)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-1011)) (-5 *2 (-570))))) -(((*1 *2 *3 *4 *5 *4) - (-12 (-5 *3 (-695 (-227))) (-5 *4 (-570)) (-5 *5 (-112)) - (-5 *2 (-1044)) (-5 *1 (-751))))) -(((*1 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1011)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-458)) (-5 *1 (-1217 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1211)))))) + (-12 (-5 *2 (-413 (-959 *3))) (-5 *1 (-459 *3 *4 *5 *6)) + (-4 *3 (-562)) (-4 *3 (-174)) (-14 *4 (-928)) + (-14 *5 (-650 (-1186))) (-14 *6 (-1277 (-695 *3)))))) (((*1 *2 *3) - (-12 (-5 *2 (-1 (-950 *3) (-950 *3))) (-5 *1 (-178 *3)) - (-4 *3 (-13 (-368) (-1211) (-1011)))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-1182 *1)) (-4 *1 (-1021))))) -(((*1 *1) (-5 *1 (-512)))) + (|partial| -12 (-5 *3 (-1277 *4)) (-4 *4 (-645 (-570))) + (-5 *2 (-1277 (-570))) (-5 *1 (-1304 *4))))) (((*1 *2 *3 *4 *2 *5 *6) (-12 (-5 *5 @@ -10308,15 +10457,22 @@ (-5 *3 (-650 *10)) (-5 *4 (-650 *11)) (-4 *10 (-1074 *7 *8 *9)) (-4 *11 (-1118 *7 *8 *9 *10)) (-4 *7 (-458)) (-4 *8 (-799)) (-4 *9 (-856)) (-5 *1 (-1154 *7 *8 *9 *10 *11))))) +(((*1 *2 *3) (-12 (-5 *3 (-868)) (-5 *2 (-1168)) (-5 *1 (-716))))) +(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) +(((*1 *2 *3 *3 *4 *5 *5 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-1168)) (-5 *5 (-695 (-227))) + (-5 *2 (-1044)) (-5 *1 (-753))))) +(((*1 *1 *1) (-4 *1 (-551)))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-512)) (-5 *3 (-1127)) (-5 *1 (-1124))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) ((*1 *2 *2) - (-12 (-4 *3 (-38 (-413 (-570)))) (-4 *4 (-1267 *3)) - (-5 *1 (-281 *3 *4 *2)) (-4 *2 (-1238 *3 *4)))) + (-12 (-4 *3 (-38 (-413 (-570)))) (-4 *4 (-1268 *3)) + (-5 *1 (-281 *3 *4 *2)) (-4 *2 (-1239 *3 *4)))) ((*1 *2 *2) - (-12 (-4 *3 (-38 (-413 (-570)))) (-4 *4 (-1236 *3)) - (-5 *1 (-282 *3 *4 *2 *5)) (-4 *2 (-1259 *3 *4)) (-4 *5 (-992 *4)))) + (-12 (-4 *3 (-38 (-413 (-570)))) (-4 *4 (-1237 *3)) + (-5 *1 (-282 *3 *4 *2 *5)) (-4 *2 (-1260 *3 *4)) (-4 *5 (-992 *4)))) ((*1 *1 *2) (-12 (-5 *1 (-335 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-344 *2 *3 *4)) (-14 *2 (-650 (-1186))) @@ -10327,281 +10483,452 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) - ((*1 *1 *1) (-4 *1 (-1214)))) + ((*1 *1 *1) (-4 *1 (-1215)))) +(((*1 *2 *3) + (|partial| -12 (-4 *4 (-13 (-562) (-148))) + (-5 *2 (-2 (|:| -4398 *3) (|:| -4411 *3))) (-5 *1 (-1247 *4 *3)) + (-4 *3 (-1253 *4))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-1166 *3)) (-4 *3 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*3)) (-4 *3 (-311)) (-5 *1 (-706 *3))))) +(((*1 *1 *2 *1) (-12 (-5 *2 (-109)) (-5 *1 (-177))))) +(((*1 *2 *3) + (-12 (-4 *4 (-799)) (-4 *5 (-856)) (-4 *6 (-311)) + (-5 *2 (-650 (-777))) (-5 *1 (-784 *3 *4 *5 *6 *7)) + (-4 *3 (-1253 *6)) (-4 *7 (-956 *6 *4 *5))))) +(((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-695 *3)) (-4 *3 (-1058)) (-5 *1 (-696 *3))))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1058)) (-4 *3 (-798)))) ((*1 *1 *1) (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1058)) (-14 *3 (-650 (-1186))))) @@ -13455,13 +13663,13 @@ (-12 (-14 *2 (-650 (-1186))) (-4 *3 (-174)) (-4 *5 (-240 (-2426 *2) (-777))) (-14 *6 - (-1 (-112) (-2 (|:| -2159 *4) (|:| -1907 *5)) - (-2 (|:| -2159 *4) (|:| -1907 *5)))) + (-1 (-112) (-2 (|:| -2160 *4) (|:| -3011 *5)) + (-2 (|:| -2160 *4) (|:| -3011 *5)))) (-5 *1 (-467 *2 *3 *4 *5 *6 *7)) (-4 *4 (-856)) (-4 *7 (-956 *3 *5 (-870 *2))))) ((*1 *1 *1) (-12 (-4 *1 (-515 *2 *3)) (-4 *2 (-1109)) (-4 *3 (-856)))) ((*1 *1 *1) - (-12 (-4 *2 (-562)) (-5 *1 (-629 *2 *3)) (-4 *3 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(-1226))))) + (-12 (-5 *3 (-570)) (-5 *2 (-1282)) (-5 *1 (-1166 *4)) + (-4 *4 (-1109)) (-4 *4 (-1227))))) (((*1 *2 *1 *3 *3 *2) - (-12 (-5 *3 (-570)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1226)) + (-12 (-5 *3 (-570)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1227)) (-4 *4 (-378 *2)) (-4 *5 (-378 *2)))) ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-570)) (-4 *1 (-57 *2 *4 *5)) (-4 *4 (-378 *2)) - (-4 *5 (-378 *2)) (-4 *2 (-1226)))) + (-4 *5 (-378 *2)) (-4 *2 (-1227)))) ((*1 *1 *1 *2) - (-12 (-5 *2 "right") (-4 *1 (-120 *3)) (-4 *3 (-1226)))) - ((*1 *1 *1 *2) (-12 (-5 *2 "left") (-4 *1 (-120 *3)) (-4 *3 (-1226)))) + (-12 (-5 *2 "right") (-4 *1 (-120 *3)) (-4 *3 (-1227)))) + ((*1 *1 *1 *2) (-12 (-5 *2 "left") (-4 *1 (-120 *3)) (-4 *3 (-1227)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-650 (-570))) (-4 *2 (-174)) (-5 *1 (-137 *4 *5 *2)) (-14 *4 (-570)) (-14 *5 (-777)))) @@ -13547,14 +13756,14 @@ (-12 (-5 *3 (-1186)) (-5 *2 (-247 (-1168))) (-5 *1 (-216 *4)) (-4 *4 (-13 (-856) - (-10 -8 (-15 -1876 ((-1168) $ *3)) (-15 -4131 ((-1281) $)) - (-15 -2919 ((-1281) $))))))) + (-10 -8 (-15 -1877 ((-1168) $ *3)) (-15 -4131 ((-1282) $)) + (-15 -3807 ((-1282) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-998)) (-5 *1 (-216 *3)) (-4 *3 (-13 (-856) - (-10 -8 (-15 -1876 ((-1168) $ (-1186))) (-15 -4131 ((-1281) $)) - (-15 -2919 ((-1281) $))))))) + (-10 -8 (-15 -1877 ((-1168) $ (-1186))) (-15 -4131 ((-1282) $)) + (-15 -3807 ((-1282) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-777)) (-5 *1 (-247 *4)) (-4 *4 (-856)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-247 *3)) (-4 *3 (-856)))) @@ -13562,12 +13771,12 @@ (-12 (-5 *2 "unique") (-5 *1 (-247 *3)) (-4 *3 (-856)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-777)) (-5 *2 (-1191)) (-5 *1 (-252)))) ((*1 *2 *1 *3) - (-12 (-4 *1 (-290 *3 *2)) (-4 *3 (-1109)) (-4 *2 (-1226)))) + (-12 (-4 *1 (-290 *3 *2)) (-4 *3 (-1109)) (-4 *2 (-1227)))) ((*1 *2 *1 *3 *2) - (-12 (-4 *1 (-292 *3 *2)) (-4 *3 (-1109)) (-4 *2 (-1226)))) + (-12 (-4 *1 (-292 *3 *2)) (-4 *3 (-1109)) (-4 *2 (-1227)))) ((*1 *2 *1 *2) (-12 (-4 *3 (-174)) (-5 *1 (-293 *3 *2 *4 *5 *6 *7)) - (-4 *2 (-1252 *3)) (-4 *4 (-23)) (-14 *5 (-1 *2 *2 *4)) + (-4 *2 (-1253 *3)) (-4 *4 (-23)) (-14 *5 (-1 *2 *2 *4)) (-14 *6 (-1 (-3 *4 "failed") *4 *4)) (-14 *7 (-1 (-3 *2 "failed") *2 *2 *4)))) ((*1 *1 *2 *3) (-12 (-5 *2 (-115)) (-5 *3 (-650 *1)) (-4 *1 (-306)))) @@ -13576,13 +13785,13 @@ ((*1 *1 *2 *1 *1) (-12 (-4 *1 (-306)) (-5 *2 (-115)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-306)) (-5 *2 (-115)))) ((*1 *2 *1 *2 *2) - (-12 (-4 *1 (-347 *2 *3 *4)) (-4 *2 (-1230)) (-4 *3 (-1252 *2)) - (-4 *4 (-1252 (-413 *3))))) + (-12 (-4 *1 (-347 *2 *3 *4)) (-4 *2 (-1231)) (-4 *3 (-1253 *2)) + (-4 *4 (-1253 (-413 *3))))) ((*1 *2 *1 *3) (-12 (-5 *3 (-570)) (-4 *1 (-423 *2)) (-4 *2 (-174)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-1186)) (-5 *2 (-1168)) (-5 *1 (-508)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-1186)) (-5 *2 (-52)) (-5 *1 (-638)))) ((*1 *1 *1 *2) - (-12 (-5 *2 (-1243 (-570))) (-4 *1 (-657 *3)) (-4 *3 (-1226)))) + (-12 (-5 *2 (-1244 (-570))) (-4 *1 (-657 *3)) (-4 *3 (-1227)))) ((*1 *2 *1 *3 *3 *3) (-12 (-5 *3 (-777)) (-5 *1 (-681 *2)) (-4 *2 (-1109)))) ((*1 *1 *1 *2 *2) @@ -13600,8 +13809,8 @@ (-12 (-5 *3 (-242 *4 *2)) (-14 *4 (-928)) (-4 *2 (-368)) (-5 *1 (-1002 *4 *2)))) ((*1 *2 *1 *3) - (-12 (-5 *3 "value") (-4 *1 (-1019 *2)) (-4 *2 (-1226)))) - ((*1 *2 *1) (-12 (-5 *1 (-1035 *2)) (-4 *2 (-1226)))) + (-12 (-5 *3 "value") (-4 *1 (-1019 *2)) (-4 *2 (-1227)))) + ((*1 *2 *1) (-12 (-5 *1 (-1035 *2)) (-4 *2 (-1227)))) ((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-570)) (-4 *1 (-1062 *4 *5 *2 *6 *7)) (-4 *2 (-1058)) (-4 *6 (-240 *5 *2)) (-4 *7 (-240 *4 *2)))) @@ -13628,29 +13837,38 @@ ((*1 *1 *1 *1) (-4 *1 (-1153))) ((*1 *1 *1 *2) (-12 (-5 *2 (-650 (-868))) (-5 *1 (-1186)))) ((*1 *2 *3 *2) - (-12 (-5 *3 (-413 *1)) (-4 *1 (-1252 *2)) (-4 *2 (-1058)) + (-12 (-5 *3 (-413 *1)) (-4 *1 (-1253 *2)) (-4 *2 (-1058)) (-4 *2 (-368)))) ((*1 *2 *2 *2) - (-12 (-5 *2 (-413 *1)) (-4 *1 (-1252 *3)) (-4 *3 (-1058)) + (-12 (-5 *2 (-413 *1)) (-4 *1 (-1253 *3)) (-4 *3 (-1058)) (-4 *3 (-562)))) ((*1 *2 *1 *3) - (-12 (-4 *1 (-1254 *2 *3)) (-4 *3 (-798)) (-4 *2 (-1058)))) + (-12 (-4 *1 (-1255 *2 *3)) (-4 *3 (-798)) (-4 *2 (-1058)))) ((*1 *2 *1 *3) - (-12 (-5 *3 "last") (-4 *1 (-1264 *2)) (-4 *2 (-1226)))) + (-12 (-5 *3 "last") (-4 *1 (-1265 *2)) (-4 *2 (-1227)))) ((*1 *1 *1 *2) - (-12 (-5 *2 "rest") (-4 *1 (-1264 *3)) (-4 *3 (-1226)))) + (-12 (-5 *2 "rest") (-4 *1 (-1265 *3)) (-4 *3 (-1227)))) ((*1 *2 *1 *3) - (-12 (-5 *3 "first") (-4 *1 (-1264 *2)) (-4 *2 (-1226))))) -(((*1 *2 *3 *1 *4) - (-12 (-5 *3 (-1149 *5 *6)) (-5 *4 (-1 (-112) *6 *6)) - (-4 *5 (-13 (-1109) (-34))) (-4 *6 (-13 (-1109) (-34))) - (-5 *2 (-112)) (-5 *1 (-1150 *5 *6))))) + (-12 (-5 *3 "first") (-4 *1 (-1265 *2)) (-4 *2 (-1227))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-777)) (-4 *1 (-1253 *3)) (-4 *3 (-1058)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-928)) (-4 *1 (-1255 *3 *4)) (-4 *3 (-1058)) + (-4 *4 (-798)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-413 (-570))) (-4 *1 (-1258 *3)) (-4 *3 (-1058))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-1186)) + (-4 *6 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) + (-4 *4 (-13 (-29 *6) (-1212) (-966))) + (-5 *2 (-2 (|:| |particular| *4) (|:| -2003 (-650 *4)))) + (-5 *1 (-807 *6 *4 *3)) (-4 *3 (-662 *4))))) (((*1 *1 *2) (-12 (-5 *2 (-650 *1)) (-4 *1 (-458)))) ((*1 *1 *1 *1) (-4 *1 (-458))) ((*1 *2 *3) - (-12 (-5 *3 (-650 *2)) (-5 *1 (-492 *2)) (-4 *2 (-1252 (-570))))) + (-12 (-5 *3 (-650 *2)) (-5 *1 (-492 *2)) (-4 *2 (-1253 (-570))))) ((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-570)) (-5 *1 (-702 *2)) (-4 *2 (-1252 *3)))) + (-12 (-5 *3 (-570)) (-5 *1 (-702 *2)) (-4 *2 (-1253 *3)))) ((*1 *1 *1 *1) (-5 *1 (-777))) ((*1 *2 *2 *2) (-12 (-4 *3 (-799)) (-4 *4 (-856)) (-4 *5 (-311)) @@ -13669,40 +13887,31 @@ ((*1 *1 *1 *1) (-5 *1 (-928))) ((*1 *2 *2 *2) (-12 (-4 *3 (-458)) (-4 *3 (-562)) (-5 *1 (-978 *3 *2)) - (-4 *2 (-1252 *3)))) + (-4 *2 (-1253 *3)))) ((*1 *2 *2 *1) (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) (-4 *4 (-856)) (-4 *2 (-458))))) +(((*1 *2 *2) + (-12 (-5 *2 (-650 *6)) (-4 *6 (-1074 *3 *4 *5)) (-4 *3 (-562)) + (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-986 *3 *4 *5 *6))))) (((*1 *2 *1) (-12 (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *2 (-650 *1)) (-4 *1 (-956 *3 *4 *5))))) -(((*1 *2 *3 *3 *3 *4) - (-12 (-5 *3 (-1 (-227) (-227) (-227))) - (-5 *4 (-1 (-227) (-227) (-227) (-227))) - (-5 *2 (-1 (-950 (-227)) (-227) (-227))) (-5 *1 (-703))))) -(((*1 *1) (-5 *1 (-565)))) -(((*1 *2) (-12 (-5 *2 (-777)) (-5 *1 (-451 *3)) (-4 *3 (-1058))))) -(((*1 *2 *3) - (|partial| -12 (-5 *2 (-570)) (-5 *1 (-1208 *3)) (-4 *3 (-1058))))) -(((*1 *2 *3 *4 *5) - (-12 (-4 *6 (-1252 *9)) (-4 *7 (-799)) (-4 *8 (-856)) (-4 *9 (-311)) - (-4 *10 (-956 *9 *7 *8)) - (-5 *2 - (-2 (|:| |deter| (-650 (-1182 *10))) - (|:| |dterm| - (-650 (-650 (-2 (|:| -2174 (-777)) (|:| |pcoef| *10))))) - (|:| |nfacts| (-650 *6)) (|:| |nlead| (-650 *10)))) - (-5 *1 (-784 *6 *7 *8 *9 *10)) (-5 *3 (-1182 *10)) (-5 *4 (-650 *6)) - (-5 *5 (-650 *10))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1166 *4)) (-5 *3 (-1 *4 (-570))) (-4 *4 (-1058)) - (-5 *1 (-1170 *4))))) -(((*1 *1 *1) (-4 *1 (-175))) - ((*1 *1 *1) - (-12 (-4 *1 (-369 *2 *3)) (-4 *2 (-1109)) (-4 *3 (-1109))))) -(((*1 *2 *1) (-12 (-5 *2 (-570)) (-5 *1 (-158)))) - ((*1 *2 *1) (-12 (-5 *2 (-158)) (-5 *1 (-880)))) - ((*1 *2 *3) (-12 (-5 *3 (-950 *2)) (-5 *1 (-991 *2)) (-4 *2 (-1058))))) +(((*1 *2 *2) (-12 (-5 *2 (-650 (-320 (-227)))) (-5 *1 (-270))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-650 *5)) (-5 *4 (-928)) (-4 *5 (-856)) + (-5 *2 (-59 (-650 (-678 *5)))) (-5 *1 (-678 *5))))) +(((*1 *1 *2) (-12 (-5 *2 (-650 (-145))) (-5 *1 (-142)))) + ((*1 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-142))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1 (-1166 *3))) (-5 *1 (-1166 *3)) (-4 *3 (-1227))))) +(((*1 *2 *3 *3) + (-12 (-4 *2 (-562)) (-4 *2 (-458)) (-5 *1 (-978 *2 *3)) + (-4 *3 (-1253 *2))))) +(((*1 *2 *2 *3 *4) + (-12 (-5 *2 (-650 *8)) (-5 *3 (-1 (-112) *8 *8)) + (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1074 *5 *6 *7)) (-4 *5 (-562)) + (-4 *6 (-799)) (-4 *7 (-856)) (-5 *1 (-986 *5 *6 *7 *8))))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-798)) (-4 *2 (-1058)))) ((*1 *2 *1) (-12 (-4 *2 (-1058)) (-5 *1 (-50 *2 *3)) (-14 *3 (-650 (-1186))))) @@ -13714,13 +13923,13 @@ ((*1 *2 *1) (-12 (-14 *3 (-650 (-1186))) (-4 *5 (-240 (-2426 *3) (-777))) (-14 *6 - (-1 (-112) (-2 (|:| -2159 *4) (|:| -1907 *5)) - (-2 (|:| -2159 *4) (|:| -1907 *5)))) + (-1 (-112) (-2 (|:| -2160 *4) (|:| -3011 *5)) + (-2 (|:| -2160 *4) (|:| -3011 *5)))) (-4 *2 (-174)) (-5 *1 (-467 *3 *2 *4 *5 *6 *7)) (-4 *4 (-856)) (-4 *7 (-956 *2 *5 (-870 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-515 *2 *3)) (-4 *3 (-856)) (-4 *2 (-1109)))) ((*1 *2 *1) - (-12 (-4 *2 (-562)) (-5 *1 (-629 *2 *3)) (-4 *3 (-1252 *2)))) + (-12 (-4 *2 (-562)) (-5 *1 (-629 *2 *3)) (-4 *3 (-1253 *2)))) ((*1 *2 *1) (-12 (-4 *1 (-714 *2)) (-4 *2 (-1058)))) ((*1 *2 *1) (-12 (-4 *2 (-1058)) (-5 *1 (-741 *2 *3)) (-4 *3 (-856)) @@ -13732,44 +13941,30 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1074 *3 *4 *2)) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *2 (-856))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112)) - (-5 *1 (-997 *4 *5 *6 *7 *3)) (-4 *3 (-1080 *4 *5 *6 *7)))) - ((*1 *2 *3 *3) - (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112)) - (-5 *1 (-1116 *4 *5 *6 *7 *3)) (-4 *3 (-1080 *4 *5 *6 *7))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-650 *2)) (-4 *2 (-1226))))) -(((*1 *2 *3 *3) - (-12 (-4 *3 (-1230)) (-4 *5 (-1252 *3)) (-4 *6 (-1252 (-413 *5))) - (-5 *2 (-112)) (-5 *1 (-346 *4 *3 *5 *6)) (-4 *4 (-347 *3 *5 *6)))) - ((*1 *2 *3 *3) - (-12 (-4 *1 (-347 *3 *4 *5)) (-4 *3 (-1230)) (-4 *4 (-1252 *3)) - (-4 *5 (-1252 (-413 *4))) (-5 *2 (-112))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) - (-4 *3 (-1074 *5 *6 *7)) - (-5 *2 (-650 (-2 (|:| |val| *3) (|:| -3593 *4)))) - (-5 *1 (-1117 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-1109)) (-5 *2 (-112))))) -(((*1 *2 *3 *4 *5 *3) - (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 (-1 (-3 (-2 (|:| -1400 *6) (|:| |coeff| *6)) "failed") *6)) - (-4 *6 (-368)) (-4 *7 (-1252 *6)) +(((*1 *1 *1) (-5 *1 (-1072)))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-650 *2)) (-4 *2 (-1227))))) +(((*1 *2 *3) + (-12 (-14 *4 (-650 (-1186))) (-4 *5 (-458)) (-5 *2 - (-3 (-2 (|:| |answer| (-413 *7)) (|:| |a0| *6)) - (-2 (|:| -1400 (-413 *7)) (|:| |coeff| (-413 *7))) "failed")) - (-5 *1 (-580 *6 *7)) (-5 *3 (-413 *7))))) -(((*1 *2 *3 *3) - (-12 - (-5 *3 - (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-777)) (|:| |poli| *7) - (|:| |polj| *7))) - (-4 *5 (-799)) (-4 *7 (-956 *4 *5 *6)) (-4 *4 (-458)) (-4 *6 (-856)) - (-5 *2 (-112)) (-5 *1 (-455 *4 *5 *6 *7))))) + (-2 (|:| |glbase| (-650 (-249 *4 *5))) (|:| |glval| (-650 (-570))))) + (-5 *1 (-637 *4 *5)) (-5 *3 (-650 (-249 *4 *5)))))) (((*1 *2 *1) - (-12 (-4 *2 (-1109)) (-5 *1 (-971 *3 *2)) (-4 *3 (-1109))))) + (-12 (-5 *2 (-650 (-950 *4))) (-5 *1 (-1174 *3 *4)) (-14 *3 (-928)) + (-4 *4 (-1058))))) +(((*1 *2 *3) + (-12 (-5 *3 (-227)) (-5 *2 (-112)) (-5 *1 (-303 *4 *5)) (-14 *4 *3) + (-14 *5 *3))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1103 (-849 (-227)))) (-5 *3 (-227)) (-5 *2 (-112)) + (-5 *1 (-309)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-368)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *2 (-112)) + (-5 *1 (-510 *3 *4 *5 *6)) (-4 *6 (-956 *3 *4 *5))))) +(((*1 *2 *1) (-12 (-4 *1 (-1019 *3)) (-4 *3 (-1227)) (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-1174 *3 *4)) (-14 *3 (-928)) + (-4 *4 (-1058))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-283))))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1058)) (-4 *3 (-798)))) ((*1 *2 *1) (-12 (-4 *1 (-387 *3 *2)) (-4 *3 (-1058)) (-4 *2 (-1109)))) @@ -13777,8 +13972,8 @@ (-12 (-14 *3 (-650 (-1186))) (-4 *4 (-174)) (-4 *6 (-240 (-2426 *3) (-777))) (-14 *7 - (-1 (-112) (-2 (|:| -2159 *5) (|:| -1907 *6)) - (-2 (|:| -2159 *5) (|:| -1907 *6)))) + (-1 (-112) (-2 (|:| -2160 *5) (|:| -3011 *6)) + (-2 (|:| -2160 *5) (|:| -3011 *6)))) (-5 *2 (-719 *5 *6 *7)) (-5 *1 (-467 *3 *4 *5 *6 *7 *8)) (-4 *5 (-856)) (-4 *8 (-956 *4 *6 (-870 *3))))) ((*1 *2 *1) @@ -13787,334 +13982,245 @@ ((*1 *1 *1) (-12 (-4 *1 (-982 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-798)) (-4 *4 (-856))))) -(((*1 *2 *2) - (-12 (-4 *3 (-458)) (-5 *1 (-1217 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1211)))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-1186)) (-5 *5 (-1103 (-227))) (-5 *2 (-934)) - (-5 *1 (-932 *3)) (-4 *3 (-620 (-542))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1186)) (-5 *2 (-934)) (-5 *1 (-932 *3)) - (-4 *3 (-620 (-542))))) - ((*1 *1 *2) (-12 (-5 *2 (-1 (-227) (-227))) (-5 *1 (-934)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1 (-227) (-227))) (-5 *3 (-1103 (-227))) - (-5 *1 (-934))))) -(((*1 *1 *2 *3) - (-12 (-5 *1 (-433 *3 *2)) (-4 *3 (-13 (-174) (-38 (-413 (-570))))) - (-4 *2 (-13 (-856) (-21)))))) -(((*1 *2 *1) (-12 (-4 *1 (-395)) (-5 *2 (-1168))))) -(((*1 *2) - (-12 (-5 *2 (-413 (-959 *3))) (-5 *1 (-459 *3 *4 *5 *6)) - (-4 *3 (-562)) (-4 *3 (-174)) (-14 *4 (-928)) - (-14 *5 (-650 (-1186))) (-14 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*3) + (-12 (-5 *2 (-650 (-570))) (-5 *3 (-695 (-570))) (-5 *1 (-1119))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-570)) (-4 *1 (-57 *4 *3 *5)) (-4 *4 (-1227)) + (-4 *3 (-378 *4)) (-4 *5 (-378 *4))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) + (-12 (-5 *3 (-1 *5 *7)) (-5 *4 (-1182 *7)) (-4 *5 (-1058)) + (-4 *7 (-1058)) (-4 *2 (-1253 *5)) (-5 *1 (-507 *5 *2 *6 *7)) + (-4 *6 (-1253 *2)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-1058)) (-4 *7 (-1058)) + (-4 *4 (-1253 *5)) (-5 *2 (-1182 *7)) (-5 *1 (-507 *5 *4 *6 *7)) + (-4 *6 (-1253 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-512)) (-5 *1 (-337))))) (((*1 *1 *2) (-12 (-5 *2 (-650 *1)) (-4 *1 (-458)))) ((*1 *1 *1 *1) (-4 *1 (-458)))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-985 *4 *5 *3 *6)) (-4 *4 (-1058)) (-4 *5 (-799)) - (-4 *3 (-856)) (-4 *6 (-1074 *4 *5 *3)) (-5 *2 (-112))))) -(((*1 *2 *1) (-12 (-5 *2 (-1168)) (-5 *1 (-542))))) (((*1 *2 *1) (-12 (-4 *1 (-330 *2 *3)) (-4 *3 (-798)) (-4 *2 (-1058)))) 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singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1166 (-227))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -3758 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))))) - (-5 *2 (-1044)) (-5 *1 (-309))))) -(((*1 *2 *1) - (-12 (-4 *1 (-693 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-378 *3)) - (-4 *5 (-378 *3)) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1062 *3 *4 *5 *6 *7)) (-4 *5 (-1058)) - (-4 *6 (-240 *4 *5)) (-4 *7 (-240 *3 *5)) (-5 *2 (-112))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-570)) (-5 *2 (-112)) (-5 *1 (-559))))) -(((*1 *2 *1 *1) - (-12 - (-5 *2 - (-2 (|:| |polnum| (-788 *3)) (|:| |polden| *3) (|:| -3184 (-777)))) - (-5 *1 (-788 *3)) 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*6 (-1227)) (-5 *2 (-59 *6)) (-5 *1 (-58 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *8 *7)) (-5 *4 (-137 *5 *6 *7)) (-14 *5 (-570)) (-14 *6 (-777)) (-4 *7 (-174)) (-4 *8 (-174)) @@ -17076,16 +17099,16 @@ (-5 *1 (-225 *3 *4)) (-14 *4 (-650 (-1186))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) - (-4 *6 (-1226)) (-4 *7 (-1226)) (-5 *2 (-242 *5 *7)) + (-4 *6 (-1227)) (-4 *7 (-1227)) (-5 *2 (-242 *5 *7)) (-5 *1 (-241 *5 *6 *7)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-298 *5)) (-4 *5 (-1226)) - (-4 *6 (-1226)) (-5 *2 (-298 *6)) (-5 *1 (-297 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-298 *5)) (-4 *5 (-1227)) + (-4 *6 (-1227)) (-5 *2 (-298 *6)) (-5 *1 (-297 *5 *6)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1226)) (-5 *1 (-298 *3)))) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1227)) (-5 *1 (-298 *3)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1168)) (-5 *5 (-618 *6)) - (-4 *6 (-306)) (-4 *2 (-1226)) (-5 *1 (-301 *6 *2)))) + (-4 *6 (-306)) (-4 *2 (-1227)) (-5 *1 (-301 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *2 *5)) (-5 *4 (-618 *5)) (-4 *5 (-306)) (-4 *2 (-306)) (-5 *1 (-302 *5 *2)))) @@ -17099,20 +17122,20 @@ (-4 *6 (-1109)) (-5 *2 (-320 *6)) (-5 *1 (-318 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-341 *5 *6 *7 *8)) (-4 *5 (-368)) - (-4 *6 (-1252 *5)) (-4 *7 (-1252 (-413 *6))) (-4 *8 (-347 *5 *6 *7)) - (-4 *9 (-368)) (-4 *10 (-1252 *9)) (-4 *11 (-1252 (-413 *10))) + (-4 *6 (-1253 *5)) (-4 *7 (-1253 (-413 *6))) (-4 *8 (-347 *5 *6 *7)) + (-4 *9 (-368)) (-4 *10 (-1253 *9)) (-4 *11 (-1253 (-413 *10))) (-5 *2 (-341 *9 *10 *11 *12)) (-5 *1 (-338 *5 *6 *7 *8 *9 *10 *11 *12)) (-4 *12 (-347 *9 *10 *11)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-343 *3)) (-4 *3 (-1109)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1230)) (-4 *8 (-1230)) - (-4 *6 (-1252 *5)) (-4 *7 (-1252 (-413 *6))) (-4 *9 (-1252 *8)) + (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1231)) (-4 *8 (-1231)) + (-4 *6 (-1253 *5)) (-4 *7 (-1253 (-413 *6))) (-4 *9 (-1253 *8)) (-4 *2 (-347 *8 *9 *10)) (-5 *1 (-345 *5 *6 *7 *4 *8 *9 *10 *2)) - (-4 *4 (-347 *5 *6 *7)) (-4 *10 (-1252 (-413 *9))))) + (-4 *4 (-347 *5 *6 *7)) (-4 *10 (-1253 (-413 *9))))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1226)) (-4 *6 (-1226)) + (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1227)) (-4 *6 (-1227)) (-4 *2 (-378 *6)) (-5 *1 (-376 *5 *4 *6 *2)) (-4 *4 (-378 *5)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-387 *3 *4)) (-4 *3 (-1058)) @@ -17125,9 +17148,9 @@ (-4 *6 (-562)) (-5 *2 (-413 *6)) (-5 *1 (-412 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-419 *5 *6 *7 *8)) (-4 *5 (-311)) - (-4 *6 (-1001 *5)) (-4 *7 (-1252 *6)) + (-4 *6 (-1001 *5)) (-4 *7 (-1253 *6)) (-4 *8 (-13 (-415 *6 *7) (-1047 *6))) (-4 *9 (-311)) - (-4 *10 (-1001 *9)) (-4 *11 (-1252 *10)) + (-4 *10 (-1001 *9)) (-4 *11 (-1253 *10)) (-5 *2 (-419 *9 *10 *11 *12)) (-5 *1 (-418 *5 *6 *7 *8 *9 *10 *11 *12)) (-4 *12 (-13 (-415 *10 *11) (-1047 *10))))) @@ -17143,7 +17166,7 @@ (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1109)) (-4 *6 (-1109)) (-4 *2 (-431 *6)) (-5 *1 (-429 *5 *4 *6 *2)) (-4 *4 (-431 *5)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-495 *3)) (-4 *3 (-1226)))) + (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-495 *3)) (-4 *3 (-1227)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-515 *3 *4)) (-4 *3 (-1109)) (-4 *4 (-856)))) @@ -17152,9 +17175,9 @@ (-4 *6 (-368)) (-5 *2 (-592 *6)) (-5 *1 (-590 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -1400 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -3585 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-368)) (-4 *6 (-368)) - (-5 *2 (-2 (|:| -1400 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -3585 *6) (|:| |coeff| *6))) (-5 *1 (-590 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -17174,31 +17197,31 @@ (-650 (-2 (|:| |coeff| *6) (|:| |logand| *6)))))) (-5 *1 (-590 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-607 *5)) (-4 *5 (-1226)) - (-4 *6 (-1226)) (-5 *2 (-607 *6)) (-5 *1 (-604 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-607 *5)) (-4 *5 (-1227)) + (-4 *6 (-1227)) (-5 *2 (-607 *6)) (-5 *1 (-604 *5 *6)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-607 *6)) (-5 *5 (-607 *7)) - (-4 *6 (-1226)) (-4 *7 (-1226)) (-4 *8 (-1226)) (-5 *2 (-607 *8)) + (-4 *6 (-1227)) (-4 *7 (-1227)) (-4 *8 (-1227)) (-5 *2 (-607 *8)) (-5 *1 (-605 *6 *7 *8)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-1166 *6)) (-5 *5 (-607 *7)) - (-4 *6 (-1226)) (-4 *7 (-1226)) (-4 *8 (-1226)) (-5 *2 (-1166 *8)) + (-4 *6 (-1227)) (-4 *7 (-1227)) (-4 *8 (-1227)) (-5 *2 (-1166 *8)) (-5 *1 (-605 *6 *7 *8)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-607 *6)) (-5 *5 (-1166 *7)) - (-4 *6 (-1226)) (-4 *7 (-1226)) (-4 *8 (-1226)) (-5 *2 (-1166 *8)) + (-4 *6 (-1227)) (-4 *7 (-1227)) (-4 *8 (-1227)) (-5 *2 (-1166 *8)) (-5 *1 (-605 *6 *7 *8)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1226)) (-5 *1 (-607 *3)))) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1227)) (-5 *1 (-607 *3)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-650 *5)) (-4 *5 (-1226)) - (-4 *6 (-1226)) (-5 *2 (-650 *6)) (-5 *1 (-648 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-650 *5)) (-4 *5 (-1227)) + (-4 *6 (-1227)) (-5 *2 (-650 *6)) (-5 *1 (-648 *5 *6)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-650 *6)) (-5 *5 (-650 *7)) - (-4 *6 (-1226)) (-4 *7 (-1226)) (-4 *8 (-1226)) (-5 *2 (-650 *8)) + (-4 *6 (-1227)) (-4 *7 (-1227)) (-4 *8 (-1227)) (-5 *2 (-650 *8)) (-5 *1 (-649 *6 *7 *8)))) ((*1 *1 *2 *1 *1) - (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-657 *3)) (-4 *3 (-1226)))) + (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-657 *3)) (-4 *3 (-1227)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1058)) (-4 *8 (-1058)) (-4 *6 (-378 *5)) (-4 *7 (-378 *5)) (-4 *2 (-693 *8 *9 *10)) @@ -17211,9 +17234,9 @@ (-4 *4 (-693 *5 *6 *7)) (-4 *9 (-378 *8)) (-4 *10 (-378 *8)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-562)) (-4 *7 (-562)) - (-4 *6 (-1252 *5)) (-4 *2 (-1252 (-413 *8))) - (-5 *1 (-715 *5 *6 *4 *7 *8 *2)) (-4 *4 (-1252 (-413 *6))) - (-4 *8 (-1252 *7)))) + (-4 *6 (-1253 *5)) (-4 *2 (-1253 (-413 *8))) + (-5 *1 (-715 *5 *6 *4 *7 *8 *2)) (-4 *4 (-1253 (-413 *6))) + (-4 *8 (-1253 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *9 *8)) (-4 *8 (-1058)) (-4 *9 (-1058)) (-4 *5 (-856)) (-4 *6 (-799)) (-4 *2 (-956 *9 *7 *5)) @@ -17250,14 +17273,14 @@ (-12 (-5 *2 (-849 *6)) (-5 *3 (-1 *6 *5)) (-5 *4 (-849 *5)) (-4 *5 (-1109)) (-4 *6 (-1109)) (-5 *1 (-848 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-884 *5)) (-4 *5 (-1226)) - (-4 *6 (-1226)) (-5 *2 (-884 *6)) (-5 *1 (-883 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-884 *5)) (-4 *5 (-1227)) + (-4 *6 (-1227)) (-5 *2 (-884 *6)) (-5 *1 (-883 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-886 *5)) (-4 *5 (-1226)) - (-4 *6 (-1226)) (-5 *2 (-886 *6)) (-5 *1 (-885 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-886 *5)) (-4 *5 (-1227)) + (-4 *6 (-1227)) (-5 *2 (-886 *6)) (-5 *1 (-885 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-889 *5)) (-4 *5 (-1226)) - (-4 *6 (-1226)) (-5 *2 (-889 *6)) (-5 *1 (-888 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-889 *5)) (-4 *5 (-1227)) + (-4 *6 (-1227)) (-5 *2 (-889 *6)) (-5 *1 (-888 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-896 *5 *6)) (-4 *5 (-1109)) (-4 *6 (-1109)) (-4 *7 (-1109)) (-5 *2 (-896 *5 *7)) @@ -17273,11 +17296,11 @@ (-4 *8 (-1058)) (-4 *6 (-799)) (-4 *2 (-13 (-1109) - (-10 -8 (-15 -2954 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-777)))))) + (-10 -8 (-15 -2953 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-777)))))) (-5 *1 (-958 *6 *7 *8 *5 *2)) (-4 *5 (-956 *8 *6 *7)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-965 *5)) (-4 *5 (-1226)) - (-4 *6 (-1226)) (-5 *2 (-965 *6)) (-5 *1 (-964 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-965 *5)) (-4 *5 (-1227)) + (-4 *6 (-1227)) (-5 *2 (-965 *6)) (-5 *1 (-964 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-973 *5)) (-4 *5 (-1109)) (-4 *6 (-1109)) (-5 *2 (-973 *6)) (-5 *1 (-975 *5 *6)))) @@ -17289,7 +17312,7 @@ (-4 *2 (-956 (-959 *4) *5 *6)) (-4 *5 (-799)) (-4 *6 (-13 (-856) - (-10 -8 (-15 -1416 ((-1186) $)) + (-10 -8 (-15 -1417 ((-1186) $)) (-15 -2643 ((-3 $ "failed") (-1186)))))) (-5 *1 (-993 *4 *5 *6 *2)))) ((*1 *2 *3 *4) @@ -17312,1030 +17335,1006 @@ (-4 *4 (-1062 *5 *6 *7 *8 *9)) (-4 *11 (-240 *6 *10)) (-4 *12 (-240 *5 *10)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1103 *5)) (-4 *5 (-1226)) - (-4 *6 (-1226)) (-5 *2 (-1103 *6)) (-5 *1 (-1098 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1103 *5)) (-4 *5 (-1227)) + (-4 *6 (-1227)) (-5 *2 (-1103 *6)) (-5 *1 (-1098 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1103 *5)) (-4 *5 (-854)) - (-4 *5 (-1226)) (-4 *6 (-1226)) (-5 *2 (-650 *6)) + (-4 *5 (-1227)) (-4 *6 (-1227)) (-5 *2 (-650 *6)) (-5 *1 (-1098 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1101 *5)) (-4 *5 (-1226)) - (-4 *6 (-1226)) (-5 *2 (-1101 *6)) (-5 *1 (-1100 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1101 *5)) (-4 *5 (-1227)) + (-4 *6 (-1227)) (-5 *2 (-1101 *6)) (-5 *1 (-1100 *5 *6)))) ((*1 *2 *3 *1) (-12 (-5 *3 (-1 *4 *4)) (-4 *1 (-1104 *4 *2)) (-4 *4 (-854)) (-4 *2 (-1158 *4)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1166 *5)) (-4 *5 (-1226)) - (-4 *6 (-1226)) (-5 *2 (-1166 *6)) (-5 *1 (-1164 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1166 *5)) (-4 *5 (-1227)) + (-4 *6 (-1227)) (-5 *2 (-1166 *6)) (-5 *1 (-1164 *5 *6)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-1166 *6)) (-5 *5 (-1166 *7)) - (-4 *6 (-1226)) (-4 *7 (-1226)) (-4 *8 (-1226)) (-5 *2 (-1166 *8)) + (-4 *6 (-1227)) (-4 *7 (-1227)) (-4 *8 (-1227)) (-5 *2 (-1166 *8)) (-5 *1 (-1165 *6 *7 *8)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1182 *5)) (-4 *5 (-1058)) (-4 *6 (-1058)) (-5 *2 (-1182 *6)) (-5 *1 (-1180 *5 *6)))) ((*1 *1 *2 *1 *1) - (-12 (-5 *2 (-1 *4 *4 *4)) (-4 *1 (-1202 *3 *4)) (-4 *3 (-1109)) + (-12 (-5 *2 (-1 *4 *4 *4)) (-4 *1 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\ No newline at end of file |