diff options
| author | dos-reis <gdr@axiomatics.org> | 2011-05-19 21:38:54 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2011-05-19 21:38:54 +0000 |
| commit | 09469d002d15b88c105731142bce403a1aa5a21b (patch) | |
| tree | c91273f9d8a7b5ae5bd3efb0f67734db0fb49dee /src/share | |
| parent | 0d25890bd7bc8bd697294a3288396c23a2438879 (diff) | |
| download | open-axiom-09469d002d15b88c105731142bce403a1aa5a21b.tar.gz | |
* algebra/aggcat.spad.pamphlet (Aggregate) [more?,less?,size?]:
Move to StreamAggregate.
* algebra/array2.spad.pamphlet (TwoDimensionalArrayCategory):
Don't implement them.
* algebra/tree.spad.pamphlet (Tree): Likewise.
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 646 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1574 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1334 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9142 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 30662 |
5 files changed, 21683 insertions, 21675 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index f731e903..59c65b35 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2294555 . 3514591832) +(2294555 . 3514823548) (-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 @@ -56,16 +56,16 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -4131) +(-32 R -4164) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-33 S) -((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|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} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) +((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL ((|HasAttribute| |#1| (QUOTE -4510))) (-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} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) +((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL NIL (-35) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) NIL NIL -(-40 -4131 UP UPUP -3851) +(-40 -4164 UP UPUP -3871) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-4133 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-4133 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4133 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4133 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-4133 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-4133 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) -(-41 R -4131) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-4144 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-4144 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4144 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4144 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-4144 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-4144 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +(-41 R -4164) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -435) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4510 . T) (-4511 . T)) -((-4133 (-12 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1580) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3432) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1580) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3432) (|devaluate| |#2|))))))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-872))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1580) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3432) (|devaluate| |#2|))))))) +((-4144 (-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#2|))))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-872))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -4131) +(-54 |Base| R -4164) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -163,7 +163,7 @@ NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-59 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -171,64 +171,64 @@ NIL (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray's."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -3665) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -4401) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-62 -3665) +(-62 -4401) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-63 -3665) +(-63 -4401) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-64 -3665) +(-64 -4401) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-65 -3665) +(-65 -4401) ((|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 -3665) +(-66 -4401) ((|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 -3665) +(-67 -4401) ((|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 -3665) +(-68 -4401) ((|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 -3665) +(-69 -4401) ((|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 -3665) +(-70 -4401) ((|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 -3665) +(-71 -4401) ((|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 -3665) +(-72 -4401) ((|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 -3665) +(-73 -4401) ((|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 -3665) +(-74 -4401) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-75 -3665) +(-75 -4401) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -240,51 +240,51 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives wrt \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-78 -3665) +(-78 -4401) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -3665) +(-79 -4401) ((|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 -3665) +(-80 -4401) ((|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 -3665) +(-81 -4401) ((|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 -3665) +(-82 -4401) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -3665) +(-83 -4401) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3665) +(-84 -4401) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3665) +(-85 -4401) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -3665) +(-86 -4401) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -3665) +(-87 -4401) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-88 -3665) +(-88 -4401) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-89 -3665) +(-89 -4401) ((|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 @@ -295,7 +295,7 @@ NIL (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values pl and pr. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} := \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -363,7 +363,7 @@ NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4133 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4144 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -396,7 +396,7 @@ NIL ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) NIL NIL -(-117 -4131 UP) +(-117 -4164 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL @@ -407,7 +407,7 @@ NIL (-119 |p|) ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-118 |#1|) (QUOTE (-940))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1052))) (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872))) (-4133 (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1184))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) +((|HasCategory| (-118 |#1|) (QUOTE (-940))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1052))) (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872))) (-4144 (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1184))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) (-120 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -423,7 +423,7 @@ NIL (-123 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-124 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -443,11 +443,11 @@ NIL (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) NIL @@ -455,7 +455,7 @@ NIL (-131) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-4133 (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-130) (QUOTE (-872))) (-4133 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) +((-4144 (-12 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-4144 (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-130) (QUOTE (-872))) (-4144 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-132) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -476,11 +476,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4512 "*") . T)) NIL -(-137 |minix| -4478 R) +(-137 |minix| -2127 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL -(-138 |minix| -4478 S T$) +(-138 |minix| -2127 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL @@ -503,7 +503,7 @@ NIL (-143) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4510 . T) (-4500 . T) (-4511 . T)) -((-4133 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-4144 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-144 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL @@ -528,7 +528,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4507 . T)) NIL -(-150 -4131 UP UPUP) +(-150 -4164 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) NIL NIL @@ -568,7 +568,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-160 R -4131) +(-160 R -4164) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})/P(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} n!.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} n!/(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} n!/(r! * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -602,7 +602,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasAttribute| |#2| (QUOTE -4509)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571)))) (-168 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4503 -4133 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-2804 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 -4144 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-2873 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-169 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -614,8 +614,8 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4503 -4133 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-2804 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . 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T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-4144 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-363)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-940))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-940)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-940))))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1235)))) (|HasCategory| |#1| (QUOTE (-1235))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-571)))) (-4144 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-1235)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4509)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-363))))) (-172 R S) ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL @@ -692,7 +692,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL -(-191 R -4131) +(-191 R -4164) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -804,23 +804,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-219 -4131 UP UPUP R) +(-219 -4164 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-220 -4131 FP) +(-220 -4164 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and q= size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-221) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4133 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4144 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-222) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `d'.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-223 R -4131) +(-223 R -4164) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -835,18 +835,18 @@ NIL (-226 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-227 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4507 . T)) NIL -(-228 R -4131) +(-228 R -4164) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-229) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-2793 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2862 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-230) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -855,7 +855,7 @@ NIL (-231 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-232 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL @@ -904,19 +904,19 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-244 S -4478 R) +(-244 S -2127 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (QUOTE (-872))) (|HasAttribute| |#3| (QUOTE -4507)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (QUOTE (-1133)))) -(-245 -4478 R) +(-245 -2127 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) ((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . T)) NIL -(-246 -4478 R) +(-246 -2127 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) ((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . 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The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL @@ -939,7 +939,7 @@ NIL (-252 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}"))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-253 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's algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -951,7 +951,7 @@ NIL (-255 |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"))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (-4133 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4133 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4133 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4133 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4133 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (-4144 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4144 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-256) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|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 `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|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 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In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := 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 @@ -1031,7 +1031,7 @@ NIL (-275 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1076,11 +1076,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-287 R -4131) +(-287 R -4164) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-288 R -4131) +(-288 R -4164) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1132,7 +1132,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-301 S R |Mod| -1740 -2237 |exactQuo|) +(-301 S R |Mod| -2386 -2834 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1150,8 +1150,8 @@ NIL NIL (-305 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4507 -4133 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4504 |has| |#1| (-1081)) (-4505 |has| |#1| (-1081))) -((|HasCategory| |#1| (QUOTE (-376))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-4133 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4133 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4133 (|HasCategory| |#1| (|%list| 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(|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1144)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-4144 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-4144 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-748)))) (-306 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL @@ -1159,7 +1159,7 @@ NIL (-307 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1580) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3432) (|devaluate| |#2|)))))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#2|)))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102)))) (-308) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL @@ -1172,11 +1172,11 @@ NIL ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-311 -4131 S) +(-311 -4164 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-312 E -4131) +(-312 E -4164) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1216,7 +1216,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-322 -4131) +(-322 -4164) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL @@ -1231,11 +1231,11 @@ NIL (-325 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1052))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872))) (-4133 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1184))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| 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(|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4144 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 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(|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4507 -4133 (-12 (|has| |#1| (-571)) (-4133 (|has| |#1| (-1081)) (|has| |#1| (-487)))) (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) -((-4133 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE 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(QUOTE (-1081))) (|HasCategory| $ (|%list| (QUOTE -1070) (QUOTE (-560))))) (-327 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1244,7 +1244,7 @@ NIL ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-329 R -4131) +(-329 R -4164) ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1255,7 +1255,7 @@ NIL (-331 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . 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(|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1287,12 +1287,12 @@ NIL (-339 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -4131) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-340 S -4164) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-381)))) -(-341 -4131) +(-341 -4164) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1312,7 +1312,7 @@ NIL ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL -(-346 -4131 UP UPUP R) +(-346 -4164 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1320,11 +1320,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-348 S -4131 UP UPUP R) +(-348 S -4164 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-349 -4131 UP UPUP R) +(-349 -4164 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL @@ -1343,12 +1343,12 @@ NIL (-353 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4133 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) -(-354 S -4131 UP UPUP) +((-4144 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +(-354 S -4164 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-376)))) -(-355 -4131 UP UPUP) +(-355 -4164 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1359,15 +1359,15 @@ NIL (-357 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4133 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +((-4144 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) (-358 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(GF,{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4133 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4144 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-359 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(GF,{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4133 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4144 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-360 GF) ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1384,42 +1384,42 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-364 R UP -4131) +(-364 R UP -4164) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-365 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4133 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +((-4144 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) (-366 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4133 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4144 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-367 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4133 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4144 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-368 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4133 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4144 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-369 GF) ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-370 -4131 GF) +(-370 -4164 GF) ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}GF) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-371 -4131 FP FPP) +(-371 -4164 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL (-372 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4133 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4144 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-373 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{ls}."))) NIL @@ -1494,7 +1494,7 @@ NIL NIL (-391) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4493 . T) (-4501 . T) (-2793 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4493 . T) (-4501 . T) (-2862 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-392 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1552,7 +1552,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-406 -4131 UP UPUP R) +(-406 -4164 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL @@ -1576,11 +1576,11 @@ NIL ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) NIL NIL -(-412 -3665 |returnType| -3962 |symbols|) +(-412 -4401 |returnType| -1629 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-413 -4131 UP) +(-413 -4164 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1602,12 +1602,12 @@ NIL ((|HasAttribute| |#1| (QUOTE -4493)) (|HasAttribute| |#1| (QUOTE -4501))) (-418) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-2793 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2862 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-419 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and gcd are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1254))) (-4133 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1254)))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) +((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1254))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1254)))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) (-420 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) NIL @@ -1615,7 +1615,7 @@ NIL (-421 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4497 -12 (|has| |#1| (-6 -4508)) (|has| |#1| (-466)) (|has| |#1| (-6 -4497))) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872))) (-4133 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-4133 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (-4133 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-422 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL @@ -1636,7 +1636,7 @@ NIL ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-427 R -4131 UP A) +(-427 R -4164 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,...,fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,...,fn))} = the vector \\spad{[f1,...,fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} returns the vector \\spad{[f1,...,fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,...,fn])} returns the ideal \\spad{(f1,...,fn)}."))) ((-4507 . T)) NIL @@ -1644,7 +1644,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-429 R -4131 UP A |ibasis|) +(-429 R -4164 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,...,fn])} = the module generated by \\spad{(f1,...,fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (|%list| (QUOTE -1070) (|devaluate| |#2|)))) @@ -1670,7 +1670,7 @@ NIL ((|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (-435 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4507 -4133 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) +((-4507 -4144 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) NIL (-436 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1696,7 +1696,7 @@ NIL ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-442 R -4131) +(-442 R -4164) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1704,19 +1704,19 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4497 -12 (|has| |#1| (-6 -4497)) (|has| |#2| (-6 -4497))) (-4504 . T) (-4505 . T) (-4507 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4497)) (|HasAttribute| |#2| (QUOTE -4497)))) -(-444 R -4131) +(-444 R -4164) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL -(-445 R -4131) +(-445 R -4164) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-446 R -4131) +(-446 R -4164) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-447 R -4131) +(-447 R -4164) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1724,7 +1724,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-449 R -4131 UP) +(-449 R -4164 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-48))))) @@ -1756,7 +1756,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein's criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-457 R UP -4131) +(-457 R UP -4164) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the lp norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri's norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1803,7 +1803,7 @@ NIL (-468 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (-4133 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4133 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4133 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4133 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4133 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (-4144 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4144 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-469 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it's conditional."))) NIL @@ -1868,7 +1868,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-485 |lv| -4131 R) +(-485 |lv| -4164 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1883,11 +1883,11 @@ NIL (-488 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") 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The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4511 . T) (-4510 . T)) @@ -1903,7 +1903,7 @@ NIL (-493 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4510 . T) (-4511 . 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Hall as given in Serre's book Lie Groups -- Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight <= \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1911,11 +1911,11 @@ NIL (-495 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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(-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-4144 (|HasCategory| |#2| (QUOTE (-1081))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasAttribute| |#2| (QUOTE -4507)) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209))))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) (-497) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL @@ -1923,8 +1923,8 @@ NIL (-498 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-499 -4131 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-499 -4164 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1935,7 +1935,7 @@ NIL (-501) ((|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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4133 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4144 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-502 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1960,7 +1960,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-508 -4131 UP |AlExt| |AlPol|) +(-508 -4164 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL @@ -1971,16 +1971,16 @@ NIL (-510 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-511 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray's with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-512 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) NIL NIL -(-513 R UP -4131) +(-513 R UP -4164) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the gcd of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -2000,7 +2000,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-518 -4131 |Expon| |VarSet| |DPoly|) +(-518 -4164 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-1209))))) @@ -2051,7 +2051,7 @@ NIL (-530 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-531) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -2059,15 +2059,15 @@ NIL (-532 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4133 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) +((-4144 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) (-533 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-534 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-535 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} m*h and h*m are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2079,7 +2079,7 @@ NIL (-537 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-538) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2112,7 +2112,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL ((-12 (|HasCategory| (-793) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133))))) -(-546 K -4131 |Par|) +(-546 K -4164 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to br used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2136,7 +2136,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-552 K -4131 |Par|) +(-552 K -4164 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,lden,lvar,eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL @@ -2191,12 +2191,12 @@ NIL (-565 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1580) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3432) (|devaluate| |#2|)))))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102)))) -(-566 R -4131) +((-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#2|)))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102)))) +(-566 R -4164) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-567 R0 -4131 UP UPUP R) +(-567 R0 -4164 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f, d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL @@ -2206,7 +2206,7 @@ NIL NIL (-569 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} <= \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-2793 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2862 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-570 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2216,7 +2216,7 @@ NIL ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-572 R -4131) +(-572 R -4164) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2228,7 +2228,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-575 R -4131 L) +(-575 R -4164 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) @@ -2236,11 +2236,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-577 -4131 UP UPUP R) +(-577 -4164 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, ')} returns \\spad{[g,h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-578 -4131 UP) +(-578 -4164 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, D)} returns \\spad{[g, h, s, p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL @@ -2248,15 +2248,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\tt numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\tt \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-580 R -4131 L) +(-580 R -4164 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) -(-581 R -4131) +(-581 R -4164) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, x)} returns \\spad{[c, g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1171)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-649))))) -(-582 -4131 UP) +(-582 -4164 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2264,27 +2264,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-584 -4131) +(-584 -4164) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-585 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-2793 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2862 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-586) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL -(-587 R -4131) +(-587 R -4164) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) -(-588 -4131 UP) +(-588 -4164 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-589 R -4131) +(-589 R -4164) ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f, s, t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) NIL NIL @@ -2316,15 +2316,15 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-597 -4131) +(-597 -4164) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over F?")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) ((-4505 . T) (-4504 . T)) ((|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209))))) -(-598 E -4131) +(-598 E -4164) ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,ire)} \\undocumented"))) NIL NIL -(-599 R -4131) +(-599 R -4164) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) NIL NIL @@ -2359,7 +2359,7 @@ NIL (-607 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4133 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-4133 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-4144 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4144 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-4144 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-608 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL @@ -2367,7 +2367,7 @@ NIL (-609 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4080) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3903) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) (-610 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) (((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -2384,7 +2384,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) NIL NIL -(-614 R -4131 FG) +(-614 R -4164 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2395,7 +2395,7 @@ NIL (-616 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-617 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2410,8 +2410,8 @@ NIL NIL (-620 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4507 -4133 (-2522 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) -((-4133 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +((-4507 -4144 (-2609 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) +((-4144 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-621) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) NIL @@ -2439,7 +2439,7 @@ NIL (-627 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1580) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3432) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-102)))) (-628 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL @@ -2464,7 +2464,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-634 -4131 UP) +(-634 -4164 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2492,7 +2492,7 @@ NIL ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) ((-4507 . T)) NIL -(-641 R -4131) +(-641 R -4164) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f, t, s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t), t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f, t, s)} if it cannot compute the transform."))) NIL NIL @@ -2520,7 +2520,7 @@ NIL ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) NIL NIL -(-648 R -4131) +(-648 R -4164) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL @@ -2528,18 +2528,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-650 |lv| -4131) +(-650 |lv| -4164) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL (-651) ((|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}.")) (|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."))) ((-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1580) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3432) (QUOTE (-51))))))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1191) (QUOTE (-872))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (QUOTE (-1133)))) +((-12 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3964) (QUOTE (-51))))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1191) (QUOTE (-872))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-1133)))) (-652 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)."))) -((-4507 -4133 (-2522 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) -((-4133 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +((-4507 -4144 (-2609 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) +((-4144 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-653 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2563,7 +2563,7 @@ NIL (-658 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2511 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) +((-2598 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) (-659 K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) ((-4505 . T) (-4504 . T)) @@ -2583,7 +2583,7 @@ NIL (-663 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-664 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) NIL @@ -2607,7 +2607,7 @@ NIL (-669 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-670 R) ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) NIL @@ -2628,11 +2628,11 @@ NIL ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4505 . T) (-4504 . T)) ((|HasCategory| |#1| (QUOTE (-814)))) -(-675 R -4131 L) +(-675 R -4164 L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op, g, x, a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{op y = g, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op, g, x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL -(-676 A -1946) +(-676 A -3297) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) @@ -2652,7 +2652,7 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-681 -4131 UP) +(-681 -4164 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)))) @@ -2684,11 +2684,11 @@ NIL ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) ((-4511 . T) (-4510 . T)) NIL -(-689 -4131 |Row| |Col| M) +(-689 -4164 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-690 -4131) +(-690 -4164) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package's existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2699,7 +2699,7 @@ NIL (-692 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4507 . T) (-4510 . T) (-4504 . T) (-4505 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4133 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-4133 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-4144 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-693) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2719,7 +2719,7 @@ NIL (-697 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,x,y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,i,j,k,s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,i,j,k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,j,k)} create a matrix with all zero terms"))) NIL -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-698) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2775,7 +2775,7 @@ NIL (-711 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) ((-4510 . T) (-4511 . T)) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-712 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} ** \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2784,7 +2784,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) NIL NIL -(-714 S -4131 FLAF FLAS) +(-714 S -4164 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{ku+1},{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) 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T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2862 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-722 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2840,7 +2840,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) 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(|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-735 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2876,7 +2876,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-737 R |Mod| -1740 -2237 |exactQuo|) +(-737 R |Mod| -2386 -2834 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4507 . T)) NIL @@ -2888,7 +2888,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4505 . T) (-4504 . T)) NIL -(-740 -4131) +(-740 -4164) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,1],[1,0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,0],[0,1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,k],[0,1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,b,c,d)} returns \\spad{matrix [[a,b],[c,d]]}."))) ((-4507 . T)) NIL @@ -2924,7 +2924,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-749 -4131 UP) +(-749 -4164 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f, D)} returns \\spad{[p,n,s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f, D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p, D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m, s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p, D)} returns \\spad{[n,s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL @@ -2943,7 +2943,7 @@ NIL (-753 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (-4133 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4133 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4133 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4133 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4133 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (-4144 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4144 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-754 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -3076,11 +3076,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-787 -4131) +(-787 -4164) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-788 P -4131) +(-788 P -4164) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''."))) NIL NIL @@ -3088,7 +3088,7 @@ NIL NIL NIL NIL -(-790 UP -4131) +(-790 UP -4164) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3104,7 +3104,7 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4512 "*") . T)) NIL -(-794 R -4131) +(-794 R -4164) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,y), N(x,y), y, x)} returns \\spad{F(x,y)} such that \\spad{F(x,y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,y) dx + N(x,y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL @@ -3124,7 +3124,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}ts)} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}ts)} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-799 -4131 |ExtF| |SUEx| |ExtP| |n|) +(-799 -4164 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL @@ -3139,11 +3139,11 @@ NIL (-802 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{R^(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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(-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-804 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3219,8 +3219,8 @@ NIL (-822 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-4133 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4133 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) -(-823 -4133 R OS S) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-4144 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4144 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) +(-823 -4144 R OS S) ((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL @@ -3228,11 +3228,11 @@ NIL ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-825 R -4131 L) +(-825 R -4164 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-826 R -4131) +(-826 R -4164) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3240,7 +3240,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE's.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-828 R -4131) +(-828 R -4164) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f, x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f, x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3248,11 +3248,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-830 -4131 UP UPUP R) +(-830 -4164 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-831 -4131 UP L LQ) +(-831 -4164 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3260,38 +3260,38 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-833 -4131 UP L LQ) +(-833 -4164 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'s such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of pj. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {gcd(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-834 -4131 UP) +(-834 -4164 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-835 -4131 L UP A LO) +(-835 -4164 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, g)} returns \\spad{[m, v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-836 -4131 UP) +(-836 -4164 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-837 -4131 LO) +(-837 -4164 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-838 -4131 LODO) +(-838 -4164 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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(|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) (-840 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4133 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4133 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4133 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-841 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4512 "*") |has| |#2| (-376)) (-4503 |has| |#2| (-376)) (-4508 |has| |#2| (-376)) (-4502 |has| |#2| (-376)) (-4507 . T) (-4505 . T) (-4504 . T)) @@ -3355,7 +3355,7 @@ NIL (-856 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) ((-4507 |has| |#1| (-871))) -((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-4133 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4133 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-4144 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4144 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-857 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL @@ -3395,7 +3395,7 @@ NIL (-866 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4507 |has| |#1| (-871))) -((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-4133 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4133 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-4144 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4144 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-867 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL @@ -3404,7 +3404,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-869 -4478 S) +(-869 -2127 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3444,11 +3444,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) -(-879 R |sigma| -1879) +(-879 R |sigma| -1337) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p, x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) -(-880 |x| R |sigma| -1879) +(-880 |x| R |sigma| -1337) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376)))) @@ -3515,15 +3515,15 @@ NIL (-896 |p|) ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-894 |#1|) (QUOTE (-940))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-894 |#1|) (QUOTE (-1052))) (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872))) (-4133 (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-1184))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -894) (|devaluate| |#1|)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))))) +((|HasCategory| (-894 |#1|) (QUOTE (-940))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-894 |#1|) (QUOTE (-1052))) (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872))) (-4144 (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-1184))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -894) (|devaluate| |#1|)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))))) (-897 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of Qp.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872))) (-4133 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872))) (-4144 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-898 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of `s' and `t'."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-899) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it's highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it's lowest value."))) NIL @@ -3583,7 +3583,7 @@ NIL (-913 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,...,vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,...,en], pat)} matches the pattern pat on the list of expressions \\spad{[e1,...,en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,...,en], pat)} tests if the list of expressions \\spad{[e1,...,en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr, pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-2511 (|HasCategory| |#2| (QUOTE (-1081)))) (-2511 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (-2511 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) +((-12 (-2598 (|HasCategory| |#2| (QUOTE (-1081)))) (-2598 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (-2598 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) (-914 R S) ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don't,{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}\\spad{e1}),{}...,{}(vn,{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL @@ -3596,7 +3596,7 @@ NIL ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-917 R -2421) +(-917 R -4219) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and fn to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3624,7 +3624,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-924 UP -4131) +(-924 UP -4164) ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,m,n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL @@ -3655,11 +3655,11 @@ NIL (-931 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-932 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4507 . T)) -((-4133 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) +((-4144 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (-933 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3692,7 +3692,7 @@ NIL ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-941 R0 -4131 UP UPUP R) +(-941 R0 -4164 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) NIL NIL @@ -3720,7 +3720,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik's group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik's Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-948 -4131) +(-948 -4164) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any gcd domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3736,11 +3736,11 @@ NIL ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-952 |xx| -4131) +(-952 |xx| -4164) ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,lf,lg)} \\undocumented"))) NIL NIL -(-953 -4131 P) +(-953 -4164 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL @@ -3768,7 +3768,7 @@ NIL ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-960 R -4131) +(-960 R -4164) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3776,7 +3776,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-962 S R -4131) +(-962 S R -4164) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL @@ -3796,11 +3796,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -912) (|devaluate| |#1|)))) -(-967 -2421) +(-967 -4219) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-968 R -4131 -2421) +(-968 R -4164 -4219) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL @@ -3823,7 +3823,7 @@ NIL (-973 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-974 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3835,7 +3835,7 @@ NIL (-976 R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4133 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4133 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4133 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-977 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL @@ -3852,7 +3852,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) NIL -(-981 E V R P -4131) +(-981 E V R P -4164) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}mn] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3860,7 +3860,7 @@ NIL ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-983 E V R P -4131) +(-983 E V R P -4164) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-466)))) @@ -3875,7 +3875,7 @@ NIL (-986 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4133 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4508))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4508))) (-987 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL @@ -3883,7 +3883,7 @@ NIL (-988 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-989 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -3892,7 +3892,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) NIL NIL -(-991 -4131) +(-991 -4164) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3907,7 +3907,7 @@ NIL (-994 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented"))) ((-4507 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-995) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3996,7 +3996,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-1017 K R UP -4131) +(-1017 K R UP -4164) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -4043,7 +4043,7 @@ NIL (-1028 R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) ((-4503 |has| |#1| (-302)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-4133 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-4133 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-4144 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559)))) (-1029 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL @@ -4059,7 +4059,7 @@ NIL (-1032 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,y,...,z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1033 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4068,14 +4068,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1035 -4131 UP UPUP |radicnd| |n|) +(-1035 -4164 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-4133 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-4133 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4133 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4133 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-4133 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-4133 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-4144 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-4144 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4144 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4144 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-4144 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-4144 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (-1036 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,3,4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,1,4,2,8,5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4133 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4144 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-1037) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -4108,19 +4108,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) NIL -(-1045 R -4131) +(-1045 R -4164) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n, f, g, x, lim, ext)} returns \\spad{[y, h, b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-1046 R -4131) +(-1046 R -4164) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n, f, g_1, g_2, x,lim,ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,dy2/dx) + ((0, - n df/dx),(n df/dx,0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-1047 -4131 UP) +(-1047 -4164 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a, B, C, n, D)} returns either: 1. \\spad{[Q, b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1, C1, m, \\alpha, \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f, g)} returns a \\spad{[y, b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,g,D)} returns \\spad{[A, B, C, T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-1048 -4131 UP) +(-1048 -4164 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f, g1, g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,g1,g2,D)} returns \\spad{[A, B, H, C1, C2, T]} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} has a solution if and only if \\spad{y1 = Q1 / T, y2 = Q2 / T},{} where \\spad{B,C1,C2,Q1,Q2} have no normal poles and satisfy A \\spad{(Q1', Q2') + ((H, -B), (B, H)) (Q1,Q2) = (C1,C2)} \\spad{D} is the derivation to use."))) NIL NIL @@ -4155,8 +4155,8 @@ NIL (-1056 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) ((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) -((-4133 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560))))) -(-1057 -4131 L) +((-4144 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560))))) +(-1057 -4164 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4192,14 +4192,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1066 -4131 |Expon| |VarSet| |FPol| |LFPol|) +(-1066 -4164 |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) (((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-1067) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1580) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3432) (QUOTE (-51))))))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3964) (QUOTE (-51))))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-102)))) (-1068) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4256,7 +4256,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4507 . T)) NIL -(-1082 |xx| -4131) +(-1082 |xx| -4164) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4275,7 +4275,7 @@ NIL (-1086 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4510 . T) (-4505 . T) (-4504 . T)) -((|HasCategory| |#3| (QUOTE (-175))) (-4133 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888))))) +((|HasCategory| |#3| (QUOTE (-175))) (-4144 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888))))) (-1087 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4311,7 +4311,7 @@ NIL (-1095) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE's")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE's")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1580) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3432) (QUOTE (-51))))))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3964) (QUOTE (-51))))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-102)))) (-1096 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -4356,7 +4356,7 @@ NIL ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1107 |Base| R -4131) +(-1107 |Base| R -4164) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}fn are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL @@ -4364,7 +4364,7 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1109 |Base| R -4131) +(-1109 |Base| R -4164) ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,...,rn])} creates the rule set \\spad{{r1,...,rn}}."))) NIL NIL @@ -4375,7 +4375,7 @@ NIL (-1111 R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) ((-4503 |has| |#1| (-376)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-4133 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-4133 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-1112 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4407,7 +4407,7 @@ NIL (-1119 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4133 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4133 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4133 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4133 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1120 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 @@ -4447,7 +4447,7 @@ NIL (-1129 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) ((-4510 . T) (-4500 . T) (-4511 . T)) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-1130 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL @@ -4511,7 +4511,7 @@ NIL (-1145 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4504 |has| |#3| (-1081)) (-4505 |has| |#3| (-1081)) (-4507 |has| |#3| (-6 -4507)) (-4510 . 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(|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (-1146 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4524,7 +4524,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) NIL NIL -(-1149 R -4131) +(-1149 R -4164) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4559,16 +4559,16 @@ NIL (-1157 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1159 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) ((-4511 . T) (-4510 . T)) NIL -(-1160 UP -4131) +(-1160 UP -4164) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,g,h,i,k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,g,h,j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,g,h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,g,h,i,j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,g,h,i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,g,h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL @@ -4623,11 +4623,11 @@ NIL (-1173 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in ls]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}lt)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}ls)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))) (-4133 (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (-4133 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))))) (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102)))) +((-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))) (-4144 (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (-4144 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))))) (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102)))) (-1174 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4507 . T) (-4499 |has| |#2| (-6 (-4512 "*"))) (-4510 . T) (-4504 . T) (-4505 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4133 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (-4133 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (-4144 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-1175 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4651,19 +4651,19 @@ NIL (-1180 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,y,...,z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1181 A S) -((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|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})}."))) +((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL (-1182 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})}."))) +((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL (-1183 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1580) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3432) (|devaluate| |#2|)))))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-872))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133)))) +((-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#2|)))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133)))) (-1184) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}'s are never \\spad{nothing}.}")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4679,7 +4679,7 @@ NIL (-1187 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1188 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) NIL @@ -4695,11 +4695,11 @@ NIL (-1191) ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4133 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-4133 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-4144 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4144 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-4144 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-1192 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1580) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3432) (|devaluate| |#1|)))))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4133 (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#1|)))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-102)))) (-1193 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 r: \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4730,9 +4730,9 @@ NIL NIL (-1200 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) 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We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -4080) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-4133 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3538) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2985) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3903) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-4144 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2884) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3648) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1208) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4775,7 +4775,7 @@ NIL (-1211 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4133 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1003) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4508))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1003) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4508))) (-1212) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4815,7 +4815,7 @@ NIL (-1221 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1580) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3432) (|devaluate| |#2|)))))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4133 (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#2|)))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102)))) (-1222 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL @@ -4875,7 +4875,7 @@ NIL (-1236 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4511 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1237 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4884,7 +4884,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1239 R -4131) +(-1239 R -4164) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -4892,14 +4892,14 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1241 R -4131) +(-1241 R -4164) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on f:\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on f:\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (|devaluate| |#1|))))) (-1242 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1243 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL @@ -4920,7 +4920,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) -(-1248 -4131) +(-1248 -4164) ((|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 @@ -4966,8 +4966,8 @@ NIL NIL (-1259 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) 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(|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-147)))))) (-1265 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -5003,7 +5003,7 @@ NIL (-1268 |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}"))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4506 |has| |#2| (-376)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4133 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| 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(-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-1269 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -5039,7 +5039,7 @@ NIL (-1277 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1144))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -4080) (|%list| (|devaluate| |#2|) (QUOTE (-1209)))))) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1144))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3903) (|%list| (|devaluate| |#2|) (QUOTE (-1209)))))) (-1278 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -5051,7 +5051,7 @@ NIL (-1280 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4133 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -4080) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4133 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3538) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2985) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3903) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4144 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2884) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3648) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1281 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL @@ -5071,11 +5071,11 @@ NIL (-1285 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4133 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -4080) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4133 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3538) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2985) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) +((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3903) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4144 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2884) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3648) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-1286 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) (((-4512 "*") |has| (-1280 |#2| |#3| |#4|) (-175)) (-4503 |has| (-1280 |#2| |#3| |#4|) (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-175))) (-4133 (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-571)))) +((|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-175))) (-4144 (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-571)))) (-1287 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5087,7 +5087,7 @@ NIL (-1289 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4133 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -4080) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-4133 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3538) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2985) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3903) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-4144 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2884) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3648) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1290 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL @@ -5095,7 +5095,7 @@ NIL (-1291 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-990))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasSignature| |#2| (|%list| (QUOTE -2985) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3538) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) +((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-990))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasSignature| |#2| (|%list| (QUOTE -3648) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -2884) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) (-1292 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -5104,7 +5104,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1294 -4131 UP L UTS) +(-1294 -4164 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-571)))) @@ -5127,7 +5127,7 @@ NIL (-1299 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4511 . T) (-4510 . T)) -((-4133 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4133 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4133 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4133 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-1300 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL @@ -5164,7 +5164,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*v + A[2]\\spad{*v**2} + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1309 K R UP -4131) +(-1309 K R UP -4164) ((|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 @@ -5196,11 +5196,11 @@ NIL ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1317 S -4131) +(-1317 S -4164) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1318 -4131) +(-1318 -4164) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -5264,4 +5264,4 @@ NIL NIL NIL NIL -((-3 NIL 2294535 2294540 2294545 2294550) (-2 NIL 2294515 2294520 2294525 2294530) (-1 NIL 2294495 2294500 2294505 2294510) (0 NIL 2294475 2294480 2294485 2294490) (-1329 "ZMOD.spad" 2294284 2294297 2294413 2294470) (-1328 "ZLINDEP.spad" 2293382 2293393 2294274 2294279) (-1327 "ZDSOLVE.spad" 2283342 2283364 2293372 2293377) (-1326 "YSTREAM.spad" 2282837 2282848 2283332 2283337) (-1325 "YDIAGRAM.spad" 2282471 2282480 2282827 2282832) (-1324 "XRPOLY.spad" 2281691 2281711 2282327 2282396) (-1323 "XPR.spad" 2279486 2279499 2281409 2281508) (-1322 "XPOLYC.spad" 2278805 2278821 2279412 2279481) (-1321 "XPOLY.spad" 2278360 2278371 2278661 2278730) (-1320 "XPBWPOLY.spad" 2276799 2276819 2278134 2278203) (-1319 "XFALG.spad" 2273847 2273863 2276725 2276794) (-1318 "XF.spad" 2272310 2272325 2273749 2273842) (-1317 "XF.spad" 2270753 2270770 2272194 2272199) (-1316 "XEXPPKG.spad" 2270012 2270038 2270743 2270748) (-1315 "XDPOLY.spad" 2269626 2269642 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2175971 2178050 2178147) (-1277 "UPSCAT.spad" 2173427 2173453 2175532 2175537) (-1276 "UPOLYC2.spad" 2172898 2172917 2173417 2173422) (-1275 "UPOLYC.spad" 2167978 2167989 2172740 2172893) (-1274 "UPOLYC.spad" 2162944 2162957 2167708 2167713) (-1273 "UPMP.spad" 2161876 2161889 2162934 2162939) (-1272 "UPDIVP.spad" 2161441 2161455 2161866 2161871) (-1271 "UPDECOMP.spad" 2159702 2159716 2161431 2161436) (-1270 "UPCDEN.spad" 2158919 2158935 2159692 2159697) (-1269 "UP2.spad" 2158283 2158304 2158909 2158914) (-1268 "UP.spad" 2155311 2155326 2155698 2155851) (-1267 "UNISEG2.spad" 2154808 2154821 2155267 2155272) (-1266 "UNISEG.spad" 2154161 2154172 2154727 2154732) (-1265 "UNIFACT.spad" 2153264 2153276 2154151 2154156) (-1264 "ULSCONS.spad" 2144176 2144196 2144546 2144695) (-1263 "ULSCCAT.spad" 2141913 2141933 2144022 2144171) (-1262 "ULSCCAT.spad" 2139758 2139780 2141869 2141874) (-1261 "ULSCAT.spad" 2137998 2138014 2139604 2139753) (-1260 "ULS2.spad" 2137512 2137565 2137988 2137993) (-1259 "ULS.spad" 2127083 2127111 2128028 2128457) (-1258 "UINT8.spad" 2126960 2126969 2127073 2127078) (-1257 "UINT64.spad" 2126836 2126845 2126950 2126955) (-1256 "UINT32.spad" 2126712 2126721 2126826 2126831) (-1255 "UINT16.spad" 2126588 2126597 2126702 2126707) (-1254 "UFD.spad" 2125653 2125662 2126514 2126583) (-1253 "UFD.spad" 2124780 2124791 2125643 2125648) (-1252 "UDVO.spad" 2123661 2123670 2124770 2124775) (-1251 "UDPO.spad" 2121242 2121253 2123617 2123622) (-1250 "TYPEAST.spad" 2121161 2121170 2121232 2121237) (-1249 "TYPE.spad" 2121093 2121102 2121151 2121156) (-1248 "TWOFACT.spad" 2119745 2119760 2121083 2121088) (-1247 "TUPLE.spad" 2119236 2119247 2119641 2119646) (-1246 "TUBETOOL.spad" 2116103 2116112 2119226 2119231) (-1245 "TUBE.spad" 2114750 2114767 2116093 2116098) (-1244 "TSETCAT.spad" 2102821 2102838 2114718 2114745) (-1243 "TSETCAT.spad" 2090878 2090897 2102777 2102782) (-1242 "TS.spad" 2089471 2089487 2090437 2090534) (-1241 "TRMANIP.spad" 2083835 2083852 2089159 2089164) (-1240 "TRIMAT.spad" 2082798 2082823 2083825 2083830) (-1239 "TRIGMNIP.spad" 2081325 2081342 2082788 2082793) (-1238 "TRIGCAT.spad" 2080837 2080846 2081315 2081320) (-1237 "TRIGCAT.spad" 2080347 2080358 2080827 2080832) (-1236 "TREE.spad" 2078793 2078804 2079825 2079852) (-1235 "TRANFUN.spad" 2078632 2078641 2078783 2078788) (-1234 "TRANFUN.spad" 2078469 2078480 2078622 2078627) (-1233 "TOPSP.spad" 2078143 2078152 2078459 2078464) (-1232 "TOOLSIGN.spad" 2077806 2077817 2078133 2078138) (-1231 "TEXTFILE.spad" 2076367 2076376 2077796 2077801) (-1230 "TEX1.spad" 2075923 2075934 2076357 2076362) (-1229 "TEX.spad" 2073117 2073126 2075913 2075918) (-1228 "TEMUTL.spad" 2072672 2072681 2073107 2073112) (-1227 "TBCMPPK.spad" 2070773 2070796 2072662 2072667) (-1226 "TBAGG.spad" 2069831 2069854 2070753 2070768) (-1225 "TBAGG.spad" 2068897 2068922 2069821 2069826) (-1224 "TANEXP.spad" 2068305 2068316 2068887 2068892) (-1223 "TALGOP.spad" 2068029 2068040 2068295 2068300) (-1222 "TABLEAU.spad" 2067510 2067521 2068019 2068024) (-1221 "TABLE.spad" 2065443 2065466 2065713 2065740) (-1220 "TABLBUMP.spad" 2062222 2062233 2065433 2065438) (-1219 "SYSTEM.spad" 2061450 2061459 2062212 2062217) (-1218 "SYSSOLP.spad" 2058933 2058944 2061440 2061445) (-1217 "SYSPTR.spad" 2058832 2058841 2058923 2058928) (-1216 "SYSNNI.spad" 2058055 2058066 2058822 2058827) (-1215 "SYSINT.spad" 2057459 2057470 2058045 2058050) (-1214 "SYNTAX.spad" 2053793 2053802 2057449 2057454) (-1213 "SYMTAB.spad" 2051861 2051870 2053783 2053788) (-1212 "SYMS.spad" 2047884 2047893 2051851 2051856) (-1211 "SYMPOLY.spad" 2046863 2046874 2046945 2047072) (-1210 "SYMFUNC.spad" 2046364 2046375 2046853 2046858) (-1209 "SYMBOL.spad" 2043859 2043868 2046354 2046359) (-1208 "SWITCH.spad" 2040630 2040639 2043849 2043854) (-1207 "SUTS.spad" 2037609 2037637 2039028 2039125) (-1206 "SUPXS.spad" 2034811 2034839 2035660 2035809) (-1205 "SUPFRACF.spad" 2033916 2033934 2034801 2034806) (-1204 "SUP2.spad" 2033308 2033321 2033906 2033911) (-1203 "SUP.spad" 2029950 2029961 2030723 2030876) (-1202 "SUMRF.spad" 2028924 2028935 2029940 2029945) (-1201 "SUMFS.spad" 2028553 2028570 2028914 2028919) (-1200 "SULS.spad" 2018111 2018139 2019069 2019498) (-1199 "SUCHTAST.spad" 2017880 2017889 2018101 2018106) (-1198 "SUCH.spad" 2017570 2017585 2017870 2017875) (-1197 "SUBSPACE.spad" 2009701 2009716 2017560 2017565) (-1196 "SUBRESP.spad" 2008871 2008885 2009657 2009662) (-1195 "STTFNC.spad" 2005339 2005355 2008861 2008866) (-1194 "STTF.spad" 2001438 2001454 2005329 2005334) (-1193 "STTAYLOR.spad" 1994083 1994094 2001313 2001318) (-1192 "STRTBL.spad" 1992098 1992115 1992247 1992274) (-1191 "STRING.spad" 1990864 1990873 1991085 1991112) (-1190 "STREAM3.spad" 1990437 1990452 1990854 1990859) (-1189 "STREAM2.spad" 1989565 1989578 1990427 1990432) (-1188 "STREAM1.spad" 1989271 1989282 1989555 1989560) (-1187 "STREAM.spad" 1986057 1986068 1988664 1988679) (-1186 "STINPROD.spad" 1984993 1985009 1986047 1986052) (-1185 "STEPAST.spad" 1984227 1984236 1984983 1984988) (-1184 "STEP.spad" 1983436 1983445 1984217 1984222) (-1183 "STBL.spad" 1981484 1981512 1981651 1981666) (-1182 "STAGG.spad" 1980559 1980570 1981474 1981479) (-1181 "STAGG.spad" 1979632 1979645 1980549 1980554) (-1180 "STACK.spad" 1978860 1978871 1979110 1979137) (-1179 "SRING.spad" 1978620 1978629 1978850 1978855) (-1178 "SREGSET.spad" 1976319 1976336 1978221 1978248) (-1177 "SRDCMPK.spad" 1974896 1974916 1976309 1976314) (-1176 "SRAGG.spad" 1970079 1970088 1974864 1974891) (-1175 "SRAGG.spad" 1965282 1965293 1970069 1970074) (-1174 "SQMATRIX.spad" 1962777 1962795 1963693 1963780) (-1173 "SPLTREE.spad" 1957243 1957256 1962039 1962066) (-1172 "SPLNODE.spad" 1953863 1953876 1957233 1957238) (-1171 "SPFCAT.spad" 1952672 1952681 1953853 1953858) (-1170 "SPECOUT.spad" 1951224 1951233 1952662 1952667) (-1169 "SPADXPT.spad" 1943315 1943324 1951214 1951219) (-1168 "spad-parser.spad" 1942780 1942789 1943305 1943310) (-1167 "SPADAST.spad" 1942481 1942490 1942770 1942775) (-1166 "SPACEC.spad" 1926696 1926707 1942471 1942476) (-1165 "SPACE3.spad" 1926472 1926483 1926686 1926691) (-1164 "SORTPAK.spad" 1926021 1926034 1926428 1926433) (-1163 "SOLVETRA.spad" 1923784 1923795 1926011 1926016) (-1162 "SOLVESER.spad" 1922240 1922251 1923774 1923779) (-1161 "SOLVERAD.spad" 1918266 1918277 1922230 1922235) (-1160 "SOLVEFOR.spad" 1916728 1916746 1918256 1918261) (-1159 "SNTSCAT.spad" 1916328 1916345 1916696 1916723) (-1158 "SMTS.spad" 1914610 1914636 1915887 1915984) (-1157 "SMP.spad" 1912013 1912033 1912403 1912530) (-1156 "SMITH.spad" 1910858 1910883 1912003 1912008) (-1155 "SMATCAT.spad" 1908976 1909006 1910802 1910853) (-1154 "SMATCAT.spad" 1907026 1907058 1908854 1908859) (-1153 "SKAGG.spad" 1905995 1906006 1906994 1907021) (-1152 "SINT.spad" 1904935 1904944 1905861 1905990) (-1151 "SIMPAN.spad" 1904663 1904672 1904925 1904930) (-1150 "SIGNRF.spad" 1903781 1903792 1904653 1904658) (-1149 "SIGNEF.spad" 1903060 1903077 1903771 1903776) (-1148 "SIGAST.spad" 1902477 1902486 1903050 1903055) (-1147 "SIG.spad" 1901839 1901848 1902467 1902472) (-1146 "SHP.spad" 1899783 1899798 1901795 1901800) (-1145 "SHDP.spad" 1887138 1887165 1887655 1887754) (-1144 "SGROUP.spad" 1886746 1886755 1887128 1887133) (-1143 "SGROUP.spad" 1886352 1886363 1886736 1886741) (-1142 "SGCF.spad" 1879491 1879500 1886342 1886347) (-1141 "SFRTCAT.spad" 1878437 1878454 1879459 1879486) (-1140 "SFRGCD.spad" 1877500 1877520 1878427 1878432) (-1139 "SFQCMPK.spad" 1872313 1872333 1877490 1877495) (-1138 "SFORT.spad" 1871752 1871766 1872303 1872308) (-1137 "SEXOF.spad" 1871595 1871635 1871742 1871747) (-1136 "SEXCAT.spad" 1869423 1869463 1871585 1871590) (-1135 "SEX.spad" 1869315 1869324 1869413 1869418) (-1134 "SETMN.spad" 1867773 1867790 1869305 1869310) (-1133 "SETCAT.spad" 1867258 1867267 1867763 1867768) (-1132 "SETCAT.spad" 1866741 1866752 1867248 1867253) (-1131 "SETAGG.spad" 1863290 1863301 1866721 1866736) (-1130 "SETAGG.spad" 1859847 1859860 1863280 1863285) (-1129 "SET.spad" 1858120 1858131 1859217 1859256) (-1128 "SEQAST.spad" 1857823 1857832 1858110 1858115) (-1127 "SEGXCAT.spad" 1856979 1856992 1857813 1857818) (-1126 "SEGCAT.spad" 1855904 1855915 1856969 1856974) (-1125 "SEGBIND2.spad" 1855602 1855615 1855894 1855899) (-1124 "SEGBIND.spad" 1855360 1855371 1855549 1855554) (-1123 "SEGAST.spad" 1855090 1855099 1855350 1855355) (-1122 "SEG2.spad" 1854525 1854538 1855046 1855051) (-1121 "SEG.spad" 1854338 1854349 1854444 1854449) (-1120 "SDVAR.spad" 1853614 1853625 1854328 1854333) (-1119 "SDPOL.spad" 1850869 1850880 1851160 1851287) (-1118 "SCPKG.spad" 1848958 1848969 1850859 1850864) (-1117 "SCOPE.spad" 1848135 1848144 1848948 1848953) (-1116 "SCACHE.spad" 1846831 1846842 1848125 1848130) (-1115 "SASTCAT.spad" 1846740 1846749 1846821 1846826) (-1114 "SAOS.spad" 1846612 1846621 1846730 1846735) (-1113 "SAERFFC.spad" 1846325 1846345 1846602 1846607) (-1112 "SAEFACT.spad" 1846026 1846046 1846315 1846320) (-1111 "SAE.spad" 1843460 1843476 1844071 1844206) (-1110 "RURPK.spad" 1841119 1841135 1843450 1843455) (-1109 "RULESET.spad" 1840572 1840596 1841109 1841114) (-1108 "RULECOLD.spad" 1840424 1840437 1840562 1840567) (-1107 "RULE.spad" 1838672 1838696 1840414 1840419) (-1106 "RTVALUE.spad" 1838407 1838416 1838662 1838667) (-1105 "RSTRCAST.spad" 1838124 1838133 1838397 1838402) (-1104 "RSETGCD.spad" 1834566 1834586 1838114 1838119) (-1103 "RSETCAT.spad" 1824534 1824551 1834534 1834561) (-1102 "RSETCAT.spad" 1814522 1814541 1824524 1824529) (-1101 "RSDCMPK.spad" 1813022 1813042 1814512 1814517) (-1100 "RRCC.spad" 1811406 1811436 1813012 1813017) (-1099 "RRCC.spad" 1809788 1809820 1811396 1811401) (-1098 "RPTAST.spad" 1809490 1809499 1809778 1809783) (-1097 "RPOLCAT.spad" 1788994 1789009 1809358 1809485) (-1096 "RPOLCAT.spad" 1768193 1768210 1788559 1788564) (-1095 "ROUTINE.spad" 1763594 1763603 1766342 1766369) (-1094 "ROMAN.spad" 1762922 1762931 1763460 1763589) (-1093 "ROIRC.spad" 1762002 1762034 1762912 1762917) (-1092 "RNS.spad" 1760978 1760987 1761904 1761997) (-1091 "RNS.spad" 1760040 1760051 1760968 1760973) (-1090 "RNGBIND.spad" 1759200 1759214 1759995 1760000) (-1089 "RNG.spad" 1758935 1758944 1759190 1759195) (-1088 "RMODULE.spad" 1758716 1758727 1758925 1758930) (-1087 "RMCAT2.spad" 1758136 1758193 1758706 1758711) (-1086 "RMATRIX.spad" 1756906 1756925 1757249 1757288) (-1085 "RMATCAT.spad" 1752485 1752516 1756862 1756901) (-1084 "RMATCAT.spad" 1747954 1747987 1752333 1752338) (-1083 "RLINSET.spad" 1747658 1747669 1747944 1747949) (-1082 "RINTERP.spad" 1747546 1747566 1747648 1747653) (-1081 "RING.spad" 1747016 1747025 1747526 1747541) (-1080 "RING.spad" 1746494 1746505 1747006 1747011) (-1079 "RIDIST.spad" 1745886 1745895 1746484 1746489) (-1078 "RGCHAIN.spad" 1744407 1744423 1745301 1745328) (-1077 "RGBCSPC.spad" 1744196 1744208 1744397 1744402) (-1076 "RGBCMDL.spad" 1743758 1743770 1744186 1744191) (-1075 "RFFACTOR.spad" 1743220 1743231 1743748 1743753) (-1074 "RFFACT.spad" 1742955 1742967 1743210 1743215) (-1073 "RFDIST.spad" 1741951 1741960 1742945 1742950) (-1072 "RF.spad" 1739625 1739636 1741941 1741946) (-1071 "RETSOL.spad" 1739044 1739057 1739615 1739620) (-1070 "RETRACT.spad" 1738472 1738483 1739034 1739039) (-1069 "RETRACT.spad" 1737898 1737911 1738462 1738467) (-1068 "RETAST.spad" 1737710 1737719 1737888 1737893) (-1067 "RESULT.spad" 1735272 1735281 1735859 1735886) (-1066 "RESRING.spad" 1734619 1734666 1735210 1735267) (-1065 "RESLATC.spad" 1733943 1733954 1734609 1734614) (-1064 "REPSQ.spad" 1733674 1733685 1733933 1733938) (-1063 "REPDB.spad" 1733381 1733392 1733664 1733669) (-1062 "REP2.spad" 1723095 1723106 1733223 1733228) (-1061 "REP1.spad" 1717315 1717326 1723045 1723050) (-1060 "REP.spad" 1714869 1714878 1717305 1717310) (-1059 "REGSET.spad" 1712661 1712678 1714470 1714497) (-1058 "REF.spad" 1711996 1712007 1712616 1712621) (-1057 "REDORDER.spad" 1711202 1711219 1711986 1711991) (-1056 "RECLOS.spad" 1709961 1709981 1710665 1710758) (-1055 "REALSOLV.spad" 1709101 1709110 1709951 1709956) (-1054 "REAL0Q.spad" 1706399 1706414 1709091 1709096) (-1053 "REAL0.spad" 1703243 1703258 1706389 1706394) (-1052 "REAL.spad" 1703115 1703124 1703233 1703238) (-1051 "RDUCEAST.spad" 1702836 1702845 1703105 1703110) (-1050 "RDIV.spad" 1702491 1702516 1702826 1702831) (-1049 "RDIST.spad" 1702058 1702069 1702481 1702486) (-1048 "RDETRS.spad" 1700922 1700940 1702048 1702053) (-1047 "RDETR.spad" 1699061 1699079 1700912 1700917) (-1046 "RDEEFS.spad" 1698160 1698177 1699051 1699056) (-1045 "RDEEF.spad" 1697170 1697187 1698150 1698155) (-1044 "RCFIELD.spad" 1694388 1694397 1697072 1697165) (-1043 "RCFIELD.spad" 1691692 1691703 1694378 1694383) (-1042 "RCAGG.spad" 1689628 1689639 1691682 1691687) (-1041 "RCAGG.spad" 1687491 1687504 1689547 1689552) (-1040 "RATRET.spad" 1686851 1686862 1687481 1687486) (-1039 "RATFACT.spad" 1686543 1686555 1686841 1686846) (-1038 "RANDSRC.spad" 1685862 1685871 1686533 1686538) (-1037 "RADUTIL.spad" 1685618 1685627 1685852 1685857) (-1036 "RADIX.spad" 1682397 1682411 1683943 1684036) (-1035 "RADFF.spad" 1680100 1680137 1680219 1680375) (-1034 "RADCAT.spad" 1679695 1679704 1680090 1680095) (-1033 "RADCAT.spad" 1679288 1679299 1679685 1679690) (-1032 "QUEUE.spad" 1678507 1678518 1678766 1678793) (-1031 "QUATCT2.spad" 1678127 1678146 1678497 1678502) (-1030 "QUATCAT.spad" 1676297 1676308 1678057 1678122) (-1029 "QUATCAT.spad" 1674215 1674228 1675977 1675982) (-1028 "QUAT.spad" 1672667 1672678 1673010 1673075) (-1027 "QUAGG.spad" 1671500 1671511 1672635 1672662) (-1026 "QQUTAST.spad" 1671268 1671277 1671490 1671495) (-1025 "QFORM.spad" 1670886 1670901 1671258 1671263) (-1024 "QFCAT2.spad" 1670578 1670595 1670876 1670881) (-1023 "QFCAT.spad" 1669280 1669291 1670480 1670573) (-1022 "QFCAT.spad" 1667564 1667577 1668766 1668771) (-1021 "QEQUAT.spad" 1667122 1667131 1667554 1667559) (-1020 "QCMPACK.spad" 1662036 1662056 1667112 1667117) (-1019 "QALGSET2.spad" 1660031 1660050 1662026 1662031) (-1018 "QALGSET.spad" 1656133 1656166 1659945 1659950) (-1017 "PWFFINTB.spad" 1653548 1653570 1656123 1656128) (-1016 "PUSHVAR.spad" 1652886 1652906 1653538 1653543) (-1015 "PTRANFN.spad" 1649021 1649032 1652876 1652881) (-1014 "PTPACK.spad" 1646108 1646119 1649011 1649016) (-1013 "PTFUNC2.spad" 1645930 1645945 1646098 1646103) (-1012 "PTCAT.spad" 1645184 1645195 1645898 1645925) (-1011 "PSQFR.spad" 1644498 1644523 1645174 1645179) (-1010 "PSEUDLIN.spad" 1643383 1643394 1644488 1644493) (-1009 "PSETPK.spad" 1630087 1630104 1643261 1643266) (-1008 "PSETCAT.spad" 1624486 1624510 1630067 1630082) (-1007 "PSETCAT.spad" 1618859 1618885 1624442 1624447) (-1006 "PSCURVE.spad" 1617857 1617866 1618849 1618854) (-1005 "PSCAT.spad" 1616639 1616669 1617755 1617852) (-1004 "PSCAT.spad" 1615511 1615543 1616629 1616634) (-1003 "PRTITION.spad" 1614208 1614217 1615501 1615506) (-1002 "PRTDAST.spad" 1613926 1613935 1614198 1614203) (-1001 "PRS.spad" 1603543 1603561 1613882 1613887) (-1000 "PRQAGG.spad" 1602977 1602988 1603511 1603538) (-999 "PROPLOG.spad" 1602581 1602589 1602967 1602972) (-998 "PROPFUN2.spad" 1602204 1602217 1602571 1602576) (-997 "PROPFUN1.spad" 1601610 1601621 1602194 1602199) (-996 "PROPFRML.spad" 1600178 1600189 1601600 1601605) (-995 "PROPERTY.spad" 1599674 1599682 1600168 1600173) (-994 "PRODUCT.spad" 1597356 1597368 1597640 1597695) (-993 "PRINT.spad" 1597108 1597116 1597346 1597351) (-992 "PRIMES.spad" 1595369 1595379 1597098 1597103) (-991 "PRIMELT.spad" 1593490 1593504 1595359 1595364) (-990 "PRIMCAT.spad" 1593133 1593141 1593480 1593485) (-989 "PRIMARR2.spad" 1591900 1591912 1593123 1593128) (-988 "PRIMARR.spad" 1590739 1590749 1590909 1590936) (-987 "PREASSOC.spad" 1590121 1590133 1590729 1590734) (-986 "PR.spad" 1588486 1588498 1589185 1589312) (-985 "PPCURVE.spad" 1587623 1587631 1588476 1588481) (-984 "PORTNUM.spad" 1587414 1587422 1587613 1587618) (-983 "POLYROOT.spad" 1586263 1586285 1587370 1587375) (-982 "POLYLIFT.spad" 1585528 1585551 1586253 1586258) (-981 "POLYCATQ.spad" 1583654 1583676 1585518 1585523) (-980 "POLYCAT.spad" 1577156 1577177 1583522 1583649) (-979 "POLYCAT.spad" 1569954 1569977 1576322 1576327) (-978 "POLY2UP.spad" 1569406 1569420 1569944 1569949) (-977 "POLY2.spad" 1569003 1569015 1569396 1569401) (-976 "POLY.spad" 1566266 1566276 1566781 1566908) (-975 "POLUTIL.spad" 1565231 1565260 1566222 1566227) (-974 "POLTOPOL.spad" 1563979 1563994 1565221 1565226) (-973 "POINT.spad" 1562643 1562653 1562730 1562757) (-972 "PNTHEORY.spad" 1559345 1559353 1562633 1562638) (-971 "PMTOOLS.spad" 1558120 1558134 1559335 1559340) (-970 "PMSYM.spad" 1557669 1557679 1558110 1558115) (-969 "PMQFCAT.spad" 1557260 1557274 1557659 1557664) (-968 "PMPREDFS.spad" 1556722 1556744 1557250 1557255) (-967 "PMPRED.spad" 1556209 1556223 1556712 1556717) (-966 "PMPLCAT.spad" 1555286 1555304 1556138 1556143) (-965 "PMLSAGG.spad" 1554871 1554885 1555276 1555281) (-964 "PMKERNEL.spad" 1554450 1554462 1554861 1554866) (-963 "PMINS.spad" 1554030 1554040 1554440 1554445) (-962 "PMFS.spad" 1553607 1553625 1554020 1554025) (-961 "PMDOWN.spad" 1552897 1552911 1553597 1553602) (-960 "PMASSFS.spad" 1551872 1551888 1552887 1552892) (-959 "PMASS.spad" 1550890 1550898 1551862 1551867) (-958 "PLOTTOOL.spad" 1550670 1550678 1550880 1550885) (-957 "PLOT3D.spad" 1547134 1547142 1550660 1550665) (-956 "PLOT1.spad" 1546307 1546317 1547124 1547129) (-955 "PLOT.spad" 1541230 1541238 1546297 1546302) (-954 "PLEQN.spad" 1528632 1528659 1541220 1541225) (-953 "PINTERPA.spad" 1528416 1528432 1528622 1528627) (-952 "PINTERP.spad" 1528038 1528057 1528406 1528411) (-951 "PID.spad" 1527012 1527020 1527964 1528033) (-950 "PICOERCE.spad" 1526669 1526679 1527002 1527007) (-949 "PI.spad" 1526286 1526294 1526643 1526664) (-948 "PGROEB.spad" 1524895 1524909 1526276 1526281) (-947 "PGE.spad" 1516568 1516576 1524885 1524890) (-946 "PGCD.spad" 1515522 1515539 1516558 1516563) (-945 "PFRPAC.spad" 1514671 1514681 1515512 1515517) (-944 "PFR.spad" 1511374 1511384 1514573 1514666) (-943 "PFOTOOLS.spad" 1510632 1510648 1511364 1511369) (-942 "PFOQ.spad" 1510002 1510020 1510622 1510627) (-941 "PFO.spad" 1509421 1509448 1509992 1509997) (-940 "PFECAT.spad" 1507131 1507139 1509347 1509416) (-939 "PFECAT.spad" 1504869 1504879 1507087 1507092) (-938 "PFBRU.spad" 1502757 1502769 1504859 1504864) (-937 "PFBR.spad" 1500317 1500340 1502747 1502752) (-936 "PF.spad" 1499891 1499903 1500122 1500215) (-935 "PERMGRP.spad" 1494661 1494671 1499881 1499886) (-934 "PERMCAT.spad" 1493322 1493332 1494641 1494656) (-933 "PERMAN.spad" 1491878 1491892 1493312 1493317) (-932 "PERM.spad" 1487685 1487695 1491708 1491723) (-931 "PENDTREE.spad" 1486905 1486915 1487185 1487190) (-930 "PDSPC.spad" 1485718 1485728 1486895 1486900) (-929 "PDSPC.spad" 1484529 1484541 1485708 1485713) (-928 "PDRING.spad" 1484371 1484381 1484509 1484524) (-927 "PDMOD.spad" 1484187 1484199 1484339 1484366) (-926 "PDEPROB.spad" 1483202 1483210 1484177 1484182) (-925 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1456347) (-906 "script-parser.spad" 1455669 1455677 1456139 1456144) (-905 "PARSCURV.spad" 1455103 1455131 1455659 1455664) (-904 "PARSC2.spad" 1454894 1454910 1455093 1455098) (-903 "PARPCURV.spad" 1454356 1454384 1454884 1454889) (-902 "PARPC2.spad" 1454147 1454163 1454346 1454351) (-901 "PARAMAST.spad" 1453275 1453283 1454137 1454142) (-900 "PAN2EXPR.spad" 1452687 1452695 1453265 1453270) (-899 "PALETTE.spad" 1451673 1451681 1452677 1452682) (-898 "PAIR.spad" 1450680 1450693 1451249 1451254) (-897 "PADICRC.spad" 1447884 1447902 1449047 1449140) (-896 "PADICRAT.spad" 1445743 1445755 1445956 1446049) (-895 "PADICCT.spad" 1444292 1444304 1445669 1445738) (-894 "PADIC.spad" 1443995 1444007 1444218 1444287) (-893 "PADEPAC.spad" 1442684 1442703 1443985 1443990) (-892 "PADE.spad" 1441436 1441452 1442674 1442679) (-891 "OWP.spad" 1440684 1440714 1441294 1441361) (-890 "OVERSET.spad" 1440257 1440265 1440674 1440679) (-889 "OVAR.spad" 1440038 1440061 1440247 1440252) (-888 "OUTFORM.spad" 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305093 305964 305969) (-255 "DMP.spad" 302273 302288 302843 302970) (-254 "DMEXT.spad" 302140 302150 302241 302268) (-253 "DLP.spad" 301500 301510 302130 302135) (-252 "DLIST.spad" 299905 299915 300509 300536) (-251 "DLAGG.spad" 298322 298332 299895 299900) (-250 "DIVRING.spad" 297864 297872 298266 298317) (-249 "DIVRING.spad" 297450 297460 297854 297859) (-248 "DISPLAY.spad" 295640 295648 297440 297445) (-247 "DIRPROD2.spad" 294458 294476 295630 295635) (-246 "DIRPROD.spad" 281690 281706 282330 282429) (-245 "DIRPCAT.spad" 280883 280899 281586 281685) (-244 "DIRPCAT.spad" 279703 279721 280408 280413) (-243 "DIOSP.spad" 278528 278536 279693 279698) (-242 "DIOPS.spad" 277524 277534 278508 278523) (-241 "DIOPS.spad" 276494 276506 277480 277485) (-240 "DIFRING.spad" 276332 276340 276474 276489) (-239 "DIFFSPC.spad" 275911 275919 276322 276327) (-238 "DIFFSPC.spad" 275488 275498 275901 275906) (-237 "DIFFMOD.spad" 274977 274987 275456 275483) (-236 "DIFFDOM.spad" 274142 274153 274967 274972) (-235 "DIFFDOM.spad" 273305 273318 274132 274137) (-234 "DIFEXT.spad" 273124 273134 273285 273300) (-233 "DIAGG.spad" 272754 272764 273104 273119) (-232 "DIAGG.spad" 272392 272404 272744 272749) (-231 "DHMATRIX.spad" 270575 270585 271720 271747) (-230 "DFSFUN.spad" 264215 264223 270565 270570) (-229 "DFLOAT.spad" 260946 260954 264105 264210) (-228 "DFINTTLS.spad" 259177 259193 260936 260941) (-227 "DERHAM.spad" 257091 257123 259157 259172) (-226 "DEQUEUE.spad" 256286 256296 256569 256596) (-225 "DEGRED.spad" 255903 255917 256276 256281) (-224 "DEFINTRF.spad" 253440 253450 255893 255898) (-223 "DEFINTEF.spad" 251950 251966 253430 253435) (-222 "DEFAST.spad" 251334 251342 251940 251945) (-221 "DECIMAL.spad" 249298 249306 249659 249752) (-220 "DDFACT.spad" 247119 247136 249288 249293) (-219 "DBLRESP.spad" 246719 246743 247109 247114) (-218 "DBASIS.spad" 246345 246360 246709 246714) (-217 "DBASE.spad" 245009 245019 246335 246340) (-216 "DATAARY.spad" 244495 244508 244999 245004) (-215 "D03FAFA.spad" 244323 244331 244485 244490) (-214 "D03EEFA.spad" 244143 244151 244313 244318) (-213 "D03AGNT.spad" 243229 243237 244133 244138) (-212 "D02EJFA.spad" 242691 242699 243219 243224) (-211 "D02CJFA.spad" 242169 242177 242681 242686) (-210 "D02BHFA.spad" 241659 241667 242159 242164) (-209 "D02BBFA.spad" 241149 241157 241649 241654) (-208 "D02AGNT.spad" 236019 236027 241139 241144) (-207 "D01WGTS.spad" 234338 234346 236009 236014) (-206 "D01TRNS.spad" 234315 234323 234328 234333) (-205 "D01GBFA.spad" 233837 233845 234305 234310) (-204 "D01FCFA.spad" 233359 233367 233827 233832) (-203 "D01ASFA.spad" 232827 232835 233349 233354) (-202 "D01AQFA.spad" 232281 232289 232817 232822) (-201 "D01APFA.spad" 231721 231729 232271 232276) (-200 "D01ANFA.spad" 231215 231223 231711 231716) (-199 "D01AMFA.spad" 230725 230733 231205 231210) (-198 "D01ALFA.spad" 230265 230273 230715 230720) (-197 "D01AKFA.spad" 229791 229799 230255 230260) (-196 "D01AJFA.spad" 229314 229322 229781 229786) (-195 "D01AGNT.spad" 225381 225389 229304 229309) (-194 "CYCLOTOM.spad" 224887 224895 225371 225376) (-193 "CYCLES.spad" 221679 221687 224877 224882) (-192 "CVMP.spad" 221096 221106 221669 221674) (-191 "CTRIGMNP.spad" 219596 219612 221086 221091) (-190 "CTORKIND.spad" 219199 219207 219586 219591) (-189 "CTORCAT.spad" 218440 218448 219189 219194) (-188 "CTORCAT.spad" 217679 217689 218430 218435) (-187 "CTORCALL.spad" 217268 217278 217669 217674) (-186 "CTOR.spad" 216959 216967 217258 217263) (-185 "CSTTOOLS.spad" 216204 216217 216949 216954) (-184 "CRFP.spad" 209976 209989 216194 216199) (-183 "CRCEAST.spad" 209696 209704 209966 209971) (-182 "CRAPACK.spad" 208763 208773 209686 209691) (-181 "CPMATCH.spad" 208264 208279 208685 208690) (-180 "CPIMA.spad" 207969 207988 208254 208259) (-179 "COORDSYS.spad" 202978 202988 207959 207964) (-178 "CONTOUR.spad" 202405 202413 202968 202973) (-177 "CONTFRAC.spad" 198155 198165 202307 202400) (-176 "CONDUIT.spad" 197913 197921 198145 198150) (-175 "COMRING.spad" 197587 197595 197851 197908) (-174 "COMPPROP.spad" 197105 197113 197577 197582) (-173 "COMPLPAT.spad" 196872 196887 197095 197100) (-172 "COMPLEX2.spad" 196587 196599 196862 196867) (-171 "COMPLEX.spad" 191898 191908 192142 192403) (-170 "COMPILER.spad" 191447 191455 191888 191893) (-169 "COMPFACT.spad" 191049 191063 191437 191442) (-168 "COMPCAT.spad" 189121 189131 190783 191044) (-167 "COMPCAT.spad" 186918 186930 188582 188587) (-166 "COMMUPC.spad" 186666 186684 186908 186913) (-165 "COMMONOP.spad" 186199 186207 186656 186661) (-164 "COMMAAST.spad" 185962 185970 186189 186194) (-163 "COMM.spad" 185773 185781 185952 185957) (-162 "COMBOPC.spad" 184696 184704 185763 185768) (-161 "COMBINAT.spad" 183463 183473 184686 184691) (-160 "COMBF.spad" 180885 180901 183453 183458) (-159 "COLOR.spad" 179722 179730 180875 180880) (-158 "COLONAST.spad" 179388 179396 179712 179717) (-157 "CMPLXRT.spad" 179099 179116 179378 179383) (-156 "CLLCTAST.spad" 178761 178769 179089 179094) (-155 "CLIP.spad" 174869 174877 178751 178756) (-154 "CLIF.spad" 173524 173540 174825 174864) (-153 "CLAGG.spad" 170061 170071 173514 173519) (-152 "CLAGG.spad" 166466 166478 169921 169926) (-151 "CINTSLPE.spad" 165821 165834 166456 166461) (-150 "CHVAR.spad" 163959 163981 165811 165816) (-149 "CHARZ.spad" 163874 163882 163939 163954) (-148 "CHARPOL.spad" 163400 163410 163864 163869) (-147 "CHARNZ.spad" 163162 163170 163380 163395) (-146 "CHAR.spad" 160530 160538 163152 163157) (-145 "CFCAT.spad" 159858 159866 160520 160525) (-144 "CDEN.spad" 159078 159092 159848 159853) (-143 "CCLASS.spad" 157174 157182 158436 158475) (-142 "CATEGORY.spad" 156248 156256 157164 157169) (-141 "CATCTOR.spad" 156139 156147 156238 156243) (-140 "CATAST.spad" 155765 155773 156129 156134) (-139 "CASEAST.spad" 155479 155487 155755 155760) (-138 "CARTEN2.spad" 154869 154896 155469 155474) (-137 "CARTEN.spad" 150236 150260 154859 154864) (-136 "CARD.spad" 147531 147539 150210 150231) (-135 "CAPSLAST.spad" 147313 147321 147521 147526) (-134 "CACHSET.spad" 146937 146945 147303 147308) (-133 "CABMON.spad" 146492 146500 146927 146932) (-132 "BYTEORD.spad" 146167 146175 146482 146487) (-131 "BYTEBUF.spad" 143868 143876 145154 145181) (-130 "BYTE.spad" 143343 143351 143858 143863) (-129 "BTREE.spad" 142287 142297 142821 142848) (-128 "BTOURN.spad" 141163 141173 141765 141792) (-127 "BTCAT.spad" 140555 140565 141131 141158) (-126 "BTCAT.spad" 139967 139979 140545 140550) (-125 "BTAGG.spad" 139433 139441 139935 139962) (-124 "BTAGG.spad" 138919 138929 139423 139428) (-123 "BSTREE.spad" 137531 137541 138397 138424) (-122 "BRILL.spad" 135736 135747 137521 137526) (-121 "BRAGG.spad" 134692 134702 135726 135731) (-120 "BRAGG.spad" 133612 133624 134648 134653) (-119 "BPADICRT.spad" 131437 131449 131684 131777) (-118 "BPADIC.spad" 131109 131121 131363 131432) (-117 "BOUNDZRO.spad" 130765 130782 131099 131104) (-116 "BOP1.spad" 128223 128233 130755 130760) (-115 "BOP.spad" 123365 123373 128213 128218) (-114 "BOOLEAN.spad" 122803 122811 123355 123360) (-113 "BOOLE.spad" 122453 122461 122793 122798) (-112 "BOOLE.spad" 122101 122111 122443 122448) (-111 "BMODULE.spad" 121813 121825 122069 122096) (-110 "BITS.spad" 121187 121195 121402 121429) (-109 "BINDING.spad" 120608 120616 121177 121182) (-108 "BINARY.spad" 118577 118585 118933 119026) (-107 "BGAGG.spad" 117782 117792 118557 118572) (-106 "BGAGG.spad" 116995 117007 117772 117777) (-105 "BFUNCT.spad" 116559 116567 116975 116990) (-104 "BEZOUT.spad" 115699 115726 116509 116514) (-103 "BBTREE.spad" 112447 112457 115177 115204) (-102 "BASTYPE.spad" 111946 111954 112437 112442) (-101 "BASTYPE.spad" 111443 111453 111936 111941) (-100 "BALFACT.spad" 110902 110915 111433 111438) (-99 "AUTOMOR.spad" 110353 110362 110882 110897) (-98 "ATTREG.spad" 107076 107083 110105 110348) (-97 "ATTRBUT.spad" 103099 103106 107056 107071) (-96 "ATTRAST.spad" 102816 102823 103089 103094) (-95 "ATRIG.spad" 102286 102293 102806 102811) (-94 "ATRIG.spad" 101754 101763 102276 102281) (-93 "ASTCAT.spad" 101658 101665 101744 101749) (-92 "ASTCAT.spad" 101560 101569 101648 101653) (-91 "ASTACK.spad" 100770 100779 101038 101065) (-90 "ASSOCEQ.spad" 99604 99615 100726 100731) (-89 "ASP9.spad" 98685 98698 99594 99599) (-88 "ASP80.spad" 98007 98020 98675 98680) (-87 "ASP8.spad" 97050 97063 97997 98002) (-86 "ASP78.spad" 96501 96514 97040 97045) (-85 "ASP77.spad" 95870 95883 96491 96496) (-84 "ASP74.spad" 94962 94975 95860 95865) (-83 "ASP73.spad" 94233 94246 94952 94957) (-82 "ASP7.spad" 93393 93406 94223 94228) (-81 "ASP6.spad" 92260 92273 93383 93388) (-80 "ASP55.spad" 90769 90782 92250 92255) (-79 "ASP50.spad" 88586 88599 90759 90764) (-78 "ASP49.spad" 87585 87598 88576 88581) (-77 "ASP42.spad" 86000 86039 87575 87580) (-76 "ASP41.spad" 84587 84626 85990 85995) (-75 "ASP4.spad" 83882 83895 84577 84582) (-74 "ASP35.spad" 82870 82883 83872 83877) (-73 "ASP34.spad" 82171 82184 82860 82865) (-72 "ASP33.spad" 81731 81744 82161 82166) (-71 "ASP31.spad" 80871 80884 81721 81726) (-70 "ASP30.spad" 79763 79776 80861 80866) (-69 "ASP29.spad" 79229 79242 79753 79758) (-68 "ASP28.spad" 70502 70515 79219 79224) (-67 "ASP27.spad" 69399 69412 70492 70497) (-66 "ASP24.spad" 68486 68499 69389 69394) (-65 "ASP20.spad" 67950 67963 68476 68481) (-64 "ASP19.spad" 62636 62649 67940 67945) (-63 "ASP12.spad" 62050 62063 62626 62631) (-62 "ASP10.spad" 61321 61334 62040 62045) (-61 "ASP1.spad" 60702 60715 61311 61316) (-60 "ARRAY2.spad" 59941 59950 60180 60207) (-59 "ARRAY12.spad" 58654 58665 59931 59936) (-58 "ARRAY1.spad" 57317 57326 57663 57690) (-57 "ARR2CAT.spad" 53099 53120 57285 57312) (-56 "ARR2CAT.spad" 48901 48924 53089 53094) (-55 "ARITY.spad" 48273 48280 48891 48896) (-54 "APPRULE.spad" 47557 47579 48263 48268) (-53 "APPLYORE.spad" 47176 47189 47547 47552) (-52 "ANY1.spad" 46247 46256 47166 47171) (-51 "ANY.spad" 45098 45105 46237 46242) (-50 "ANTISYM.spad" 43543 43559 45078 45093) (-49 "ANON.spad" 43252 43259 43533 43538) (-48 "AN.spad" 41558 41565 43065 43158) (-47 "AMR.spad" 39743 39754 41456 41553) (-46 "AMR.spad" 37759 37772 39474 39479) (-45 "ALIST.spad" 34599 34620 34949 34976) (-44 "ALGSC.spad" 33734 33760 34471 34524) (-43 "ALGPKG.spad" 29517 29528 33690 33695) (-42 "ALGMFACT.spad" 28710 28724 29507 29512) (-41 "ALGMANIP.spad" 26194 26209 28537 28542) (-40 "ALGFF.spad" 23799 23826 24016 24172) (-39 "ALGFACT.spad" 22918 22928 23789 23794) (-38 "ALGEBRA.spad" 22751 22760 22874 22913) (-37 "ALGEBRA.spad" 22616 22627 22741 22746) (-36 "ALAGG.spad" 22128 22149 22584 22611) (-35 "AHYP.spad" 21509 21516 22118 22123) (-34 "AGG.spad" 19842 19849 21499 21504) (-33 "AGG.spad" 18139 18148 19798 19803) (-32 "AF.spad" 16567 16582 18071 18076) (-31 "ADDAST.spad" 16253 16260 16557 16562) (-30 "ACPLOT.spad" 14844 14851 16243 16248) (-29 "ACFS.spad" 12701 12710 14746 14839) (-28 "ACFS.spad" 10644 10655 12691 12696) (-27 "ACF.spad" 7398 7405 10546 10639) (-26 "ACF.spad" 4238 4247 7388 7393) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2294535 2294540 2294545 2294550) (-2 NIL 2294515 2294520 2294525 2294530) (-1 NIL 2294495 2294500 2294505 2294510) (0 NIL 2294475 2294480 2294485 2294490) (-1329 "ZMOD.spad" 2294284 2294297 2294413 2294470) (-1328 "ZLINDEP.spad" 2293382 2293393 2294274 2294279) (-1327 "ZDSOLVE.spad" 2283342 2283364 2293372 2293377) (-1326 "YSTREAM.spad" 2282837 2282848 2283332 2283337) (-1325 "YDIAGRAM.spad" 2282471 2282480 2282827 2282832) (-1324 "XRPOLY.spad" 2281691 2281711 2282327 2282396) (-1323 "XPR.spad" 2279486 2279499 2281409 2281508) (-1322 "XPOLYC.spad" 2278805 2278821 2279412 2279481) (-1321 "XPOLY.spad" 2278360 2278371 2278661 2278730) (-1320 "XPBWPOLY.spad" 2276799 2276819 2278134 2278203) (-1319 "XFALG.spad" 2273847 2273863 2276725 2276794) (-1318 "XF.spad" 2272310 2272325 2273749 2273842) (-1317 "XF.spad" 2270753 2270770 2272194 2272199) (-1316 "XEXPPKG.spad" 2270012 2270038 2270743 2270748) (-1315 "XDPOLY.spad" 2269626 2269642 2269868 2269937) (-1314 "XALG.spad" 2269294 2269305 2269582 2269621) (-1313 "WUTSET.spad" 2265264 2265281 2268895 2268922) (-1312 "WP.spad" 2264471 2264515 2265122 2265189) (-1311 "WHILEAST.spad" 2264269 2264278 2264461 2264466) (-1310 "WHEREAST.spad" 2263940 2263949 2264259 2264264) (-1309 "WFFINTBS.spad" 2261603 2261625 2263930 2263935) (-1308 "WEIER.spad" 2259825 2259836 2261593 2261598) (-1307 "VSPACE.spad" 2259498 2259509 2259793 2259820) (-1306 "VSPACE.spad" 2259191 2259204 2259488 2259493) (-1305 "VOID.spad" 2258868 2258877 2259181 2259186) (-1304 "VIEWDEF.spad" 2254069 2254078 2258858 2258863) (-1303 "VIEW3D.spad" 2238030 2238039 2254059 2254064) (-1302 "VIEW2D.spad" 2225929 2225938 2238020 2238025) (-1301 "VIEW.spad" 2223649 2223658 2225919 2225924) (-1300 "VECTOR2.spad" 2222288 2222301 2223639 2223644) (-1299 "VECTOR.spad" 2220788 2220799 2221039 2221066) (-1298 "VECTCAT.spad" 2218700 2218711 2220756 2220783) (-1297 "VECTCAT.spad" 2216419 2216432 2218477 2218482) (-1296 "VARIABLE.spad" 2216199 2216214 2216409 2216414) (-1295 "UTYPE.spad" 2215843 2215852 2216189 2216194) (-1294 "UTSODETL.spad" 2215138 2215162 2215799 2215804) (-1293 "UTSODE.spad" 2213354 2213374 2215128 2215133) (-1292 "UTSCAT.spad" 2210833 2210849 2213252 2213349) (-1291 "UTSCAT.spad" 2207932 2207950 2210353 2210358) (-1290 "UTS2.spad" 2207527 2207562 2207922 2207927) (-1289 "UTS.spad" 2202405 2202433 2205925 2206022) (-1288 "URAGG.spad" 2197126 2197137 2202395 2202400) (-1287 "URAGG.spad" 2191811 2191824 2197082 2197087) (-1286 "UPXSSING.spad" 2189429 2189455 2190865 2190998) (-1285 "UPXSCONS.spad" 2187107 2187127 2187480 2187629) (-1284 "UPXSCCA.spad" 2185678 2185698 2186953 2187102) (-1283 "UPXSCCA.spad" 2184391 2184413 2185668 2185673) (-1282 "UPXSCAT.spad" 2182980 2182996 2184237 2184386) (-1281 "UPXS2.spad" 2182523 2182576 2182970 2182975) (-1280 "UPXS.spad" 2179738 2179766 2180574 2180723) (-1279 "UPSQFREE.spad" 2178152 2178166 2179728 2179733) (-1278 "UPSCAT.spad" 2175947 2175971 2178050 2178147) (-1277 "UPSCAT.spad" 2173427 2173453 2175532 2175537) (-1276 "UPOLYC2.spad" 2172898 2172917 2173417 2173422) (-1275 "UPOLYC.spad" 2167978 2167989 2172740 2172893) (-1274 "UPOLYC.spad" 2162944 2162957 2167708 2167713) (-1273 "UPMP.spad" 2161876 2161889 2162934 2162939) (-1272 "UPDIVP.spad" 2161441 2161455 2161866 2161871) (-1271 "UPDECOMP.spad" 2159702 2159716 2161431 2161436) (-1270 "UPCDEN.spad" 2158919 2158935 2159692 2159697) (-1269 "UP2.spad" 2158283 2158304 2158909 2158914) (-1268 "UP.spad" 2155311 2155326 2155698 2155851) (-1267 "UNISEG2.spad" 2154808 2154821 2155267 2155272) (-1266 "UNISEG.spad" 2154161 2154172 2154727 2154732) (-1265 "UNIFACT.spad" 2153264 2153276 2154151 2154156) (-1264 "ULSCONS.spad" 2144176 2144196 2144546 2144695) (-1263 "ULSCCAT.spad" 2141913 2141933 2144022 2144171) (-1262 "ULSCCAT.spad" 2139758 2139780 2141869 2141874) (-1261 "ULSCAT.spad" 2137998 2138014 2139604 2139753) (-1260 "ULS2.spad" 2137512 2137565 2137988 2137993) (-1259 "ULS.spad" 2127083 2127111 2128028 2128457) (-1258 "UINT8.spad" 2126960 2126969 2127073 2127078) (-1257 "UINT64.spad" 2126836 2126845 2126950 2126955) (-1256 "UINT32.spad" 2126712 2126721 2126826 2126831) (-1255 "UINT16.spad" 2126588 2126597 2126702 2126707) (-1254 "UFD.spad" 2125653 2125662 2126514 2126583) (-1253 "UFD.spad" 2124780 2124791 2125643 2125648) (-1252 "UDVO.spad" 2123661 2123670 2124770 2124775) (-1251 "UDPO.spad" 2121242 2121253 2123617 2123622) (-1250 "TYPEAST.spad" 2121161 2121170 2121232 2121237) (-1249 "TYPE.spad" 2121093 2121102 2121151 2121156) (-1248 "TWOFACT.spad" 2119745 2119760 2121083 2121088) (-1247 "TUPLE.spad" 2119236 2119247 2119641 2119646) (-1246 "TUBETOOL.spad" 2116103 2116112 2119226 2119231) (-1245 "TUBE.spad" 2114750 2114767 2116093 2116098) (-1244 "TSETCAT.spad" 2102821 2102838 2114718 2114745) (-1243 "TSETCAT.spad" 2090878 2090897 2102777 2102782) (-1242 "TS.spad" 2089471 2089487 2090437 2090534) (-1241 "TRMANIP.spad" 2083835 2083852 2089159 2089164) (-1240 "TRIMAT.spad" 2082798 2082823 2083825 2083830) (-1239 "TRIGMNIP.spad" 2081325 2081342 2082788 2082793) (-1238 "TRIGCAT.spad" 2080837 2080846 2081315 2081320) (-1237 "TRIGCAT.spad" 2080347 2080358 2080827 2080832) (-1236 "TREE.spad" 2078793 2078804 2079825 2079852) (-1235 "TRANFUN.spad" 2078632 2078641 2078783 2078788) (-1234 "TRANFUN.spad" 2078469 2078480 2078622 2078627) (-1233 "TOPSP.spad" 2078143 2078152 2078459 2078464) (-1232 "TOOLSIGN.spad" 2077806 2077817 2078133 2078138) (-1231 "TEXTFILE.spad" 2076367 2076376 2077796 2077801) (-1230 "TEX1.spad" 2075923 2075934 2076357 2076362) (-1229 "TEX.spad" 2073117 2073126 2075913 2075918) (-1228 "TEMUTL.spad" 2072672 2072681 2073107 2073112) (-1227 "TBCMPPK.spad" 2070773 2070796 2072662 2072667) (-1226 "TBAGG.spad" 2069831 2069854 2070753 2070768) (-1225 "TBAGG.spad" 2068897 2068922 2069821 2069826) (-1224 "TANEXP.spad" 2068305 2068316 2068887 2068892) (-1223 "TALGOP.spad" 2068029 2068040 2068295 2068300) (-1222 "TABLEAU.spad" 2067510 2067521 2068019 2068024) (-1221 "TABLE.spad" 2065443 2065466 2065713 2065740) (-1220 "TABLBUMP.spad" 2062222 2062233 2065433 2065438) (-1219 "SYSTEM.spad" 2061450 2061459 2062212 2062217) (-1218 "SYSSOLP.spad" 2058933 2058944 2061440 2061445) (-1217 "SYSPTR.spad" 2058832 2058841 2058923 2058928) (-1216 "SYSNNI.spad" 2058055 2058066 2058822 2058827) (-1215 "SYSINT.spad" 2057459 2057470 2058045 2058050) (-1214 "SYNTAX.spad" 2053793 2053802 2057449 2057454) (-1213 "SYMTAB.spad" 2051861 2051870 2053783 2053788) (-1212 "SYMS.spad" 2047884 2047893 2051851 2051856) (-1211 "SYMPOLY.spad" 2046863 2046874 2046945 2047072) (-1210 "SYMFUNC.spad" 2046364 2046375 2046853 2046858) (-1209 "SYMBOL.spad" 2043859 2043868 2046354 2046359) (-1208 "SWITCH.spad" 2040630 2040639 2043849 2043854) (-1207 "SUTS.spad" 2037609 2037637 2039028 2039125) (-1206 "SUPXS.spad" 2034811 2034839 2035660 2035809) (-1205 "SUPFRACF.spad" 2033916 2033934 2034801 2034806) (-1204 "SUP2.spad" 2033308 2033321 2033906 2033911) (-1203 "SUP.spad" 2029950 2029961 2030723 2030876) (-1202 "SUMRF.spad" 2028924 2028935 2029940 2029945) (-1201 "SUMFS.spad" 2028553 2028570 2028914 2028919) (-1200 "SULS.spad" 2018111 2018139 2019069 2019498) (-1199 "SUCHTAST.spad" 2017880 2017889 2018101 2018106) (-1198 "SUCH.spad" 2017570 2017585 2017870 2017875) (-1197 "SUBSPACE.spad" 2009701 2009716 2017560 2017565) (-1196 "SUBRESP.spad" 2008871 2008885 2009657 2009662) (-1195 "STTFNC.spad" 2005339 2005355 2008861 2008866) (-1194 "STTF.spad" 2001438 2001454 2005329 2005334) (-1193 "STTAYLOR.spad" 1994083 1994094 2001313 2001318) (-1192 "STRTBL.spad" 1992098 1992115 1992247 1992274) (-1191 "STRING.spad" 1990864 1990873 1991085 1991112) (-1190 "STREAM3.spad" 1990437 1990452 1990854 1990859) (-1189 "STREAM2.spad" 1989565 1989578 1990427 1990432) (-1188 "STREAM1.spad" 1989271 1989282 1989555 1989560) (-1187 "STREAM.spad" 1986057 1986068 1988664 1988679) (-1186 "STINPROD.spad" 1984993 1985009 1986047 1986052) (-1185 "STEPAST.spad" 1984227 1984236 1984983 1984988) (-1184 "STEP.spad" 1983436 1983445 1984217 1984222) (-1183 "STBL.spad" 1981484 1981512 1981651 1981666) (-1182 "STAGG.spad" 1980183 1980194 1981474 1981479) (-1181 "STAGG.spad" 1978880 1978893 1980173 1980178) (-1180 "STACK.spad" 1978108 1978119 1978358 1978385) (-1179 "SRING.spad" 1977868 1977877 1978098 1978103) (-1178 "SREGSET.spad" 1975567 1975584 1977469 1977496) (-1177 "SRDCMPK.spad" 1974144 1974164 1975557 1975562) (-1176 "SRAGG.spad" 1969327 1969336 1974112 1974139) (-1175 "SRAGG.spad" 1964530 1964541 1969317 1969322) (-1174 "SQMATRIX.spad" 1962025 1962043 1962941 1963028) (-1173 "SPLTREE.spad" 1956491 1956504 1961287 1961314) (-1172 "SPLNODE.spad" 1953111 1953124 1956481 1956486) (-1171 "SPFCAT.spad" 1951920 1951929 1953101 1953106) (-1170 "SPECOUT.spad" 1950472 1950481 1951910 1951915) (-1169 "SPADXPT.spad" 1942563 1942572 1950462 1950467) (-1168 "spad-parser.spad" 1942028 1942037 1942553 1942558) (-1167 "SPADAST.spad" 1941729 1941738 1942018 1942023) (-1166 "SPACEC.spad" 1925944 1925955 1941719 1941724) (-1165 "SPACE3.spad" 1925720 1925731 1925934 1925939) (-1164 "SORTPAK.spad" 1925269 1925282 1925676 1925681) (-1163 "SOLVETRA.spad" 1923032 1923043 1925259 1925264) (-1162 "SOLVESER.spad" 1921488 1921499 1923022 1923027) (-1161 "SOLVERAD.spad" 1917514 1917525 1921478 1921483) (-1160 "SOLVEFOR.spad" 1915976 1915994 1917504 1917509) (-1159 "SNTSCAT.spad" 1915576 1915593 1915944 1915971) (-1158 "SMTS.spad" 1913858 1913884 1915135 1915232) (-1157 "SMP.spad" 1911261 1911281 1911651 1911778) (-1156 "SMITH.spad" 1910106 1910131 1911251 1911256) (-1155 "SMATCAT.spad" 1908224 1908254 1910050 1910101) (-1154 "SMATCAT.spad" 1906274 1906306 1908102 1908107) (-1153 "SKAGG.spad" 1905243 1905254 1906242 1906269) (-1152 "SINT.spad" 1904183 1904192 1905109 1905238) (-1151 "SIMPAN.spad" 1903911 1903920 1904173 1904178) (-1150 "SIGNRF.spad" 1903029 1903040 1903901 1903906) (-1149 "SIGNEF.spad" 1902308 1902325 1903019 1903024) (-1148 "SIGAST.spad" 1901725 1901734 1902298 1902303) (-1147 "SIG.spad" 1901087 1901096 1901715 1901720) (-1146 "SHP.spad" 1899031 1899046 1901043 1901048) (-1145 "SHDP.spad" 1886386 1886413 1886903 1887002) (-1144 "SGROUP.spad" 1885994 1886003 1886376 1886381) (-1143 "SGROUP.spad" 1885600 1885611 1885984 1885989) (-1142 "SGCF.spad" 1878739 1878748 1885590 1885595) (-1141 "SFRTCAT.spad" 1877685 1877702 1878707 1878734) (-1140 "SFRGCD.spad" 1876748 1876768 1877675 1877680) (-1139 "SFQCMPK.spad" 1871561 1871581 1876738 1876743) (-1138 "SFORT.spad" 1871000 1871014 1871551 1871556) (-1137 "SEXOF.spad" 1870843 1870883 1870990 1870995) (-1136 "SEXCAT.spad" 1868671 1868711 1870833 1870838) (-1135 "SEX.spad" 1868563 1868572 1868661 1868666) (-1134 "SETMN.spad" 1867021 1867038 1868553 1868558) (-1133 "SETCAT.spad" 1866506 1866515 1867011 1867016) (-1132 "SETCAT.spad" 1865989 1866000 1866496 1866501) (-1131 "SETAGG.spad" 1862538 1862549 1865969 1865984) (-1130 "SETAGG.spad" 1859095 1859108 1862528 1862533) (-1129 "SET.spad" 1857368 1857379 1858465 1858504) (-1128 "SEQAST.spad" 1857071 1857080 1857358 1857363) (-1127 "SEGXCAT.spad" 1856227 1856240 1857061 1857066) (-1126 "SEGCAT.spad" 1855152 1855163 1856217 1856222) (-1125 "SEGBIND2.spad" 1854850 1854863 1855142 1855147) (-1124 "SEGBIND.spad" 1854608 1854619 1854797 1854802) (-1123 "SEGAST.spad" 1854338 1854347 1854598 1854603) (-1122 "SEG2.spad" 1853773 1853786 1854294 1854299) (-1121 "SEG.spad" 1853586 1853597 1853692 1853697) (-1120 "SDVAR.spad" 1852862 1852873 1853576 1853581) (-1119 "SDPOL.spad" 1850117 1850128 1850408 1850535) (-1118 "SCPKG.spad" 1848206 1848217 1850107 1850112) (-1117 "SCOPE.spad" 1847383 1847392 1848196 1848201) (-1116 "SCACHE.spad" 1846079 1846090 1847373 1847378) (-1115 "SASTCAT.spad" 1845988 1845997 1846069 1846074) (-1114 "SAOS.spad" 1845860 1845869 1845978 1845983) (-1113 "SAERFFC.spad" 1845573 1845593 1845850 1845855) (-1112 "SAEFACT.spad" 1845274 1845294 1845563 1845568) (-1111 "SAE.spad" 1842708 1842724 1843319 1843454) (-1110 "RURPK.spad" 1840367 1840383 1842698 1842703) (-1109 "RULESET.spad" 1839820 1839844 1840357 1840362) (-1108 "RULECOLD.spad" 1839672 1839685 1839810 1839815) (-1107 "RULE.spad" 1837920 1837944 1839662 1839667) (-1106 "RTVALUE.spad" 1837655 1837664 1837910 1837915) (-1105 "RSTRCAST.spad" 1837372 1837381 1837645 1837650) (-1104 "RSETGCD.spad" 1833814 1833834 1837362 1837367) (-1103 "RSETCAT.spad" 1823782 1823799 1833782 1833809) (-1102 "RSETCAT.spad" 1813770 1813789 1823772 1823777) (-1101 "RSDCMPK.spad" 1812270 1812290 1813760 1813765) (-1100 "RRCC.spad" 1810654 1810684 1812260 1812265) (-1099 "RRCC.spad" 1809036 1809068 1810644 1810649) (-1098 "RPTAST.spad" 1808738 1808747 1809026 1809031) (-1097 "RPOLCAT.spad" 1788242 1788257 1808606 1808733) (-1096 "RPOLCAT.spad" 1767441 1767458 1787807 1787812) (-1095 "ROUTINE.spad" 1762842 1762851 1765590 1765617) (-1094 "ROMAN.spad" 1762170 1762179 1762708 1762837) (-1093 "ROIRC.spad" 1761250 1761282 1762160 1762165) (-1092 "RNS.spad" 1760226 1760235 1761152 1761245) (-1091 "RNS.spad" 1759288 1759299 1760216 1760221) (-1090 "RNGBIND.spad" 1758448 1758462 1759243 1759248) (-1089 "RNG.spad" 1758183 1758192 1758438 1758443) (-1088 "RMODULE.spad" 1757964 1757975 1758173 1758178) (-1087 "RMCAT2.spad" 1757384 1757441 1757954 1757959) (-1086 "RMATRIX.spad" 1756154 1756173 1756497 1756536) (-1085 "RMATCAT.spad" 1751733 1751764 1756110 1756149) (-1084 "RMATCAT.spad" 1747202 1747235 1751581 1751586) (-1083 "RLINSET.spad" 1746906 1746917 1747192 1747197) (-1082 "RINTERP.spad" 1746794 1746814 1746896 1746901) (-1081 "RING.spad" 1746264 1746273 1746774 1746789) (-1080 "RING.spad" 1745742 1745753 1746254 1746259) (-1079 "RIDIST.spad" 1745134 1745143 1745732 1745737) (-1078 "RGCHAIN.spad" 1743655 1743671 1744549 1744576) (-1077 "RGBCSPC.spad" 1743444 1743456 1743645 1743650) (-1076 "RGBCMDL.spad" 1743006 1743018 1743434 1743439) (-1075 "RFFACTOR.spad" 1742468 1742479 1742996 1743001) (-1074 "RFFACT.spad" 1742203 1742215 1742458 1742463) (-1073 "RFDIST.spad" 1741199 1741208 1742193 1742198) (-1072 "RF.spad" 1738873 1738884 1741189 1741194) (-1071 "RETSOL.spad" 1738292 1738305 1738863 1738868) (-1070 "RETRACT.spad" 1737720 1737731 1738282 1738287) (-1069 "RETRACT.spad" 1737146 1737159 1737710 1737715) (-1068 "RETAST.spad" 1736958 1736967 1737136 1737141) (-1067 "RESULT.spad" 1734520 1734529 1735107 1735134) (-1066 "RESRING.spad" 1733867 1733914 1734458 1734515) (-1065 "RESLATC.spad" 1733191 1733202 1733857 1733862) (-1064 "REPSQ.spad" 1732922 1732933 1733181 1733186) (-1063 "REPDB.spad" 1732629 1732640 1732912 1732917) (-1062 "REP2.spad" 1722343 1722354 1732471 1732476) (-1061 "REP1.spad" 1716563 1716574 1722293 1722298) (-1060 "REP.spad" 1714117 1714126 1716553 1716558) (-1059 "REGSET.spad" 1711909 1711926 1713718 1713745) (-1058 "REF.spad" 1711244 1711255 1711864 1711869) (-1057 "REDORDER.spad" 1710450 1710467 1711234 1711239) (-1056 "RECLOS.spad" 1709209 1709229 1709913 1710006) (-1055 "REALSOLV.spad" 1708349 1708358 1709199 1709204) (-1054 "REAL0Q.spad" 1705647 1705662 1708339 1708344) (-1053 "REAL0.spad" 1702491 1702506 1705637 1705642) (-1052 "REAL.spad" 1702363 1702372 1702481 1702486) (-1051 "RDUCEAST.spad" 1702084 1702093 1702353 1702358) (-1050 "RDIV.spad" 1701739 1701764 1702074 1702079) (-1049 "RDIST.spad" 1701306 1701317 1701729 1701734) (-1048 "RDETRS.spad" 1700170 1700188 1701296 1701301) (-1047 "RDETR.spad" 1698309 1698327 1700160 1700165) (-1046 "RDEEFS.spad" 1697408 1697425 1698299 1698304) (-1045 "RDEEF.spad" 1696418 1696435 1697398 1697403) (-1044 "RCFIELD.spad" 1693636 1693645 1696320 1696413) (-1043 "RCFIELD.spad" 1690940 1690951 1693626 1693631) (-1042 "RCAGG.spad" 1688876 1688887 1690930 1690935) (-1041 "RCAGG.spad" 1686739 1686752 1688795 1688800) (-1040 "RATRET.spad" 1686099 1686110 1686729 1686734) (-1039 "RATFACT.spad" 1685791 1685803 1686089 1686094) (-1038 "RANDSRC.spad" 1685110 1685119 1685781 1685786) (-1037 "RADUTIL.spad" 1684866 1684875 1685100 1685105) (-1036 "RADIX.spad" 1681645 1681659 1683191 1683284) (-1035 "RADFF.spad" 1679348 1679385 1679467 1679623) (-1034 "RADCAT.spad" 1678943 1678952 1679338 1679343) (-1033 "RADCAT.spad" 1678536 1678547 1678933 1678938) (-1032 "QUEUE.spad" 1677755 1677766 1678014 1678041) (-1031 "QUATCT2.spad" 1677375 1677394 1677745 1677750) (-1030 "QUATCAT.spad" 1675545 1675556 1677305 1677370) (-1029 "QUATCAT.spad" 1673463 1673476 1675225 1675230) (-1028 "QUAT.spad" 1671915 1671926 1672258 1672323) (-1027 "QUAGG.spad" 1670748 1670759 1671883 1671910) (-1026 "QQUTAST.spad" 1670516 1670525 1670738 1670743) (-1025 "QFORM.spad" 1670134 1670149 1670506 1670511) (-1024 "QFCAT2.spad" 1669826 1669843 1670124 1670129) (-1023 "QFCAT.spad" 1668528 1668539 1669728 1669821) (-1022 "QFCAT.spad" 1666812 1666825 1668014 1668019) (-1021 "QEQUAT.spad" 1666370 1666379 1666802 1666807) (-1020 "QCMPACK.spad" 1661284 1661304 1666360 1666365) (-1019 "QALGSET2.spad" 1659279 1659298 1661274 1661279) (-1018 "QALGSET.spad" 1655381 1655414 1659193 1659198) (-1017 "PWFFINTB.spad" 1652796 1652818 1655371 1655376) (-1016 "PUSHVAR.spad" 1652134 1652154 1652786 1652791) (-1015 "PTRANFN.spad" 1648269 1648280 1652124 1652129) (-1014 "PTPACK.spad" 1645356 1645367 1648259 1648264) (-1013 "PTFUNC2.spad" 1645178 1645193 1645346 1645351) (-1012 "PTCAT.spad" 1644432 1644443 1645146 1645173) (-1011 "PSQFR.spad" 1643746 1643771 1644422 1644427) (-1010 "PSEUDLIN.spad" 1642631 1642642 1643736 1643741) (-1009 "PSETPK.spad" 1629335 1629352 1642509 1642514) (-1008 "PSETCAT.spad" 1623734 1623758 1629315 1629330) (-1007 "PSETCAT.spad" 1618107 1618133 1623690 1623695) (-1006 "PSCURVE.spad" 1617105 1617114 1618097 1618102) (-1005 "PSCAT.spad" 1615887 1615917 1617003 1617100) (-1004 "PSCAT.spad" 1614759 1614791 1615877 1615882) (-1003 "PRTITION.spad" 1613456 1613465 1614749 1614754) (-1002 "PRTDAST.spad" 1613174 1613183 1613446 1613451) (-1001 "PRS.spad" 1602791 1602809 1613130 1613135) (-1000 "PRQAGG.spad" 1602225 1602236 1602759 1602786) (-999 "PROPLOG.spad" 1601829 1601837 1602215 1602220) (-998 "PROPFUN2.spad" 1601452 1601465 1601819 1601824) (-997 "PROPFUN1.spad" 1600858 1600869 1601442 1601447) (-996 "PROPFRML.spad" 1599426 1599437 1600848 1600853) (-995 "PROPERTY.spad" 1598922 1598930 1599416 1599421) (-994 "PRODUCT.spad" 1596604 1596616 1596888 1596943) (-993 "PRINT.spad" 1596356 1596364 1596594 1596599) (-992 "PRIMES.spad" 1594617 1594627 1596346 1596351) (-991 "PRIMELT.spad" 1592738 1592752 1594607 1594612) (-990 "PRIMCAT.spad" 1592381 1592389 1592728 1592733) (-989 "PRIMARR2.spad" 1591148 1591160 1592371 1592376) (-988 "PRIMARR.spad" 1589987 1589997 1590157 1590184) (-987 "PREASSOC.spad" 1589369 1589381 1589977 1589982) (-986 "PR.spad" 1587734 1587746 1588433 1588560) (-985 "PPCURVE.spad" 1586871 1586879 1587724 1587729) (-984 "PORTNUM.spad" 1586662 1586670 1586861 1586866) (-983 "POLYROOT.spad" 1585511 1585533 1586618 1586623) (-982 "POLYLIFT.spad" 1584776 1584799 1585501 1585506) 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1553288 1553688 1553693) (-962 "PMFS.spad" 1552855 1552873 1553268 1553273) (-961 "PMDOWN.spad" 1552145 1552159 1552845 1552850) (-960 "PMASSFS.spad" 1551120 1551136 1552135 1552140) (-959 "PMASS.spad" 1550138 1550146 1551110 1551115) (-958 "PLOTTOOL.spad" 1549918 1549926 1550128 1550133) (-957 "PLOT3D.spad" 1546382 1546390 1549908 1549913) (-956 "PLOT1.spad" 1545555 1545565 1546372 1546377) (-955 "PLOT.spad" 1540478 1540486 1545545 1545550) (-954 "PLEQN.spad" 1527880 1527907 1540468 1540473) (-953 "PINTERPA.spad" 1527664 1527680 1527870 1527875) (-952 "PINTERP.spad" 1527286 1527305 1527654 1527659) (-951 "PID.spad" 1526260 1526268 1527212 1527281) (-950 "PICOERCE.spad" 1525917 1525927 1526250 1526255) (-949 "PI.spad" 1525534 1525542 1525891 1525912) (-948 "PGROEB.spad" 1524143 1524157 1525524 1525529) (-947 "PGE.spad" 1515816 1515824 1524133 1524138) (-946 "PGCD.spad" 1514770 1514787 1515806 1515811) (-945 "PFRPAC.spad" 1513919 1513929 1514760 1514765) (-944 "PFR.spad" 1510622 1510632 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272553 272566 273380 273385) (-234 "DIFEXT.spad" 272372 272382 272533 272548) (-233 "DIAGG.spad" 272002 272012 272352 272367) (-232 "DIAGG.spad" 271640 271652 271992 271997) (-231 "DHMATRIX.spad" 269823 269833 270968 270995) (-230 "DFSFUN.spad" 263463 263471 269813 269818) (-229 "DFLOAT.spad" 260194 260202 263353 263458) (-228 "DFINTTLS.spad" 258425 258441 260184 260189) (-227 "DERHAM.spad" 256339 256371 258405 258420) (-226 "DEQUEUE.spad" 255534 255544 255817 255844) (-225 "DEGRED.spad" 255151 255165 255524 255529) (-224 "DEFINTRF.spad" 252688 252698 255141 255146) (-223 "DEFINTEF.spad" 251198 251214 252678 252683) (-222 "DEFAST.spad" 250582 250590 251188 251193) (-221 "DECIMAL.spad" 248546 248554 248907 249000) (-220 "DDFACT.spad" 246367 246384 248536 248541) (-219 "DBLRESP.spad" 245967 245991 246357 246362) (-218 "DBASIS.spad" 245593 245608 245957 245962) (-217 "DBASE.spad" 244257 244267 245583 245588) (-216 "DATAARY.spad" 243743 243756 244247 244252) (-215 "D03FAFA.spad" 243571 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index d650c1a2..14f75789 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(205700 . 3514591837) -(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((#0=(-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) #0#) |has| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (-321 (-2 (|:| -1580 |#1|) (|:| -3432 |#2|))))) -((((-560)) . T) (($) -4133 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -4133 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) +(205700 . 3514823553) +(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((#0=(-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) #0#) |has| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (-321 (-2 (|:| -2118 |#1|) (|:| -3964 |#2|))))) +((((-560)) . 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T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) (|has| |#1| (-940)) ((((-888)) . T)) ((((-888)) . T)) @@ -23,23 +23,23 @@ ((((-549)) . T) (((-1191)) . T) (((-229)) . T) (((-391)) . T) (((-916 (-391))) . T)) (((|#1|) . T)) ((((-229)) . T) (((-888)) . T)) -(-4133 (|has| |#2| (-817)) (|has| |#2| (-872))) -(-4133 (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (-12 (|has| |#1| (-872)) (|has| |#2| (-872)))) +(-4144 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-4144 (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (-12 (|has| |#1| (-872)) (|has| |#2| (-872)))) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) -(-4133 (|has| |#1| (-21)) (|has| |#1| (-871))) -((($ $) . T) ((#0=(-421 (-560)) #0#) -4133 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . 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T)) @@ -52,14 +52,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1214)) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) -(-4133 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) -(-4133 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) -(((|#2| (-496 (-2172 |#1|) (-793))) . T)) -((((-1209)) -4133 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) +(-4144 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-4144 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(((|#2| (-496 (-2236 |#1|) (-793))) . T)) +((((-1209)) -4144 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) (((|#1| (-545 (-1209))) . T)) ((((-1191)) . T) (((-988 (-130))) . T) (((-888)) . T)) ((((-888)) . T)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) (((#0=(-894 |#1|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (|has| |#4| (-381)) (|has| |#3| (-381)) @@ -75,14 +75,14 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-571)) -((((-560)) . T) (((-421 (-560))) -4133 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560))))) ((|#2|) . T) (($) -4133 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-889 |#1|)) . T)) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-571))) -((((-2 (|:| -3624 |#1|) (|:| -4403 |#2|))) . T)) +((((-560)) . T) (((-421 (-560))) -4144 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560))))) ((|#2|) . T) (($) -4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-889 |#1|)) . T)) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) +((((-2 (|:| -2183 |#1|) (|:| -4067 |#2|))) . T)) ((($) . T)) ((((-888)) |has| |#1| (-632 (-888))) ((|#1|) . T)) -((((-560)) . T) (((-421 (-560))) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T) (($) -4133 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((-1209)) . T)) -((((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-560)) . T) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T) (($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((-1209)) . T)) +((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-549)) |has| |#1| (-633 (-549)))) ((((-1209)) . T)) (((|#1|) . T)) @@ -103,12 +103,12 @@ ((((-888)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -4133 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . 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T) (($ $) -4133 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -4144 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -4144 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) ((($ $) . T)) ((($) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) @@ -132,30 +132,30 @@ (|has| |#1| (-381)) (((|#1|) . T)) ((((-888)) . T)) -((((-421 (-560))) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) +((((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) -(((|#1|) . 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T)) -(-4133 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) -(-4133 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-872)) (|has| |#1| (-1133))) (|has| |#1| (-1133)) -(-4133 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-4144 (|has| |#1| (-872)) (|has| |#1| (-1133))) (|has| |#1| (-1133)) -(-4133 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-4144 (|has| |#1| (-872)) (|has| |#1| (-1133))) (|has| |#1| (-871)) (((|#1| |#1|) . T)) ((($) . T) (((-421 (-560))) . T)) @@ -170,12 +170,12 @@ (|has| |#3| (-817)) (|has| |#3| (-817)) (((|#1| |#2|) . T)) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-363))) ((((-1214)) . T)) (((|#1| |#2|) . T)) (((|#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) (((-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|)))) -(-4133 (|has| |#1| (-102)) (|has| |#1| (-1133))) -(-4133 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) ((((-560)) . T) (((-421 (-560))) . T)) (((|#1| (-1209) (-1120 (-1209)) (-545 (-1120 (-1209)))) . T)) ((((-560) |#1|) . T)) @@ -195,29 +195,29 @@ ((((-1191) |#1|) . T)) ((((-1266 (-560)) $) . T) (((-560) (-130)) . T)) (((|#1|) . T)) -((((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) (((|#3| (-793)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) ((($) . T) (((-421 (-560))) . T)) ((($) . T)) ((($) . 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T)) ((((-421 (-560))) . T) (($) . T)) @@ -228,7 +228,7 @@ (((|#1|) . T)) (|has| |#2| (-376)) ((((-1266 (-560)) $) . T) (((-560) |#1|) . T)) -((($) -4133 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -4144 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) (((|#1| |#2|) . T)) ((((-888)) . T)) @@ -241,13 +241,13 @@ ((((-888)) . T)) ((((-888)) . T)) (((|#1| |#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -4133 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) -((($ $) -4133 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T)) -((((-2 (|:| -3624 |#1|) (|:| -4403 |#2|))) . T) (((-888)) . T)) +((((-2 (|:| -2183 |#1|) (|:| -4067 |#2|))) . T) (((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549))) (((-916 (-391))) |has| |#1| (-633 (-916 (-391)))) (((-916 (-560))) |has| |#1| (-633 (-916 (-560))))) -(((|#4|) -4133 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1081)))) -(((|#3|) -4133 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081)))) -((((-2 (|:| -3624 |#1|) (|:| -4403 |#2|))) . T)) +(((|#4|) -4144 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1081)))) +(((|#3|) -4144 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081)))) +((((-2 (|:| -2183 |#1|) (|:| -4067 |#2|))) . T)) ((((-888)) . T)) ((((-888)) . T)) ((((-549)) . T) (((-560)) . T) (((-916 (-560))) . T) (((-391)) . T) (((-229)) . T)) @@ -326,15 +326,15 @@ (((|#1|) . T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) ((($) . 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T)) @@ -349,15 +349,15 @@ (|has| |#1| (-1133)) ((((-936 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (((|#1|) . T)) -((((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-549)) |has| |#1| (-633 (-549)))) ((((-888)) . T) (((-1214)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4133 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) ((((-1214)) . 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T)) (((|#1| (-1003)) . T)) ((((-560)) . T) ((|#2|) . T)) @@ -369,7 +369,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1184)) -((((-2 (|:| -1580 (-1191)) (|:| -3432 |#1|))) . T)) +((((-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) . T)) (|has| (-1286 |#1| |#2| |#3| |#4|) (-147)) (|has| (-1286 |#1| |#2| |#3| |#4|) (-149)) (|has| |#1| (-147)) @@ -381,28 +381,28 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) -((((-1157 |#1| (-1209))) . T) (((-560)) . T) (((-842 (-1209))) . T) (($) -4133 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . T)) +((((-1157 |#1| (-1209))) . T) (((-560)) . T) (((-842 (-1209))) . T) (($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . 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T)) -((($) -4133 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -4144 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-888)) . T)) ((((-888)) . T)) (|has| (-1280 |#2| |#3| |#4|) (-149)) @@ -415,18 +415,18 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-4133 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) +(-4144 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) (((|#1|) . T)) ((($) . T)) ((((-560) |#1|) . T)) (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#1|) |has| |#1| (-175))) -(-4133 (|has| |#1| (-21)) (|has| |#1| (-871))) +(-4144 (|has| |#1| (-21)) (|has| |#1| (-871))) ((((-888)) |has| |#1| (-1133))) -((($) -4133 (|has| |#1| (-240)) (|has| |#1| (-239)))) -(-4133 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144))) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-363))) +((($) -4144 (|has| |#1| (-240)) (|has| |#1| (-239)))) +(-4144 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-363))) ((((-936 |#1|)) . T)) ((((-421 |#2|) |#3|) . T)) (|has| |#1| (-15 * (|#1| (-560) |#1|))) @@ -437,7 +437,7 @@ ((((-888)) . T)) ((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) (|has| |#1| (-376)) -(-4133 (-12 (|has| (-1289 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) +(-4144 (-12 (|has| (-1289 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-793) |#1|))) @@ -451,23 +451,23 @@ ((((-1266 (-560)) $) . T) (((-560) |#1|) . T)) ((((-888)) . T)) (((|#2|) . T)) -(-4133 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-4144 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) ((($) |has| |#1| (-571)) (((-560)) . T)) (|has| |#2| (-817)) (|has| |#2| (-817)) -((((-1289 |#1| |#2| |#3|)) . 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T) (($) -4144 (|has| |#1| (-376)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T)) (((|#1|) . T)) ((((-1209)) -12 (|has| |#3| (-928 (-1209))) (|has| |#3| (-1081)))) (((|#1|) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844))) -(-4133 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -4133 (|has| |#1| (-175)) (|has| |#1| (-571)))) +(-4144 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -4144 (|has| |#1| (-175)) (|has| |#1| (-571)))) ((($ $) |has| |#1| (-571)) ((|#1| |#1|) . T)) -((($ (-1209)) -4133 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) +((($ (-1209)) -4144 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) (((#0=(-721) (-1203 #0#)) . T)) ((((-595 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((((-421 (-560))) . T) (($) . T)) @@ -475,18 +475,18 @@ ((((-888)) . T) (((-1299 |#3|)) . T)) ((((-595 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) ((($) . T) (((-421 (-560))) . T)) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -4133 (|has| |#1| (-175)) (|has| |#1| (-571)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -4144 (|has| |#1| (-175)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) . T)) ((((-888)) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) ((($) . T)) -((($ $) -4133 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((#1=(-1289 |#1| |#2| |#3|) #1#) |has| |#1| (-376)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . T) (($ $) -4133 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376)))) -((($) -4133 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) (((-421 (-560))) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) . T)) -(((|#1|) . 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T) (($) -4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376)))) (((|#3|) |has| |#3| (-1081))) -((($) -4133 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((($ $) -4133 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($) -4144 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($ $) -4144 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) (|has| (-1121 |#1|) (-1133)) (((|#2| (-843 |#1|)) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T)) @@ -494,20 +494,20 @@ (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1|) . 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T)) -((($) -4133 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-421 $) (-421 $)) |has| |#1| (-571)) (($ $) . T) ((|#1| |#1|) . T)) -((($) -4133 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -4144 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((#0=(-1114) |#2|) . T) ((#0# $) . T) (($ $) . T)) ((((-888)) . T)) ((((-936 |#1|)) . T)) @@ -516,22 +516,22 @@ ((((-246 |#1| |#2|) |#2|) . T)) ((((-888)) . T)) (((|#3|) |has| |#3| (-1133)) (((-560)) -12 (|has| |#3| (-1070 (-560))) (|has| |#3| (-1133))) (((-421 (-560))) -12 (|has| |#3| (-1070 (-421 (-560)))) (|has| |#3| (-1133)))) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) (((|#1|) . T)) -((((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-549)) |has| |#1| (-633 (-549)))) (((|#1|) |has| |#1| (-175))) -((((-2 (|:| -1580 (-1209)) (|:| -3432 (-51)))) . T)) +((((-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))) . T)) (|has| |#1| (-376)) ((((-1214)) . T)) (((|#1|) . T)) -(-4133 (|has| |#1| (-21)) (|has| |#1| (-871))) +(-4144 (|has| |#1| (-21)) (|has| |#1| (-871))) ((($) . T)) ((((-1209) |#1|) |has| |#1| (-528 (-1209) |#1|)) ((|#1| |#1|) |has| |#1| (-321 |#1|))) (|has| |#2| (-844)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-871)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1| |#2| |#3| (-545 |#3|)) . T)) ((((-888)) . T)) @@ -540,15 +540,15 @@ (|has| |#1| (-381)) ((((-421 (-560))) . T)) (((|#1|) . T)) -(-4133 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((((-421 (-560))) . T)) ((((-1191) |#1|) . T)) (|has| |#1| (-381)) ((((-560)) . T)) ((((-560)) . T)) (((|#1|) . T) (((-560)) . T)) -(-4133 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) -(-4133 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-4144 (|has| |#1| (-872)) (|has| |#1| (-1133))) ((((-888)) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) ((((-1209)) -12 (|has| |#1| (-376)) (|has| |#1| (-928 (-1209))))) @@ -562,12 +562,12 @@ ((((-560) |#3|) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) (|has| |#2| (-1081)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) -(-4133 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +(-4144 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((((-888)) . T)) ((((-1286 |#1| |#2| |#3| |#4|)) . T)) ((((-421 (-560))) . T) (((-560)) . T)) -((((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) @@ -576,9 +576,9 @@ ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) ((((-560)) . T)) ((((-560)) . T)) -((($) . T) (((-560)) . T) (((-421 (-560))) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) +((($) . T) (((-560)) . T) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) -((((-560)) -4133 (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (|has| |#2| (-1081))) ((|#2|) |has| |#2| (-1133)) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) +((((-560)) -4144 (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (|has| |#2| (-1081))) ((|#2|) |has| |#2| (-1133)) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -595,7 +595,7 @@ ((((-888)) . T)) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . 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T)) (|has| (-421 |#2|) (-149)) (|has| (-421 |#2|) (-147)) @@ -898,15 +898,15 @@ (|has| |#1| (-571)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) ((((-888)) . T)) -((((-2 (|:| -1580 (-1191)) (|:| -3432 |#1|))) . T)) +((((-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) . T)) (|has| |#1| (-38 (-421 (-560)))) -((((-402) (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|))) . T)) +((((-402) (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#2| (-1184)) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-888)) . T) (((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) @@ -924,7 +924,7 @@ ((((-402) (-1191)) . T)) (|has| |#1| (-571)) ((((-1266 (-560)) $) . T) (((-560) |#1|) . T)) -(-4133 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-4144 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) (((|#2|) . T)) @@ -942,7 +942,7 @@ ((((-663 |#1|)) . T)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -(-4133 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-4144 (|has| |#1| (-872)) (|has| |#1| (-1133))) (((|#2|) |has| |#2| (-321 |#2|))) (((#0=(-560) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -953,14 +953,14 @@ ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) (|has| |#2| (-381)) (((#0=(-560) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) -(-4133 (|has| |#1| (-102)) (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-4144 (|has| |#1| (-102)) (|has| |#1| (-872)) (|has| |#1| (-1133))) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . 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T)) -((($) -4133 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((($) . T) (((-560)) . T) ((|#2|) . T)) ((((-560)) . T) (($) . T) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) ((((-421 (-560))) . T) (((-560)) . T)) @@ -990,29 +990,29 @@ (((|#1|) . T)) ((((-114)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) -(-4133 (|has| |#1| (-21)) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1081))) +(-4144 (|has| |#1| (-21)) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1081))) ((((-114)) . T)) ((((-549)) |has| |#1| (-633 (-549))) (((-229)) . #0=(|has| |#1| (-1052))) (((-391)) . #0#)) ((((-888)) . T)) (((|#1|) . 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T)) (((|#1|) . T)) @@ -1116,8 +1116,8 @@ (((|#1|) . T)) ((((-1209)) . T)) (|has| |#1| (-571)) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-571)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -1129,7 +1129,7 @@ (|has| |#1| (-149)) (|has| |#1| (-147)) (|has| |#1| (-149)) -(((|#2| (-246 (-2172 |#1|) (-793)) (-889 |#1|)) . T)) +(((|#2| (-246 (-2236 |#1|) (-793)) (-889 |#1|)) . T)) (((|#1| (-545 |#3|) |#3|) . T)) (|has| |#1| (-147)) (((#0=(-421 (-560)) #0#) |has| |#2| (-376)) (($ $) . T)) @@ -1143,12 +1143,12 @@ (|has| |#1| (-147)) ((((-421 (-560))) |has| |#2| (-376)) (($) . 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T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T) (($) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((($ (-1296 |#2|)) . T) (($ (-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) -((((-560)) -4133 (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (|has| |#2| (-1081))) ((|#2|) |has| |#2| (-1133)) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-560)) -4144 (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (|has| |#2| (-1081))) ((|#2|) |has| |#2| (-1133)) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1195,15 +1195,15 @@ ((((-888)) . T)) ((((-888)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) (((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) |has| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (-321 (-2 (|:| -1580 |#1|) (|:| -3432 |#2|))))) -(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) (((-2 (|:| -1580 (-1191)) (|:| -3432 |#1|))) |has| (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|)) (-321 (-2 (|:| -1580 (-1191)) (|:| -3432 |#1|))))) +(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) (((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) |has| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (-321 (-2 (|:| -2118 |#1|) (|:| -3964 |#2|))))) +(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) (((-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) |has| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (-321 (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))))) ((((-888)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) (((|#1|) . T)) ((($) . T) ((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) ((((-1209) (-51)) . T)) -((((-1209)) -4133 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +((((-1209)) -4144 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-889 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-845)) @@ -1211,10 +1211,10 @@ ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| (-1121 |#1|) (-1133)) -(((|#2| |#2|) -4133 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) -(((|#2|) -4133 (|has| |#2| (-175)) (|has| |#2| (-376)))) -((((-560) (-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -4133 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) +(((|#2| |#2|) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) +(((|#2|) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)))) +((((-560) (-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) ((((-560)) . T)) ((((-1214)) . T)) ((((-793)) . T)) @@ -1233,34 +1233,34 @@ (((|#1|) . T)) ((((-421 (-560))) . T) (($) . T)) ((($) . T) (((-421 (-560))) . T)) -(-4133 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-175)) (|has| |#1| (-571))) ((((-1214)) . T)) -(-4133 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) -(-4133 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-560)) . T)) -(-4133 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-175)) (|has| |#1| (-571))) (|has| |#1| (-147)) ((((-560)) . 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T)) -(-4133 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-4144 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((|#1|) . T) (($) . T)) (((|#2|) |has| |#2| (-175))) -((($) -4133 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) |has| |#2| (-175)) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -4144 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) |has| |#2| (-175)) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) ((((-894 |#1|)) . T)) -(-4133 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-817)) (|has| |#2| (-872)) (|has| |#2| (-1081)) (|has| |#2| (-1133))) +(-4144 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-817)) (|has| |#2| (-872)) (|has| |#2| (-1081)) (|has| |#2| (-1133))) (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (|has| |#2| (-1184)) -(((#0=(-51)) . T) (((-2 (|:| -1580 (-1209)) (|:| -3432 #0#))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2118 (-1209)) (|:| -3964 #0#))) . T)) (((|#1| |#2|) . T)) (((|#1| (-657 |#2|)) . T)) (|has| |#3| (-1081)) @@ -1269,10 +1269,10 @@ (((|#1| (-560) (-1114)) . T)) (((|#1| (-421 (-560)) (-1114)) . T)) ((((-1209)) . T)) -((($) -4133 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -4133 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) -((($) -4133 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -4144 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -4144 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) -4144 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((((-560) |#2|) . T)) -((($ (-1209)) -4133 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((($ (-1209)) -4144 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-381)) @@ -1280,46 +1280,46 @@ ((((-888)) . 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T)) (((|#1|) |has| |#1| (-321 |#1|))) @@ -1329,21 +1329,21 @@ (|has| |#1| (-381)) ((((-1209) $) |has| |#1| (-528 (-1209) $)) (($ $) |has| |#1| (-321 $)) ((|#1| |#1|) |has| |#1| (-321 |#1|)) (((-1209) |#1|) |has| |#1| (-528 (-1209) |#1|))) ((((-1209)) |has| |#1| (-928 (-1209)))) -(-4133 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-4144 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-402) |#1|) . T)) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-363))) -(-4133 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) (((|#2|) . T) (((-888)) . T)) ((((-888)) . T)) (((|#2|) . T)) ((((-936 |#1|)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4133 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -4133 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1352,7 +1352,7 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) (((|#1| |#1|) . T)) (((#0=(-894 |#1|)) |has| #0# (-321 #0#))) -((((-560)) . T) (($) -4133 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -4133 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) +((((-560)) . T) (($) -4144 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -4144 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-817)) (|has| |#2| (-817)) @@ -1361,7 +1361,7 @@ (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (|has| |#2| (-1081)) ((($) . T) (((-560)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1235)) (((#0=(-560) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) @@ -1375,7 +1375,7 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-421 (-560)) #0#) . T)) (|has| |#1| (-376)) ((((-560)) . T) (((-421 (-560))) . T) (($) . 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T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T)) ((($) . T) (((-560)) . T)) ((((-560) (-146)) . T)) -((((-560) (-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T) ((|#1| |#2|) . T)) +((((-560) (-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T) ((|#1| |#2|) . T)) ((((-421 (-560))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) ((((-888)) . T)) ((((-936 |#1|)) . T)) (|has| |#1| (-376)) @@ -1423,11 +1423,11 @@ (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-871)) -((($) -4133 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -4133 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . 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T)) -(-4133 (|has| |#1| (-102)) (|has| |#1| (-872)) (|has| |#1| (-1133))) -(((|#2| |#2|) -4133 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) +(-4144 (|has| |#1| (-102)) (|has| |#1| (-872)) (|has| |#1| (-1133))) +(((|#2| |#2|) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) (((|#2|) . T) (((-560)) . T)) ((((-888)) . T)) ((((-888)) . T)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T) ((|#2|) . T)) ((((-888)) . T)) ((((-888)) . T)) ((((-1191) (-1209) (-560) (-229) (-888)) . T)) @@ -1559,9 +1559,9 @@ ((((-421 (-560))) . T) (($) . T)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((($) . T) (((-421 (-560))) . T)) -(((|#2|) -4133 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) +(((|#2|) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) (|has| $ (-149)) ((((-421 |#2|)) . T)) ((((-421 (-560))) |has| #0=(-421 |#2|) (-1070 (-421 (-560)))) (((-560)) |has| #0# (-1070 (-560))) ((#0#) . T)) @@ -1570,11 +1570,11 @@ (|has| |#2| (-149)) (|has| |#1| (-149)) (|has| |#1| (-147)) -(-4133 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-4133 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-4133 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) (((|#1|) . T)) (|has| |#2| (-240)) @@ -1611,9 +1611,9 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-1028 |#1|)) . T) ((|#1|) . T)) -((((-1209)) -4133 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (((-842 (-1209))) . 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T)) @@ -1636,30 +1636,30 @@ (((|#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1133)))) ((((-1289 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1289 |#1| |#2| |#3|)) |has| |#1| (-376))) -(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((#0=(-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) #0#) |has| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (-321 (-2 (|:| -1580 |#1|) (|:| -3432 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((#0=(-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) #0#) |has| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (-321 (-2 (|:| -2118 |#1|) (|:| -3964 |#2|))))) (((|#2| |#2|) . T)) -(-4133 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239)))) +(-4144 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239)))) (|has| |#2| (-376)) (((|#2|) . 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T)) -((((-560)) -4133 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081))) ((|#2|) -4133 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1081))) (($) |has| |#2| (-1081))) +((((-560)) -4144 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081))) ((|#2|) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1081))) (($) |has| |#2| (-1081))) (((|#1|) . T)) ((((-560) |#3|) . T)) ((((-560) (-146)) . T)) @@ -1675,7 +1675,7 @@ ((((-560)) . T) (($) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1|) . T)) -((($ (-1209)) -4133 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +((($ (-1209)) -4144 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) ((((-888)) . T)) ((((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T)) @@ -1685,26 +1685,26 @@ (((|#1|) . 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T)) -(-4133 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) +(-4144 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) (((|#4|) . T)) -(-4133 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) +(-4144 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) ((((-1191) |#1|) . T)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -1718,24 +1718,24 @@ (((|#3|) . T)) ((((-1289 |#1| |#2| |#3|)) |has| |#1| (-376))) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) -((((-421 (-560))) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1207 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-421 (-560))) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) +((((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1207 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . 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T)) (|has| |#2| (-149)) (|has| |#1| (-487)) -(-4133 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) +(-4144 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) (|has| |#1| (-376)) ((((-888)) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -1768,8 +1768,8 @@ (|has| |#1| (-871)) ((((-888)) . T)) (((|#2|) . T)) -((((-421 (-560))) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -4133 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) -(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -4133 (|has| |#1| (-376)) (|has| |#1| (-571)))) +((((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -4144 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) +(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -4144 (|has| |#1| (-376)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . T) (((-560)) . T) (((-843 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1778,8 +1778,8 @@ ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((((-888)) . T)) ((((-888)) . T)) -(-4133 (|has| |#1| (-102)) (|has| |#1| (-1133))) -(((|#2| (-496 (-2172 |#1|) (-793)) (-889 |#1|)) . T)) +(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(((|#2| (-496 (-2236 |#1|) (-793)) (-889 |#1|)) . T)) ((((-421 (-560))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1| (-545 (-1209)) (-1209)) . T)) (((|#1|) . T)) @@ -1800,19 +1800,19 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -1580 (-1191)) (|:| -3432 |#1|))) . T)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -1580 (-1209)) (|:| -3432 (-51)))) . T)) +((((-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))) . T)) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) ((((-1209) (-51)) . 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T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) (|has| |#1| (-872)) (|has| |#1| (-872)) @@ -1833,15 +1833,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) (((|#1|) |has| |#1| (-175))) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) -(((|#3|) -4133 (|has| |#3| (-175)) (|has| |#3| (-376)))) -((($) -4133 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -(-4133 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-940))) -((($) -4133 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . 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T)) @@ -1850,7 +1850,7 @@ (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1|) . T)) -(-4133 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4144 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-871)) (|has| |#1| (-871)) (|has| |#1| (-871)) @@ -1859,14 +1859,14 @@ ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) ((((-1209)) |has| |#1| (-928 (-1209))) (((-1114)) . T)) (((|#1|) . T)) (|has| |#1| (-871)) -(((#0=(-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) #0#) |has| (-2 (|:| -1580 (-1191)) (|:| -3432 (-51))) (-321 (-2 (|:| -1580 (-1191)) (|:| -3432 (-51)))))) +(((#0=(-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) #0#) |has| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (-321 (-2 (|:| -2118 (-1191)) (|:| -3964 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (|has| |#1| (-1133)) ((((-888)) . T) (((-1214)) . T)) @@ -1889,14 +1889,14 @@ (((|#1| (-545 |#2|) |#2|) . T)) (((|#3|) . T)) (((|#1| (-793) (-1114)) . T)) -((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) -4133 (|has| |#1| (-871)) (|has| |#1| (-1070 (-560)))) ((|#1|) . T)) +((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) -4144 (|has| |#1| (-871)) (|has| |#1| (-1070 (-560)))) ((|#1|) . T)) (((|#1|) . T)) (((|#2|) . T)) ((((-146)) . 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T)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -1915,31 +1915,31 @@ ((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) ((($) |has| |#1| (-571))) (((|#2|) . T)) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -4133 (|has| |#1| (-175)) (|has| |#1| (-571)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -4144 (|has| |#1| (-175)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) . T)) ((($) |has| |#1| (-871))) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) (|has| |#1| (-940)) ((((-1209)) . T)) ((((-888)) . T)) -((($) -4133 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) (((-421 (-560))) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) . 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T)) +((((-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) ((((-694 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1973,7 +1973,7 @@ ((((-888)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((((-888)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4133 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) ((((-1214)) . T)) ((((-421 (-560))) . T) (($) . T) (((-421 |#1|)) . T) ((|#1|) . T) (((-560)) . T)) (((|#3|) . T) (((-560)) . T) (((-630 $)) . T)) @@ -1981,12 +1981,12 @@ ((((-888)) . T)) ((((-888)) . T)) (((|#2|) . 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T)) ((($) |has| |#1| (-240))) @@ -2241,12 +2241,12 @@ (|has| |#1| (-147)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#1|) |has| |#1| (-175))) -((($) -4133 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -4144 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-560)) . T) ((|#1|) . T) (($) . T) (((-421 (-560))) . T) (((-1209)) |has| |#1| (-1070 (-1209)))) (((|#1| |#2|) . T)) -((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) -4133 (|has| |#1| (-871)) (|has| |#1| (-1070 (-560)))) ((|#1|) . T)) -(-4133 (-12 (|has| |#4| (-240)) (|has| |#4| (-1081))) (-12 (|has| |#4| (-239)) (|has| |#4| (-1081)))) -(-4133 (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1081)))) +((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) -4144 (|has| |#1| (-871)) (|has| |#1| (-1070 (-560)))) ((|#1|) . T)) +(-4144 (-12 (|has| |#4| (-240)) (|has| |#4| (-1081))) (-12 (|has| |#4| (-239)) (|has| |#4| (-1081)))) +(-4144 (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1081)))) ((((-146)) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -2257,13 +2257,13 @@ ((((-888)) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . 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T) (($ (-1209)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-928 (-1209))))) (|has| |#1| (-940)) @@ -2271,7 +2271,7 @@ (((|#2|) |has| |#2| (-1081))) (|has| |#1| (-376)) ((($) . T)) -(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) (((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) |has| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (-321 (-2 (|:| -1580 |#1|) (|:| -3432 |#2|))))) +(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) (((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) |has| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (-321 (-2 (|:| -2118 |#1|) (|:| -3964 |#2|))))) (((|#1|) |has| |#1| (-175))) ((($ (-889 |#1|)) . T)) (((|#1| |#1|) . T)) @@ -2282,7 +2282,7 @@ (((|#1|) . T)) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-663 $)) . T) (((-1191)) . T) (((-1209)) . T) (((-560)) . T) (((-229)) . T) (((-888)) . T)) -((((-560)) -4133 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) ((|#3|) -4133 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1081))) (($) |has| |#3| (-1081))) +((((-560)) -4144 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) ((|#3|) -4144 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1081))) (($) |has| |#3| (-1081))) ((((-421 (-560))) . T) (((-560)) . T) (((-630 $)) . T)) (((|#1|) . T)) ((((-888)) . T)) @@ -2298,7 +2298,7 @@ (((|#1| (-793) (-1114)) . T)) ((((-888)) . T)) (((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-560)) -4133 (|has| (-421 (-560)) (-1070 (-560))) (|has| |#1| (-1070 (-560)))) (((-421 (-560))) . T)) +(((|#1|) . T) (((-560)) -4144 (|has| (-421 (-560)) (-1070 (-560))) (|has| |#1| (-1070 (-560)))) (((-421 (-560))) . T)) (((|#1| (-616 |#1| |#3|) (-616 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) @@ -2318,37 +2318,37 @@ ((((-721)) . T)) ((((-721)) . T)) (((|#2|) |has| |#2| (-175))) -(-4133 (|has| |#1| (-240)) (|has| |#1| (-239))) +(-4144 (|has| |#1| (-240)) (|has| |#1| (-239))) ((((-560)) . T) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) -((((-114)) |has| |#1| (-1133)) (((-888)) -4133 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144)) (|has| |#1| (-1133)))) +((((-114)) |has| |#1| (-1133)) (((-888)) -4144 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144)) (|has| |#1| (-1133)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . 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T)) (((|#3|) |has| |#3| (-1081))) @@ -2360,7 +2360,7 @@ ((((-1209)) |has| |#2| (-928 (-1209)))) (|has| |#1| (-872)) ((((-888)) . T)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) (|has| |#1| (-814)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-487)) @@ -2368,8 +2368,8 @@ (|has| |#1| (-381)) (|has| |#1| (-381)) (|has| |#1| (-376)) -(-4133 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1081)) (|has| |#1| (-1144))) -((($) -4133 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) +(-4144 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1081)) (|has| |#1| (-1144))) +((($) -4144 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) ((((-118 |#1|)) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-363)) @@ -2381,7 +2381,7 @@ (|has| |#1| (-38 (-421 (-560)))) (((|#2|) . T) (((-888)) . T)) (((|#2|) . T) (((-888)) . T)) -((($ (-1209)) -4133 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +((($ (-1209)) -4144 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -2391,18 +2391,18 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-872)) -((((-2 (|:| -1580 (-1191)) (|:| -3432 |#1|))) . T)) +((((-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) |has| (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)) (-321 (-2 (|:| -1580 |#1|) (|:| -3432 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) |has| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (-321 (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) (((|#2|) . 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T)) @@ -2640,13 +2640,13 @@ ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (|has| |#2| (-147)) (|has| |#2| (-149)) -(-4133 (|has| |#2| (-844)) (|has| |#2| (-872))) +(-4144 (|has| |#2| (-844)) (|has| |#2| (-872))) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) -(-4133 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) ((((-560)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-560)) . T)) (((|#2|) . T)) -((((-1209)) -4133 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((((-1209)) -4144 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-376))) ((((-421 |#2|)) . T)) @@ -2655,10 +2655,10 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) ((((-1209) |#1|) |has| |#1| (-528 (-1209) |#1|)) ((|#1| |#1|) |has| |#1| (-321 |#1|))) -(((|#1|) -4133 (|has| |#1| (-175)) (|has| |#1| (-376)))) +(((|#1|) -4144 (|has| |#1| (-175)) (|has| |#1| (-376)))) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) @@ -2668,14 +2668,14 @@ (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (((|#2|) |has| |#2| (-376))) -((($) -4133 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -4133 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) -4144 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -4144 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) (((|#2|) . T)) ((((-421 (-560))) . T) (((-721)) . T) (($) . T)) -((($) . T) (((-421 (-560))) -4133 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . 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T)) (((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) -((($ (-1209)) -4133 (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))))) +((($ (-1209)) -4144 (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))))) ((((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (|has| |#1| (-38 (-421 (-560)))) @@ -2693,13 +2693,13 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) ((($ $) . 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T)) -(-4133 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-376)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1280 |#2| |#3| |#4|)) . T) (((-421 (-560))) |has| #0# (-38 (-421 (-560))))) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) -(-4133 (-12 (|has| |#1| (-319)) (|has| |#1| (-940))) (|has| |#1| (-376)) (|has| |#1| (-363))) -(-4133 (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) +(-4144 (-12 (|has| |#1| (-319)) (|has| |#1| (-940))) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4144 (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) ((((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-888)) . T)) @@ -2830,7 +2830,7 @@ ((($) . T)) (((|#4|) . T)) ((($) . 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T) (((-560)) . T)) -((((-2 (|:| -1580 (-1191)) (|:| -3432 (-51)))) . T)) +((((-2 (|:| -2118 (-1191)) (|:| -3964 (-51)))) . T)) (((|#1|) . T)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) ((((-888)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) -(-4133 (|has| |#1| (-302)) (|has| |#1| (-376))) +(-4144 (|has| |#1| (-302)) (|has| |#1| (-376))) ((((-146)) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) (|has| |#1| (-871)) @@ -2878,7 +2878,7 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-186)) . T) (((-888)) . T)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-888)) . T)) ((((-888)) . T)) @@ -2895,8 +2895,8 @@ (|has| |#1| (-872)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -1580 (-1191)) (|:| -3432 |#1|))) . T)) -((($) -4133 (-12 (|has| (-1207 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1207 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|))))) +((((-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) . T)) +((($) -4144 (-12 (|has| (-1207 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1207 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|))))) ((((-888)) . T)) (((|#2|) |has| |#2| (-376))) ((((-888)) . T)) @@ -2911,19 +2911,19 @@ (|has| |#3| (-1081)) (|has| |#1| (-1133)) ((((-1209) (-51)) . T)) -(-4133 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . 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T) (($ $) . T)) ((((-560)) . T)) (((|#1|) . T)) @@ -2935,12 +2935,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (|has| |#1| (-844)) (((#0=(-936 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) ((((-421 |#2|)) . T)) (|has| |#1| (-871)) -((((-1236 |#1|)) . T) (((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-1236 |#1|)) . T) (((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) (((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) . T) ((#1=(-560) #1#) . T) (($ $) . T)) ((((-936 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (((|#2|) |has| |#2| (-1081)) (((-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081)))) @@ -2959,36 +2959,36 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . T)) -(-4133 (|has| |#1| (-147)) (|has| |#1| (-381))) -(-4133 (|has| |#1| (-147)) (|has| |#1| (-381))) -(-4133 (|has| |#1| (-147)) (|has| |#1| (-381))) -((((-2 (|:| -1580 (-1209)) (|:| -3432 (-51)))) . T)) +(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) +((((-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))) . T)) ((((-560) |#3|) . T)) (((|#1|) . T)) -(((#0=(-51)) . T) (((-2 (|:| -1580 (-1209)) (|:| -3432 #0#))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2118 (-1209)) (|:| -3964 #0#))) . T)) (|has| |#1| (-363)) ((((-560)) . T)) ((((-888)) . T)) (((|#1|) . T)) (((#0=(-1286 |#1| |#2| |#3| |#4|) $) |has| #0# (-298 #0# #0#))) (|has| |#1| (-376)) -(-4133 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081)))) -(((|#1|) -4133 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1081))) (($) -4133 (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) (((-560)) -4133 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)))) +(-4144 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081)))) +(((|#1|) -4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1081))) (($) -4144 (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) (((-560)) -4144 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)))) (((#0=(-1114) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-363))) (((#0=(-421 (-560)) #0#) . T) ((#1=(-721) #1#) . T) (($ $) . T)) ((((-326 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-376))) ((((-888)) . T)) (|has| |#1| (-1133)) (((|#1|) . T)) -(((|#1|) -4133 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) -(((|#1|) -4133 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) +(((|#1|) -4144 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) +(((|#1|) -4144 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) (((|#2|) . T)) ((((-421 (-560))) . T) (((-721)) . T) (($) . T)) ((((-593)) . T)) (((|#3| |#3|) . T)) -((($ (-1209)) -4133 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((($ (-1209)) -4144 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (|has| |#1| (-872)) (|has| |#2| (-240)) ((((-889 |#1|)) . T)) @@ -3009,10 +3009,10 @@ (|has| |#1| (-1133)) (((|#2|) . T)) (((|#1|) . T)) -((($) -4133 (|has| |#1| (-240)) (|has| |#1| (-239)))) +((($) -4144 (|has| |#1| (-240)) (|has| |#1| (-239)))) ((((-560)) . T)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((|#1|) . T) (($) . T) (((-560)) . T)) -(-4133 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3055,7 +3055,7 @@ (|has| |#2| (-1052)) ((($) . T)) (|has| |#1| (-940)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3065,32 +3065,32 @@ (|has| |#1| (-376)) ((((-936 |#1|)) . T)) ((($) . T) (((-560)) . T) ((|#1|) . T) (((-421 (-560))) . 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T)) -(-4133 (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1081)))) +(-4144 (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1081)))) ((($) . T) (((-421 (-560))) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T) (((-630 $)) . T)) ((((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T)) ((((-793) |#1|) . T)) -(((|#2| (-246 (-2172 |#1|) (-793))) . T)) +(((|#2| (-246 (-2236 |#1|) (-793))) . T)) (((|#1| (-545 |#3|)) . T)) ((((-421 (-560))) . T)) -(-4133 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((((-1191)) . T) (((-888)) . T)) -(((#0=(-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) #0#) |has| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (-321 (-2 (|:| -1580 (-1209)) (|:| -3432 (-51)))))) +(((#0=(-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) #0#) |has| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (-321 (-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))))) ((((-1191)) . T)) (|has| |#1| (-940)) (|has| |#2| (-376)) (((|#1|) . T) (($) . T) (((-560)) . T)) -(-4133 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-4144 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-888)) . T)) (((|#1|) . T)) @@ -3107,12 +3107,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-4133 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4144 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (-12 (|has| |#1| (-559)) (|has| |#1| (-845))) ((((-888)) . T)) (|has| |#1| (-376)) -((((-1209)) -4133 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))))) +((((-1209)) -4144 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))))) (|has| |#1| (-376)) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) ((((-421 (-560))) . T) (($) . T)) @@ -3124,13 +3124,13 @@ ((((-560) |#1|) . T)) ((((-1209)) |has| |#1| (-928 (-1209)))) (((|#1|) . T)) -(-4133 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-4144 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#2|) |has| |#1| (-376))) (((|#2|) |has| |#1| (-376))) -(-4133 (|has| |#4| (-817)) (|has| |#4| (-872))) -(-4133 (|has| |#3| (-817)) (|has| |#3| (-872))) +(-4144 (|has| |#4| (-817)) (|has| |#4| (-872))) +(-4144 (|has| |#3| (-817)) (|has| |#3| (-872))) ((((-560)) . T) (($) . T)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-175))) @@ -3165,7 +3165,7 @@ (|has| |#1| (-872)) ((((-888)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (((|#1|) . T)) ((($) . T) (((-560)) . T) ((|#2|) . T)) @@ -3174,27 +3174,27 @@ (((|#3|) . T)) ((((-1191)) . T) (((-520)) . T) (((-229)) . T) (((-560)) . T)) (((|#1|) . T)) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) -(-4133 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-4144 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) (((|#2|) . T)) (((|#2|) . T)) (|has| |#2| (-1081)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) -((((-2 (|:| -1580 (-1191)) (|:| -3432 |#1|))) . T)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) (|has| |#1| (-38 (-421 (-560)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-421 (-560)))) -(-4133 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) ((($) . T)) (|has| |#1| (-149)) -(-4133 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-4133 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) ((($) . T)) ((((-595 |#1|)) . T)) @@ -3210,7 +3210,7 @@ ((((-421 (-560))) |has| |#2| . #0=((-1070 (-560)))) (((-560)) |has| |#2| . #0#) (((-1209)) |has| |#2| (-1070 (-1209))) ((|#2|) . T)) (((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-4133 (|has| |#1| (-147)) (|has| |#1| (-363))) +(-4144 (|has| |#1| (-147)) (|has| |#1| (-363))) (|has| |#1| (-149)) ((((-888)) . T)) ((($) . T)) @@ -3230,15 +3230,15 @@ ((((-421 |#2|)) . T)) ((((-888)) . T)) (((|#1|) . T)) -((((-1209)) -4133 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) -(-4133 (|has| |#1| (-102)) (|has| |#1| (-1133))) +((((-1209)) -4144 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) (|has| |#1| (-814)) (|has| |#1| (-814)) ((((-888)) . T)) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3248,7 +3248,7 @@ (((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571)) (((-421 (-560))) |has| |#1| (-571))) ((((-888)) . T)) ((((-888)) . T)) -(-4133 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081)))) +(-4144 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081)))) (((#0=(-936 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -3260,10 +3260,10 @@ ((((-888)) . T)) (((|#2|) . T)) ((((-560)) . T)) -((((-1209)) -4133 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) +((((-1209)) -4144 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) ((((-888)) . T)) ((((-560)) . T)) -(-4133 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-4144 (|has| |#2| (-817)) (|has| |#2| (-872))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-888)) . T)) ((((-888)) . T)) @@ -3275,11 +3275,11 @@ (((|#1|) . T) (($) . T) (((-421 (-560))) . 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T)) @@ -3289,22 +3289,22 @@ (((#0=(-118 |#1|) $) |has| #0# (-298 #0# #0#))) (((|#1|) |has| |#1| (-175))) ((((-326 |#1|)) . T) (((-560)) . T)) -(-4133 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-4144 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1| |#1|) . T)) ((((-888)) . T)) (((|#1|) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-888)) . T)) -((((-1209)) -4133 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((((-1209)) -4144 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (((|#1|) |has| |#1| (-321 |#1|))) ((((-560) |#1|) . T) (((-1266 (-560)) $) . T)) (((|#1| |#2|) . T)) ((((-1209) |#1|) . T)) -(((|#1|) -4133 (|has| |#1| (-175)) (|has| |#1| (-376)))) +(((|#1|) -4144 (|has| |#1| (-175)) (|has| |#1| (-376)))) (((|#1|) . T)) ((($ (-1209)) . T)) -(((|#1|) -4133 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1081)))) +(((|#1|) -4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1081)))) ((((-560)) . T) (((-421 (-560))) . T)) (((|#1|) . T)) (|has| |#1| (-571)) @@ -3313,15 +3313,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T)) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) ((($) . T)) (|has| |#1| (-1133)) ((((-802 |#1| (-889 |#2|))) |has| (-802 |#1| (-889 |#2|)) (-321 (-802 |#1| (-889 |#2|))))) -(-4133 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3330,17 +3330,17 @@ (((|#1| (-793)) . T)) (|has| |#1| (-240)) (((|#1| (-545 (-1120 (-1209)))) . T)) -((($) -4133 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))))) +((($) -4144 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))))) ((((-595 |#1|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) -((((-2 (|:| -1580 (-1191)) (|:| -3432 (-51)))) . T)) +((((-2 (|:| -2118 (-1191)) (|:| -3964 (-51)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-560)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (|has| |#2| (-376)) ((((-888)) . T)) ((((-888)) . T)) -(-4133 (|has| |#3| (-817)) (|has| |#3| (-872))) +(-4144 (|has| |#3| (-817)) (|has| |#3| (-872))) ((((-888)) . T)) ((((-1152)) . T) (((-888)) . T)) ((((-549)) . T) (((-888)) . T)) @@ -3351,14 +3351,14 @@ ((((-560)) . T)) (((|#3|) . T)) ((((-888)) . T)) -(-4133 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) -((((-560)) . 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T) (((-421 (-560))) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . T)) +((((-1157 |#1| (-1209))) . T) (((-560)) . T) (((-1120 (-1209))) . T) (($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1| (-1299 |#1|) (-1299 |#1|)) . T)) ((((-595 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) @@ -3373,7 +3373,7 @@ ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (((|#1|) . T)) ((((-888)) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -4133 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -4144 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) ((((-305 |#3|)) . T)) (((|#1|) . T)) @@ -3382,30 +3382,30 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) -((($ $) -4133 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) -((($ $) -4133 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -4144 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . 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T)) -(-4133 (|has| |#2| (-817)) (|has| |#2| (-872))) -(-4133 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-4144 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) (((|#1|) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) ((((-1209)) . T) ((|#1|) . T)) @@ -3417,15 +3417,15 @@ (((#0=(-421 (-560)) #0#) . T)) ((((-421 (-560))) . T)) (((|#1|) |has| |#1| (-175))) -(-4133 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081))) +(-4144 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081))) (((|#1|) . T)) (((|#1|) . T)) -(-4133 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-4144 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) (((|#1|) . T)) ((((-421 (-560))) . T) (((-560)) . 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T) (((-560)) |has| |#2| (-1070 (-560))) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) ((((-1114)) . T) ((|#2|) . T) (((-560)) |has| |#2| (-1070 (-560))) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) (((|#1|) . T)) @@ -3475,11 +3475,11 @@ ((($) |has| |#1| (-381))) (|has| |#2| (-844)) (|has| |#2| (-844)) -((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) +((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) ((($ (-1209)) |has| |#1| (-928 (-1209)))) (((|#1|) . T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) -((($) -4133 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) -(((|#1|) . T) (((-421 (-560))) -4133 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) +((($) -4144 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) +(((|#1|) . T) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((((-560)) |has| |#1| (-912 (-560))) (((-391)) |has| |#1| (-912 (-391)))) (((|#1|) . T)) @@ -3494,7 +3494,7 @@ (-12 (|has| |#1| (-376)) (|has| |#2| (-940))) (|has| |#1| (-376)) (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) -(((|#2|) -4133 (|has| |#2| (-6 (-4512 "*"))) (|has| |#2| (-175)))) +(((|#2|) -4144 (|has| |#2| (-6 (-4512 "*"))) (|has| |#2| (-175)))) (((|#2|) . T)) (|has| |#1| (-376)) (((|#2|) . T)) @@ -3508,12 +3508,12 @@ (((|#2| (-793)) . T)) ((((-1209)) . T)) ((((-894 |#1|)) . 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T) (((-421 (-560))) . T) (((-560)) |has| |#2| (-660 (-560)))) -(-4133 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) @@ -3540,7 +3540,7 @@ (((|#1|) . T)) ((((-888)) . T)) (|has| |#2| (-940)) -((((-2 (|:| -1580 (-1209)) (|:| -3432 (-51)))) . T)) +((((-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-916 (-391))) |has| |#2| (-633 (-916 (-391)))) (((-916 (-560))) |has| |#2| (-633 (-916 (-560))))) ((((-888)) . T)) ((((-888)) . T)) @@ -3551,7 +3551,7 @@ ((((-1203 |#1|)) . T) (((-888)) . T)) ((((-888)) . T)) ((((-421 (-560))) |has| |#2| (-1070 (-421 (-560)))) (((-560)) |has| |#2| (-1070 (-560))) ((|#2|) . T) (((-889 |#1|)) . T)) -((((-1209)) -4133 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (((-1114)) . T)) +((((-1209)) -4144 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (((-1114)) . T)) ((((-118 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) |has| |#1| (-1070 (-560))) ((|#1|) . T) (((-1209)) . T)) ((((-888)) . T)) @@ -3571,10 +3571,10 @@ ((((-663 |#1|)) . T)) ((($) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|)))) ((($) . T) (((-560)) . T) (((-1286 |#1| |#2| |#3| |#4|)) . T) (((-421 (-560))) . 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T)) @@ -3589,16 +3589,16 @@ ((((-421 |#2|) |#3|) . T)) (((|#1|) . T)) ((((-888)) . T)) -(-4133 (|has| |#1| (-102)) (|has| |#1| (-1133))) -(((|#2| (-496 (-2172 |#1|) (-793))) . T)) +(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(((|#2| (-496 (-2236 |#1|) (-793))) . T)) ((((-560) |#1|) . T)) ((((-1191)) . T) (((-888)) . T)) (((|#2| |#2|) . T)) (((|#1| (-545 (-1209))) . T)) -(-4133 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-4144 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) ((((-560)) . T)) (((|#2|) . T)) -((($) -4133 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))))) +((($) -4144 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))))) (((|#2|) . T)) ((((-1209)) |has| |#1| (-928 (-1209))) (((-1114)) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) @@ -3607,9 +3607,9 @@ ((($) . T) (((-421 (-560))) . T)) ((($) . T)) ((($) . T)) -(-4133 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-4144 (|has| |#1| (-872)) (|has| |#1| (-1133))) (((|#1|) . T)) -((($) -4133 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -4144 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-888)) . T)) ((((-146)) . T)) (((|#1|) . T) (((-421 (-560))) . T)) @@ -3618,7 +3618,7 @@ ((((-888)) . T)) (((|#1|) . T)) (|has| |#1| (-1184)) -((($ (-1209)) -4133 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) +((($ (-1209)) -4144 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) (((|#1|) . T)) (((|#1| (-545 (-889 |#2|)) (-889 |#2|) (-802 |#1| (-889 |#2|))) . 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T)) ((((-888)) . T) (((-1214)) . T)) -((((-663 |#1|)) . T) (((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-663 |#1|)) . T) (((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-1214)) . T)) ((((-1214)) . T)) ((((-1214)) . T)) @@ -3750,19 +3750,19 @@ ((((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) -((((-2 (|:| -1580 (-1209)) (|:| -3432 (-51)))) |has| (-2 (|:| -1580 (-1209)) (|:| -3432 (-51))) (-321 (-2 (|:| -1580 (-1209)) (|:| -3432 (-51)))))) -(-4133 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +((((-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))) |has| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (-321 (-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))))) +(-4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((((-560) |#1|) . T)) ((((-560) |#1|) . T)) ((((-560) |#1|) . 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T)) (((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-421 (-560))) . T) (($) . T)) @@ -3884,7 +3884,7 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-888)) . T)) -(-4133 (|has| |#1| (-240)) (|has| |#1| (-239))) +(-4144 (|has| |#1| (-240)) (|has| |#1| (-239))) (((|#1|) . T) (((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) ((((-888)) . T)) @@ -3893,21 +3893,21 @@ ((((-657 |#2|)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| (-545 (-889 |#2|)) (-889 |#2|) (-802 |#1| (-889 |#2|))) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4133 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) ((($) . T) (((-560)) . T)) -((($) -4133 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-1135)) . T)) ((((-888)) . T)) ((((-1214)) . T) (((-888)) . T)) ((((-1214)) . T) (((-888)) . T)) ((((-1214)) . T)) ((((-1214)) . T)) -((($) -4133 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -4144 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((($) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) ((($) . T) (((-560)) . T)) -((($) -4133 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| |#2| (-940)) (((|#1| |#2| (-246 |#1| |#2|) (-246 |#1| |#2|)) . T)) ((((-888)) . T)) @@ -3923,9 +3923,9 @@ (((|#1| |#1|) |has| |#1| (-175))) ((((-721)) . T)) ((((-721)) . T)) -((((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-1214)) . T)) -(-4133 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-4144 (|has| |#2| (-817)) (|has| |#2| (-872))) (((|#1|) |has| |#1| (-175))) ((((-1214)) . T)) (((|#1| |#1|) . T)) @@ -3938,19 +3938,19 @@ (((|#1| (-560)) . T)) (((|#1|) . T)) ((((-421 (-560))) . T) (((-560)) . T) (($) . T)) -((($ (-1209)) -4133 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (($ (-1114)) . T)) +((($ (-1209)) -4144 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (($ (-1114)) . T)) (((|#1|) |has| |#1| (-175))) ((((-1214)) . T)) ((((-1214)) . T)) ((((-1214)) . T)) ((((-1214)) . T)) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-363))) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-363))) ((((-1214)) . T)) ((((-1214)) . T)) (|has| |#1| (-376)) (|has| |#1| (-376)) -(-4133 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-175)) (|has| |#1| (-571))) (((|#1| (-560)) . T)) (((|#1| (-421 (-560))) . T)) (((|#1| (-793)) . T)) @@ -3958,24 +3958,24 @@ (((|#1| (-545 |#2|) |#2|) . T)) ((((-560) |#1|) . T)) ((((-560) |#1|) . T)) -(-4133 (|has| |#1| (-102)) (|has| |#1| (-1133))) -(-4133 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239))) +(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-4144 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239))) ((((-560) |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-916 (-391))) . T) (((-916 (-560))) . T) (((-1209)) . T) (((-549)) . T)) -(-4133 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) -(-4133 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-133)) (|has| |#2| (-133))) (-12 (|has| |#1| (-817)) (|has| |#2| (-817)))) +(-4144 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-4144 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-133)) (|has| |#2| (-133))) (-12 (|has| |#1| (-817)) (|has| |#2| (-817)))) ((((-888)) . T)) ((((-560)) . T)) ((((-560)) . T)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1209)) -12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081)))) (|has| |#2| (-1081)) -(-4133 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) +(-4144 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-376)) @@ -4008,7 +4008,7 @@ (((|#1| |#2|) . T)) ((((-560)) . T) ((|#2|) |has| |#2| (-175))) ((((-115)) . T) ((|#1|) . T) (((-560)) . T)) -(-4133 (|has| |#1| (-363)) (|has| |#1| (-381))) +(-4144 (|has| |#1| (-363)) (|has| |#1| (-381))) (((|#1| |#2|) . T)) ((((-229)) . T)) ((((-421 (-560))) . T) (($) . T) (((-560)) . T)) @@ -4017,11 +4017,11 @@ ((($) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) |has| |#2| (-1133)) (((-560)) -12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) -(-4133 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-4144 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1|) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-560) $) . T) (((-663 (-560)) $) . T)) ((($) . T) (((-421 (-560))) . T)) (|has| |#1| (-940)) @@ -4033,14 +4033,14 @@ (((|#1| |#1|) |has| |#1| (-175))) (((|#1|) . T) (((-560)) . T)) ((((-1214)) . T)) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-4133 (|has| |#1| (-21)) (|has| |#1| (-871))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4144 (|has| |#1| (-21)) (|has| |#1| (-871))) (((|#2|) . T)) -(-4133 (|has| |#1| (-21)) (|has| |#1| (-871))) +(-4144 (|has| |#1| (-21)) (|has| |#1| (-871))) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) (((|#1|) . T)) -((((-888)) -4133 (-12 (|has| |#1| (-632 (-888))) (|has| |#2| (-632 (-888)))) (-12 (|has| |#1| (-1133)) (|has| |#2| (-1133))))) +((((-888)) -4144 (-12 (|has| |#1| (-632 (-888))) (|has| |#2| (-632 (-888)))) (-12 (|has| |#1| (-1133)) (|has| |#2| (-1133))))) ((((-421 |#2|) |#3|) . T)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -4049,7 +4049,7 @@ ((($) . T) (((-560)) . T)) (|has| (-421 |#2|) (-149)) (|has| (-421 |#2|) (-147)) -(-4133 (|has| |#3| (-817)) (|has| |#3| (-872))) +(-4144 (|has| |#3| (-817)) (|has| |#3| (-872))) ((($) . T)) ((((-721)) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) @@ -4065,7 +4065,7 @@ ((((-1214)) . T)) ((((-560)) . T)) (((|#2|) . T)) -((((-1209)) -4133 (-12 (|has| (-1207 |#1| |#2| |#3|) (-928 (-1209))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))))) +((((-1209)) -4144 (-12 (|has| (-1207 |#1| |#2| |#3|) (-928 (-1209))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))))) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-928 (-1209))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4081,11 +4081,11 @@ ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1172 |#1| |#2|)) . T)) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) -(((|#2|) . T) (((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) -((((-2 (|:| -1580 (-1209)) (|:| -3432 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))) . T)) ((($) . T)) (|has| |#1| (-1052)) -(((|#2|) . T) (((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) ((($) . T)) ((((-888)) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-916 (-560))) |has| |#2| (-633 (-916 (-560)))) (((-916 (-391))) |has| |#2| (-633 (-916 (-391)))) (((-391)) . #0=(|has| |#2| (-1052))) (((-229)) . #0#)) @@ -4094,7 +4094,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-1209)) -4133 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((((-1209)) -4144 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) ((((-888)) . T)) (((|#2|) . T)) ((((-888)) . T)) @@ -4104,15 +4104,15 @@ ((((-1207 |#1| |#2| |#3|)) . T)) ((((-1207 |#1| |#2| |#3|)) . T) (((-1200 |#1| |#2| |#3|)) . T)) ((((-888)) . T)) -((((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-560) |#1|) . T)) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-376)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -4133 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1081))) (($) |has| |#4| (-1081)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1081)))) -(((|#2|) . T) ((|#3|) -4133 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) (($) |has| |#3| (-1081)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1081)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -4144 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1081))) (($) |has| |#4| (-1081)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1081)))) +(((|#2|) . T) ((|#3|) -4144 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) (($) |has| |#3| (-1081)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1081)))) (((|#1|) . T)) (((|#1|) . T)) ((((-118 |#1|)) . T)) @@ -4126,7 +4126,7 @@ ((((-186)) . T) (((-888)) . T)) ((((-888)) . T)) (((|#1|) . T)) -((((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-560) |#1|) . T) (((-1266 (-560)) $) . T)) ((((-888)) . T)) (((|#1|) . T)) @@ -4134,14 +4134,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) (($ $) . T) (((-560) |#1|) . T)) ((($ $) . T) (((-421 (-560)) |#1|) . T)) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-940))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-940))) ((($ (-1209)) |has| |#1| (-1081))) -(-4133 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-4144 (|has| |#1| (-872)) (|has| |#1| (-1133))) ((((-888)) . T)) ((((-888)) . T)) ((((-888)) . T)) (((|#1| (-545 |#2|)) . T)) -((((-2 (|:| -1580 (-1209)) (|:| -3432 (-51)))) . T)) +((((-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))) . T)) ((((-560) (-130)) . T)) (((|#1| (-560)) . T)) (((|#1| (-421 (-560))) . T)) @@ -4156,8 +4156,8 @@ ((((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) -(-4133 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) -(-4133 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((($) . T)) (((|#2| (-545 (-889 |#1|))) . T)) ((((-1214)) . T)) @@ -4172,7 +4172,7 @@ ((((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) -((((-888)) -4133 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1191) |#1|) . T)) @@ -4180,7 +4180,7 @@ ((((-421 |#2|)) . T)) (|has| |#1| (-571)) (|has| |#1| (-571)) -((((-2 (|:| -1580 |#1|) (|:| -3432 |#2|))) . T)) +((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) (((|#2| (-793)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-421 (-560))) . T)) @@ -4190,14 +4190,14 @@ ((((-560)) . T) (($) . T)) (((|#2| $) |has| |#2| (-298 |#2| |#2|))) (((|#1| (-663 |#1|)) |has| |#1| (-871))) -(-4133 (|has| |#1| (-240)) (|has| |#1| (-363))) -(-4133 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4144 (|has| |#1| (-240)) (|has| |#1| (-363))) +(-4144 (|has| |#1| (-376)) (|has| |#1| (-363))) ((((-1296 |#1|)) . T) (((-560)) . T) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) (|has| |#1| (-1133)) (((|#1|) . T)) ((((-421 (-560))) . T) (($) . T)) -((((-1296 |#1|)) . T) (((-560)) . T) (($) -4133 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-1114)) . T) ((|#2|) . T) (((-421 (-560))) -4133 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560)))))) -((((-1028 |#1|)) . T) ((|#1|) . T) (((-560)) -4133 (|has| (-1028 |#1|) (-1070 (-560))) (|has| |#1| (-1070 (-560)))) (((-421 (-560))) -4133 (|has| (-1028 |#1|) (-1070 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560)))))) +((((-1296 |#1|)) . T) (((-560)) . T) (($) -4144 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-1114)) . T) ((|#2|) . T) (((-421 (-560))) -4144 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560)))))) +((((-1028 |#1|)) . T) ((|#1|) . T) (((-560)) -4144 (|has| (-1028 |#1|) (-1070 (-560))) (|has| |#1| (-1070 (-560)))) (((-421 (-560))) -4144 (|has| (-1028 |#1|) (-1070 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560)))))) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) @@ -4214,11 +4214,11 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1172 |#1| |#2|) #0#) |has| (-1172 |#1| |#2|) (-321 (-1172 |#1| |#2|)))) (((|#1|) . 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. -1070) 196875) ((-1203 . -670) 196764) ((-1157 . -670) 196653) ((-879 . -670) 196627) ((-740 . -632) 196609) ((-561 . -381) T) ((-1321 . -23) T) ((-716 . -930) NIL) ((-1320 . -23) T) ((-505 . -1133) T) ((-391 . -635) 196559) ((-391 . -637) 196541) ((-1066 . -1081) T) ((-890 . -102) T) ((-1221 . -298) 196520) ((-171 . -381) 196471) ((-1036 . -1249) T) ((-1003 . -1249) T) ((-944 . -1249) T) ((-858 . -635) 196425) ((-852 . -635) 196380) ((-44 . -23) T) ((-1329 . -102) T) ((-493 . -298) 196359) ((-597 . -1133) T) ((-1178 . -1141) 196328) ((-443 . -1249) T) ((-1135 . -1136) 196280) ((-404 . -21) T) ((-404 . -25) T) ((-154 . -1144) T) ((-1242 . -739) 196177) ((-1229 . -1133) T) ((-1036 . -910) 196159) ((-1036 . -912) 196141) ((-642 . -234) 196125) ((-642 . -274) 196109) ((-638 . -21) T) ((-301 . -571) T) ((-638 . -25) T) ((-1036 . -1070) 196069) ((-733 . -739) 196034) ((-246 . -390) 196003) ((-391 . -1081) T) ((-227 . -1089) T) ((-119 . -274) 195980) ((-119 . -234) 195957) ((-58 . -298) 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. -1133) T) ((-530 . -19) 194483) ((-510 . -19) 194467) ((-58 . -618) 194444) ((-1035 . -239) 194381) ((-931 . -102) 194331) ((-879 . -748) T) ((-803 . -1133) T) ((-530 . -618) 194308) ((-510 . -618) 194285) ((-802 . -1133) T) ((-802 . -1097) 194252) ((-475 . -1133) T) ((-468 . -1133) T) ((-597 . -739) 194227) ((-671 . -1133) T) ((-1289 . -47) 194204) ((-1286 . -102) T) ((-1280 . -47) 194174) ((-1259 . -47) 194151) ((-1242 . -175) 194102) ((-1206 . -319) 194081) ((-1200 . -319) 194060) ((-1128 . -635) 194041) ((-1123 . -635) 194022) ((-1111 . -571) 193973) ((-1111 . -1254) 193924) ((-1105 . -635) 193905) ((-1036 . -928) NIL) ((-1098 . -635) 193886) ((-692 . -133) T) ((-646 . -1144) T) ((-1068 . -635) 193867) ((-1051 . -635) 193848) ((-736 . -1088) 193818) ((-734 . -922) 193721) ((-721 . -668) 193671) ((-286 . -1133) T) ((-86 . -455) T) ((-86 . -410) T) ((-733 . -175) T) ((-659 . -1088) 193655) ((-50 . -1133) T) ((-609 . -47) 193632) ((-229 . -670) 193597) ((-595 . -1133) T) ((-532 . 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. -1144) T) ((-492 . -93) T) ((-421 . -239) 191123) ((-368 . -632) 191105) ((-366 . -632) 191087) ((-358 . -632) 191069) ((-275 . -633) 190817) ((-275 . -632) 190799) ((-255 . -632) 190781) ((-255 . -633) 190642) ((-140 . -93) T) ((-139 . -93) T) ((-135 . -93) T) ((-1173 . -632) 190624) ((-1152 . -662) 190611) ((-1152 . -1083) 190598) ((-843 . -748) T) ((-843 . -882) T) ((-616 . -300) 190575) ((-595 . -739) 190540) ((-493 . -633) NIL) ((-493 . -632) 190522) ((-532 . -739) 190467) ((-326 . -102) T) ((-325 . -102) T) ((-301 . -23) T) ((-154 . -133) T) ((-936 . -632) 190449) ((-936 . -633) 190431) ((-400 . -748) T) ((-897 . -1088) 190383) ((-897 . -111) 190321) ((-736 . -1081) T) ((-734 . -1275) 190305) ((-716 . -363) NIL) ((-115 . -102) T) ((-141 . -102) T) ((-137 . -102) T) ((-533 . -632) 190237) ((-391 . -821) T) ((-170 . -1249) T) ((-227 . -1133) T) ((-391 . -816) T) ((-58 . -633) 190198) ((-229 . -818) T) ((-229 . -814) T) ((-58 . -632) 190110) ((-229 . -748) T) ((-530 . -633) 190071) ((-530 . -632) 189983) ((-511 . -632) 189915) ((-510 . -633) 189876) ((-510 . -632) 189788) ((-1111 . -376) 189739) ((-40 . -426) 189716) ((-78 . -1249) T) ((-896 . -940) NIL) ((-372 . -341) 189700) ((-372 . -376) T) ((-367 . -341) 189684) ((-367 . -376) T) ((-359 . -341) 189668) ((-359 . -376) T) ((-326 . -296) 189647) ((-108 . -376) T) ((-70 . -1249) T) ((-661 . -1133) T) ((-1259 . -351) 189599) ((-896 . -670) 189544) ((-1259 . -390) 189496) ((-994 . -133) 189351) ((-839 . -133) 189222) ((-45 . -875) NIL) ((-988 . -673) 189206) ((-1258 . -684) T) ((-1119 . -175) 189117) ((-988 . -385) 189101) ((-1094 . -818) T) ((-1094 . -814) T) ((-897 . -635) 188999) ((-803 . -175) 188890) ((-802 . -175) 188801) ((-840 . -47) 188763) ((-1094 . -748) T) ((-339 . -503) 188747) ((-976 . -748) T) ((-1313 . -321) 188685) ((-1289 . -928) 188598) ((-468 . -175) 188509) ((-252 . -298) 188461) ((-1285 . -1088) 188296) ((-1280 . -928) 188202) ((-1264 . -1088) 188010) ((-495 . -748) T) ((-1259 . -928) 187843) ((-1242 . -302) 187822) ((-1219 . -1249) T) ((-1216 . -381) T) ((-1215 . -381) T) ((-1178 . -153) 187806) ((-1152 . -102) T) ((-1147 . -1133) T) ((-1111 . -23) T) ((-1111 . -1144) T) ((-1108 . -102) T) ((-1090 . -632) 187773) ((-1035 . -424) 187745) ((-955 . -985) T) ((-758 . -321) 187683) ((-76 . -1249) T) ((-686 . -397) 187655) ((-171 . -940) 187608) ((-30 . -985) T) ((-114 . -868) T) ((-1 . -632) 187590) ((-1028 . -922) 187511) ((-131 . -673) 187493) ((-50 . -640) 187477) ((-716 . -668) 187412) ((-609 . -928) 187325) ((-452 . -102) T) ((-143 . -321) NIL) ((-131 . -385) 187307) ((-897 . -1081) T) ((-856 . -872) 187286) ((-81 . -1249) T) ((-733 . -302) T) ((-40 . -1089) T) ((-595 . -175) T) ((-532 . -175) T) ((-526 . -632) 187268) ((-171 . -670) 187142) ((-521 . -632) 187124) ((-365 . -149) 187106) ((-365 . -147) T) ((-372 . -1144) T) ((-367 . -1144) T) ((-359 . -1144) T) ((-1036 . -319) T) ((-944 . -319) T) ((-897 . -250) T) ((-108 . -1144) T) ((-897 . -240) 187085) ((-1285 . -111) 186906) ((-1264 . -111) 186695) ((-252 . -1288) 186679) ((-560 . -871) T) ((-372 . -23) T) ((-353 . -363) T) ((-326 . -321) 186666) ((-325 . -321) 186607) ((-367 . -23) T) ((-331 . -133) T) ((-359 . -23) T) ((-1036 . -1052) T) ((-31 . -635) 186588) ((-108 . -23) T) ((-678 . -1083) 186572) ((-252 . -618) 186549) ((-661 . -739) 186533) ((-345 . -1133) T) ((-678 . -662) 186503) ((-1286 . -38) 186395) ((-1268 . -940) 186374) ((-114 . -1133) T) ((-840 . -1249) T) ((-427 . -1249) T) ((-1067 . -102) T) ((-1268 . -670) 186263) ((-896 . -818) NIL) ((-880 . -670) 186237) ((-896 . -814) NIL) ((-840 . -912) NIL) ((-896 . -748) T) ((-1119 . -528) 186104) ((-803 . -528) 186051) ((-802 . -528) 186003) ((-585 . -670) 185990) ((-840 . -1070) 185818) ((-468 . -528) 185761) ((-402 . -403) T) ((-1285 . -635) 185574) ((-1264 . -635) 185322) ((-60 . -1249) T) ((-638 . -872) 185301) ((-514 . -684) T) ((-1178 . -1008) 185270) ((-1056 . -668) 185207) ((-1035 . -466) T) ((-721 . -871) T) ((-525 . -816) T) ((-488 . -1088) 185042) ((-514 . -113) T) ((-357 . -1133) T) ((-325 . -1184) NIL) ((-301 . -133) T) ((-407 . -1133) T) ((-894 . -1089) T) ((-716 . -383) 185009) ((-353 . -668) 184939) ((-227 . -640) 184916) ((-339 . -298) 184868) ((-488 . -111) 184689) ((-1285 . -1081) T) ((-1264 . -1081) T) ((-840 . -390) 184673) ((-850 . -1249) T) ((-171 . -748) T) ((-1315 . -1249) T) ((-678 . -102) T) ((-1285 . -250) 184652) ((-1285 . -240) 184604) ((-1264 . -240) 184509) ((-1264 . -250) 184488) ((-1035 . -416) NIL) ((-692 . -660) 184436) ((-326 . -38) 184346) ((-325 . -38) 184275) ((-69 . -632) 184257) ((-331 . -507) 184223) ((-48 . -668) 184173) ((-1221 . -300) 184152) ((-1258 . -872) T) ((-1145 . -1144) 184130) ((-84 . -1249) T) ((-62 . -632) 184112) ((-889 . -875) T) ((-493 . -300) 184091) ((-1315 . -1070) 184068) ((-1197 . -1133) T) ((-1145 . -23) 183920) ((-840 . -928) 183856) ((-1268 . -748) T) ((-1129 . -1249) T) ((-488 . -635) 183682) ((-365 . -239) T) ((-1119 . -302) 183613) ((-996 . -1133) T) ((-919 . -102) T) ((-803 . -302) 183524) ((-339 . -19) 183508) ((-58 . -300) 183485) ((-802 . -302) 183416) ((-880 . -748) T) ((-119 . -871) NIL) ((-530 . -300) 183393) ((-339 . -618) 183370) ((-510 . -300) 183347) ((-468 . -302) 183278) ((-1067 . -321) 183129) ((-901 . -504) 183110) ((-901 . -632) 183076) ((-703 . -504) 183057) ((-585 . -748) T) ((-698 . -504) 183038) ((-703 . -632) 182988) ((-698 . -632) 182954) ((-674 . -632) 182936) ((-492 . -504) 182917) ((-492 . -632) 182883) ((-252 . -633) 182844) ((-252 . -504) 182821) ((-140 . -504) 182802) ((-139 . -504) 182783) ((-135 . -504) 182764) ((-252 . -632) 182656) ((-216 . -102) T) ((-140 . -632) 182622) ((-139 . -632) 182588) ((-135 . -632) 182554) ((-1180 . -34) T) ((-973 . -1249) T) ((-357 . -739) 182499) ((-692 . -25) T) ((-692 . -21) T) ((-1209 . -635) 182480) ((-343 . -1249) T) ((-488 . -1081) T) ((-652 . -432) 182445) ((-620 . -432) 182410) ((-1152 . -1184) T) ((-1280 . -319) 182389) ((-734 . -1083) 182212) ((-595 . -302) T) ((-532 . -302) T) ((-1259 . -319) 182191) ((-488 . -240) 182143) ((-488 . -250) 182122) ((-453 . -1249) T) ((-734 . -662) 181951) ((-1259 . -1052) NIL) ((-1111 . -133) T) ((-897 . -821) 181930) ((-146 . -102) T) ((-40 . -1133) T) ((-897 . -816) 181909) ((-663 . -1042) 181893) ((-594 . -1089) T) ((-560 . -1089) T) ((-509 . -1089) T) ((-421 . -466) T) ((-372 . -133) T) ((-326 . -414) 181877) ((-325 . -414) 181838) ((-367 . -133) T) ((-359 . -133) T) ((-1214 . -1133) T) ((-1152 . -38) 181825) ((-1121 . -632) 181792) ((-108 . -133) T) ((-984 . -1133) T) ((-949 . -1133) T) ((-793 . -1133) T) ((-694 . -1133) T) ((-723 . -149) T) ((-623 . -102) T) ((-118 . -149) T) ((-1321 . -21) T) ((-1321 . -25) T) ((-1320 . -21) T) ((-1320 . -25) T) ((-686 . -1088) 181776) ((-545 . -872) T) ((-514 . -872) T) ((-377 . -1249) T) ((-368 . -1088) 181728) ((-366 . -1088) 181680) ((-358 . -1088) 181632) ((-260 . -1249) T) ((-259 . -1249) T) ((-275 . -1088) 181475) ((-255 . -1088) 181318) ((-686 . -111) 181297) ((-841 . -1254) 181276) ((-562 . -868) T) ((-326 . -930) 181242) ((-368 . -111) 181180) ((-366 . -111) 181118) ((-358 . -111) 181056) ((-275 . -111) 180885) ((-255 . -111) 180714) ((-325 . -930) NIL) ((-642 . -426) 180698) ((-44 . -21) T) ((-44 . -25) T) ((-932 . -875) 180649) ((-130 . -684) T) ((-839 . -660) 180555) ((-841 . -571) 180534) ((-501 . -875) T) ((-260 . -1070) 180361) ((-259 . -1070) 180188) ((-128 . -121) 180172) ((-221 . -875) T) ((-936 . -1088) 180137) ((-734 . -102) T) ((-721 . -1089) T) ((-611 . -635) 180118) ((-600 . -635) 180099) ((-549 . -637) 180002) ((-357 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-87 . -632) 179984) ((-936 . -111) 179940) ((-40 . -739) 179885) ((-894 . -1133) T) ((-686 . -635) 179862) ((-667 . -635) 179843) ((-368 . -635) 179780) ((-366 . -635) 179717) ((-358 . -635) 179654) ((-562 . -1133) T) ((-339 . -633) 179615) ((-339 . -632) 179527) ((-275 . -635) 179280) ((-255 . -635) 179065) ((-190 . -1249) T) ((-1264 . -816) 179018) ((-1264 . -821) 178971) ((-260 . -390) 178940) ((-259 . -390) 178909) ((-564 . -875) T) ((-678 . -38) 178879) ((-627 . -34) T) ((-496 . -1144) 178857) ((-489 . -34) T) ((-1145 . -133) 178728) ((-994 . -25) 178539) ((-936 . -635) 178489) ((-899 . -632) 178471) ((-218 . -868) T) ((-994 . -21) 178426) ((-839 . -25) 178259) ((-839 . -21) 178170) ((-1256 . -381) T) ((-642 . -1089) T) ((-1211 . -571) 178149) ((-1203 . -47) 178126) ((-368 . -1081) T) ((-366 . -1081) T) ((-496 . -23) 177978) ((-358 . -1081) T) ((-275 . -1081) T) ((-255 . -1081) T) ((-1157 . -47) 177950) ((-119 . -1089) T) ((-1066 . -670) 177924) ((-988 . -34) T) ((-368 . -240) 177903) ((-368 . -250) T) ((-366 . -240) 177882) ((-366 . -250) T) ((-358 . -240) 177861) ((-358 . -250) T) ((-275 . -338) 177833) ((-255 . -338) 177790) ((-275 . -240) 177769) ((-1187 . -153) 177753) ((-260 . -928) 177685) ((-259 . -928) 177617) ((-1174 . -922) 177538) ((-1114 . -872) T) ((-1266 . -1249) 177516) ((-429 . -1144) T) ((-1242 . -1034) 177482) ((-1086 . -23) T) ((-1056 . -871) T) ((-936 . -1081) T) ((-334 . -670) 177464) ((-723 . -239) T) ((-692 . -236) 177409) ((-1206 . -951) 177388) ((-1200 . -951) 177367) ((-1200 . -844) NIL) ((-1028 . -1083) 177263) ((-997 . -1249) T) ((-936 . -250) T) ((-841 . -376) 177242) ((-218 . -1133) T) ((-394 . -23) T) ((-129 . -1133) 177220) ((-123 . -1133) 177198) ((-936 . -240) T) ((-131 . -34) T) ((-391 . -670) 177163) ((-1028 . -662) 177111) ((-894 . -739) 177098) ((-1329 . -668) 177070) ((-1078 . -153) 177035) ((-1025 . -1249) T) ((-888 . -1249) T) ((-40 . -175) T) ((-716 . -426) 177017) ((-734 . -321) 177004) ((-858 . -670) 176964) ((-852 . -670) 176938) ((-331 . -25) T) ((-331 . -21) T) ((-676 . -298) 176917) ((-594 . -1133) T) ((-560 . -1133) T) ((-509 . -1133) T) ((-1203 . -1249) T) ((-252 . -300) 176894) ((-1157 . -1249) T) ((-879 . -1249) T) ((-325 . -274) 176855) ((-325 . -234) 176816) ((-1255 . -875) T) ((-1203 . -912) NIL) ((-55 . -1133) T) ((-1157 . -912) 176675) ((-130 . -872) T) ((-1203 . -1070) 176555) ((-1157 . -1070) 176438) ((-187 . -632) 176420) ((-879 . -1070) 176316) ((-803 . -298) 176243) ((-841 . -1144) T) ((-1066 . -748) T) ((-1078 . -1008) 176172) ((-616 . -673) 176156) ((-1035 . -922) 176063) ((-1028 . -102) T) ((-841 . -23) T) ((-734 . -1184) 176041) ((-716 . -1089) T) ((-616 . -385) 176025) ((-365 . -466) T) ((-357 . -302) T) ((-1302 . -1133) T) ((-256 . -1133) T) ((-413 . -102) T) ((-301 . -21) T) ((-301 . -25) T) ((-374 . -748) T) ((-732 . -1133) T) ((-721 . -1133) T) ((-374 . -487) T) ((-1242 . -632) 176007) ((-1203 . -390) 175991) ((-1157 . -390) 175975) ((-1056 . -426) 175937) ((-143 . -233) 175919) ((-391 . -818) T) ((-391 . -814) T) ((-894 . -175) T) ((-391 . -748) T) ((-733 . -632) 175901) ((-734 . -38) 175730) ((-1299 . -1298) 175714) ((-365 . -416) T) ((-1299 . -1133) 175664) ((-1223 . -1133) T) ((-594 . -739) 175651) ((-560 . -739) 175638) ((-509 . -739) 175603) ((-1286 . -668) 175493) ((-326 . -649) 175472) ((-858 . -748) T) 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T) ((-901 . -635) 174654) ((-736 . -670) 174614) ((-501 . -1254) T) ((-703 . -635) 174595) ((-698 . -635) 174576) ((-659 . -670) 174560) ((-221 . -1254) T) ((-421 . -922) 174481) ((-229 . -1070) 174441) ((-40 . -302) T) ((-501 . -571) T) ((-492 . -635) 174422) ((-372 . -25) T) ((-326 . -668) 174077) ((-325 . -668) 173991) ((-372 . -21) T) ((-367 . -25) T) ((-367 . -21) T) ((-221 . -571) T) ((-359 . -25) T) ((-359 . -21) T) ((-331 . -236) 173937) ((-252 . -635) 173914) ((-140 . -635) 173895) ((-139 . -635) 173876) ((-135 . -635) 173857) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1089) T) ((-594 . -175) T) ((-560 . -175) T) ((-509 . -175) T) ((-1094 . -1249) T) ((-976 . -1249) T) ((-735 . -1249) T) ((-661 . -298) 173824) ((-676 . -632) 173806) ((-495 . -1249) T) ((-758 . -759) 173790) ((-346 . -632) 173772) ((-68 . -396) T) ((-68 . -410) T) ((-1129 . -107) 173756) ((-1094 . -912) 173738) ((-976 . -912) 173663) ((-677 . -1144) T) ((-642 . -739) 173650) ((-495 . -912) NIL) ((-1178 . -102) T) ((-1121 . -637) 173634) ((-1094 . -1070) 173616) ((-97 . -632) 173598) ((-491 . -149) T) ((-976 . -1070) 173478) ((-119 . -739) 173423) ((-734 . -930) 173330) ((-677 . -23) T) ((-495 . -1070) 173206) ((-1119 . -633) NIL) ((-1119 . -632) 173188) ((-803 . -633) NIL) ((-803 . -632) 173149) ((-802 . -633) 172783) ((-802 . -632) 172697) ((-1145 . -660) 172603) ((-822 . -875) 172582) ((-475 . -632) 172564) ((-468 . -632) 172546) ((-468 . -633) 172407) ((-1067 . -233) 172353) ((-897 . -940) 172332) ((-128 . -34) T) ((-841 . -133) T) ((-671 . -632) 172314) ((-592 . -102) T) ((-368 . -1318) 172298) ((-366 . -1318) 172282) ((-358 . -1318) 172266) ((-123 . -528) 172199) ((-129 . -528) 172132) ((-526 . -816) T) ((-526 . -821) T) ((-525 . -818) T) ((-103 . -321) 172070) ((-226 . -102) 172020) ((-721 . -175) T) ((-716 . -1133) T) ((-897 . -670) 171936) ((-65 . -398) T) ((-286 . -632) 171918) ((-65 . -410) T) ((-976 . -390) 171902) ((-894 . -302) T) ((-50 . -632) 171884) ((-1152 . -668) 171856) 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169678) ((-359 . -236) 169651) ((-177 . -466) T) ((-82 . -455) T) ((-226 . -321) 169589) ((-82 . -410) T) ((-227 . -632) 169571) ((-108 . -236) 169558) ((-221 . -23) T) ((-1324 . -1319) 169537) ((-699 . -1070) 169521) ((-594 . -302) T) ((-560 . -302) T) ((-509 . -302) T) ((-1268 . -1249) T) ((-137 . -484) 169476) ((-880 . -1249) T) ((-678 . -668) 169435) ((-48 . -1133) T) ((-734 . -274) 169419) ((-734 . -234) 169403) ((-896 . -928) NIL) ((-585 . -1249) T) ((-1268 . -912) NIL) ((-914 . -102) T) ((-911 . -102) T) ((-661 . -632) 169385) ((-402 . -1133) T) ((-171 . -390) 169369) ((-171 . -351) 169353) ((-1268 . -1070) 169233) ((-880 . -1070) 169129) ((-1174 . -102) T) ((-1028 . -930) 169052) ((-677 . -133) T) ((-674 . -816) 169031) ((-674 . -821) 169010) ((-119 . -528) 168918) ((-585 . -1070) 168900) ((-305 . -1307) 168870) ((-1200 . -875) NIL) ((-891 . -102) T) ((-986 . -571) 168849) ((-1242 . -1088) 168732) ((-1035 . -1083) 168677) ((-496 . -660) 168583) ((-935 . -1133) T) ((-1056 . -739) 168520) ((-733 . -1088) 168485) ((-1035 . -662) 168430) ((-636 . -102) T) ((-616 . -34) T) ((-1180 . -1249) T) ((-1242 . -111) 168299) ((-488 . -670) 168196) ((-353 . -739) 168141) ((-171 . -928) 168100) ((-721 . -302) T) ((-716 . -175) T) ((-733 . -111) 168056) ((-1329 . -1089) T) ((-1268 . -390) 168040) ((-419 . -1254) 168018) ((-1147 . -632) 168000) ((-325 . -871) NIL) ((-419 . -571) T) ((-229 . -319) T) ((-1264 . -814) 167953) ((-1264 . -818) 167906) ((-1285 . -748) T) ((-1264 . -748) T) ((-48 . -739) 167871) ((-229 . -1052) T) ((-1286 . -426) 167837) ((-1268 . -928) 167780) ((-365 . -1307) 167757) ((-1242 . -635) 167639) ((-740 . -748) T) ((-345 . -632) 167621) ((-534 . -875) 167600) ((-1145 . -236) 167491) ((-114 . -632) 167473) ((-114 . -633) 167455) ((-740 . -487) T) ((-733 . -635) 167405) ((-1323 . -1083) 167389) ((-496 . -25) 167222) ((-129 . -503) 167206) ((-123 . -503) 167190) ((-496 . -21) 167101) ((-1323 . -662) 167071) ((-642 . -302) T) ((-597 . -1088) 167046) 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-1249) T) ((-48 . -175) T) ((-723 . -401) T) ((-723 . -145) T) ((-1323 . -102) T) ((-1231 . -1249) T) ((-1229 . -635) 166379) ((-1120 . -1249) T) ((-1119 . -1088) 166222) ((-1107 . -1249) T) ((-275 . -940) 166201) ((-255 . -940) 166180) ((-803 . -1088) 166003) ((-802 . -1088) 165846) ((-627 . -1249) T) ((-1197 . -632) 165828) ((-1119 . -111) 165657) ((-1078 . -102) T) ((-489 . -1249) T) ((-475 . -1088) 165628) ((-468 . -1088) 165471) ((-686 . -670) 165455) ((-896 . -319) T) ((-803 . -111) 165264) ((-802 . -111) 165093) ((-368 . -670) 165045) ((-366 . -670) 164997) ((-358 . -670) 164949) ((-275 . -670) 164838) ((-255 . -670) 164727) ((-1191 . -872) T) ((-1120 . -1070) 164711) ((-1107 . -1070) 164688) ((-1036 . -875) T) ((-1032 . -34) T) ((-475 . -111) 164649) ((-468 . -111) 164478) ((-1003 . -875) T) ((-996 . -632) 164460) ((-988 . -1249) T) ((-986 . -1144) T) ((-128 . -1042) 164444) ((-873 . -1249) T) ((-896 . -1052) NIL) ((-757 . -1144) T) ((-737 . -1144) T) ((-676 . -635) 164362) 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-1133) T) ((-421 . -321) 160966) ((-1174 . -930) 160889) ((-894 . -632) 160871) ((-858 . -1070) 160840) ((-661 . -1088) 160824) ((-206 . -809) T) ((-205 . -809) T) ((-204 . -809) T) ((-203 . -809) T) ((-202 . -809) T) ((-201 . -809) T) ((-200 . -809) T) ((-199 . -809) T) ((-198 . -809) T) ((-197 . -809) T) ((-562 . -632) 160806) ((-509 . -1034) T) ((-285 . -863) T) ((-284 . -863) T) ((-283 . -863) T) ((-282 . -863) T) ((-48 . -302) T) ((-281 . -863) T) ((-280 . -863) T) ((-279 . -863) T) ((-196 . -809) T) ((-661 . -111) 160785) ((-630 . -872) T) ((-678 . -426) 160769) ((-692 . -239) 160720) ((-227 . -635) 160682) ((-110 . -872) T) ((-677 . -21) T) ((-677 . -25) T) ((-1323 . -38) 160652) ((-119 . -298) 160603) ((-1299 . -19) 160587) ((-1259 . -875) NIL) ((-1299 . -618) 160564) ((-1313 . -1133) T) ((-365 . -1083) 160509) ((-1109 . -1133) T) ((-1018 . -1133) T) ((-986 . -133) T) ((-841 . -236) 160496) ((-758 . -1133) T) ((-365 . -662) 160441) ((-757 . -133) T) ((-737 . -133) T) ((-526 . -817) T) ((-526 . -818) T) ((-467 . -133) T) ((-421 . -1184) 160419) ((-227 . -1081) T) ((-305 . -102) 160201) ((-143 . -1133) T) ((-721 . -1034) T) ((-1137 . -298) 160157) ((-91 . -1249) T) ((-218 . -632) 160139) ((-129 . -632) 160071) ((-123 . -632) 160003) ((-1329 . -175) T) ((-1206 . -376) 159982) ((-1200 . -376) 159961) ((-326 . -1133) T) ((-419 . -133) T) ((-325 . -1133) T) ((-421 . -38) 159913) ((-1165 . -102) T) ((-1286 . -739) 159805) ((-1167 . -1295) T) ((-1128 . -1249) T) ((-1123 . -1249) T) ((-678 . -1089) T) ((-1105 . -1249) T) ((-1098 . -1249) T) ((-1068 . -1249) T) ((-1051 . -1249) T) ((-331 . -147) 159784) ((-331 . -149) 159763) ((-141 . -1133) T) ((-137 . -1133) T) ((-115 . -1133) T) ((-883 . -102) T) ((-645 . -1249) T) ((-497 . -1249) T) ((-594 . -632) 159745) ((-560 . -633) 159644) ((-560 . -632) 159626) ((-509 . -632) 159608) ((-509 . -633) 159553) ((-499 . -23) T) ((-222 . -1249) T) ((-496 . -872) 159504) ((-501 . -660) 159486) ((-995 . -632) 159468) ((-1035 . -930) 159377) ((-221 . -660) 159359) ((-229 . -418) T) ((-674 . -670) 159343) ((-55 . -632) 159325) ((-1203 . -951) 159304) ((-753 . -1144) T) ((-657 . -102) T) ((-529 . -1249) T) ((-525 . -1249) T) ((-522 . -1249) T) ((-365 . -102) T) ((-1250 . -1115) T) ((-1152 . -868) T) ((-842 . -872) T) ((-753 . -23) T) ((-357 . -1088) 159249) ((-1180 . -107) 159233) ((-1302 . -632) 159215) ((-1207 . -23) T) ((-1207 . -1144) T) ((-1206 . -1144) T) ((-659 . -1249) T) ((-1206 . -23) T) ((-1200 . -1144) T) ((-1200 . -23) T) ((-1174 . -274) 159199) ((-529 . -1070) 159183) ((-1174 . -234) 159167) ((-1158 . -1144) T) ((-357 . -111) 159096) ((-1036 . -1254) T) ((-128 . -1249) T) ((-944 . -1254) T) ((-1158 . -23) T) ((-1108 . -1133) T) ((-716 . -298) NIL) ((-736 . -1249) T) ((-1036 . -571) T) ((-944 . -571) T) ((-839 . -239) 158993) ((-625 . -684) T) ((-624 . -684) T) ((-257 . -1249) T) ((-186 . -1249) T) ((-163 . -1249) T) ((-159 . -1249) T) ((-256 . -632) 158975) ((-622 . -684) T) ((-822 . -133) T) 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156858) ((-391 . -1052) T) ((-108 . -149) T) ((-108 . -147) NIL) ((-45 . -242) 156808) ((-678 . -1133) T) ((-627 . -107) 156755) ((-499 . -133) T) ((-489 . -107) 156705) ((-246 . -1144) 156683) ((-31 . -1249) T) ((-897 . -390) 156667) ((-897 . -351) 156651) ((-246 . -23) 156503) ((-40 . -635) 156433) ((-1313 . -528) 156366) ((-1094 . -951) T) ((-1094 . -844) T) ((-595 . -381) T) ((-532 . -381) T) ((-1289 . -571) 156345) ((-1285 . -1249) T) ((-1280 . -1254) 156324) ((-1280 . -571) 156275) ((-1264 . -1249) T) ((-365 . -1184) T) ((-339 . -34) T) ((-44 . -432) 156259) ((-1214 . -635) 156195) ((-898 . -1249) T) ((-404 . -766) 156179) ((-1264 . -912) 156052) ((-1264 . -910) 156022) ((-1174 . -668) 155981) ((-753 . -133) T) ((-694 . -635) 155965) ((-1259 . -1254) 155944) ((-1259 . -571) 155895) ((-1207 . -133) T) ((-1206 . -133) T) ((-1200 . -133) T) ((-1158 . -133) T) ((-324 . -1115) T) ((-1056 . -1034) T) ((-758 . -528) 155828) ((-1036 . -23) T) ((-1036 . -1144) T) ((-919 . -1133) T) ((-146 . -868) T) ((-1035 . -363) NIL) ((-713 . -632) 155810) ((-973 . -875) 155789) ((-537 . -321) 155727) ((-1003 . -23) T) ((-143 . -528) NIL) ((-891 . -668) 155672) ((-944 . -1144) T) ((-944 . -23) T) ((-897 . -928) 155631) ((-365 . -38) 155596) ((-894 . -1088) 155583) ((-343 . -875) T) ((-83 . -632) 155565) ((-40 . -1081) T) ((-894 . -111) 155550) ((-740 . -1249) T) ((-723 . -102) T) ((-716 . -632) 155532) ((-616 . -1249) T) ((-610 . -571) 155511) ((-443 . -1144) T) ((-352 . -1083) 155495) ((-216 . -1133) T) ((-177 . -1083) 155427) ((-488 . -47) 155397) ((-40 . -240) 155369) ((-40 . -250) T) ((-136 . -102) T) ((-118 . -102) T) ((-609 . -571) 155348) ((-352 . -662) 155332) ((-716 . -633) 155240) ((-326 . -528) 155206) ((-177 . -662) 155138) ((-325 . -528) 155030) ((-501 . -236) 155017) ((-1285 . -1070) 155001) ((-1264 . -1070) 154787) ((-1028 . -426) 154771) ((-221 . -236) 154758) ((-443 . -23) T) ((-1152 . -175) T) ((-626 . -504) 154725) ((-621 . -504) 154707) ((-626 . -632) 154659) 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153581) ((-421 . -845) 153534) ((-1207 . -507) 153500) ((-171 . -951) 153431) ((-1206 . -507) 153397) ((-1200 . -507) 153363) ((-734 . -1133) T) ((-1158 . -507) 153329) ((-594 . -1088) 153316) ((-560 . -1088) 153303) ((-509 . -1088) 153268) ((-326 . -302) 153247) ((-325 . -302) T) ((-353 . -632) 153229) ((-419 . -25) T) ((-419 . -21) T) ((-99 . -298) 153208) ((-594 . -111) 153193) ((-560 . -111) 153178) ((-509 . -111) 153134) ((-1209 . -912) 153101) ((-931 . -503) 153085) ((-48 . -632) 153067) ((-48 . -633) 153012) ((-246 . -133) 152883) ((-1323 . -668) 152842) ((-1268 . -951) 152821) ((-840 . -1254) 152800) ((-402 . -504) 152781) ((-1067 . -528) 152625) ((-402 . -632) 152591) ((-840 . -571) 152522) ((-597 . -670) 152497) ((-275 . -47) 152469) ((-255 . -47) 152426) ((-545 . -523) 152403) ((-594 . -635) 152375) ((-560 . -635) 152347) ((-509 . -635) 152280) ((-1289 . -23) T) ((-1106 . -1249) T) ((-1032 . -1249) T) ((-1289 . -1144) T) ((-1280 . -1144) T) ((-1280 . -23) T) ((-1259 . -1144) T) ((-1259 . -23) T) ((-721 . -1088) 152245) ((-1255 . -684) T) ((-1242 . -748) T) ((-1152 . -302) T) ((-1145 . -239) 152142) ((-1036 . -133) T) ((-1035 . -383) 152114) ((-114 . -381) T) ((-488 . -928) 152020) ((-1003 . -133) T) ((-935 . -632) 152002) ((-55 . -635) 151984) ((-91 . -107) 151968) ((-944 . -133) T) ((-932 . -872) 151919) ((-723 . -1184) T) ((-721 . -111) 151875) ((-866 . -668) 151792) ((-610 . -1144) T) ((-609 . -1144) T) ((-734 . -739) 151621) ((-733 . -748) T) ((-822 . -25) T) ((-822 . -21) T) ((-501 . -872) T) ((-611 . -1249) T) ((-610 . -23) T) ((-600 . -1249) T) ((-221 . -872) T) ((-421 . -668) 151558) ((-594 . -1081) T) ((-560 . -1081) T) ((-549 . -1249) T) ((-509 . -1081) T) ((-357 . -1318) 151535) ((-331 . -466) 151514) ((-352 . -321) 151501) ((-609 . -23) T) ((-443 . -133) T) ((-676 . -670) 151475) ((-252 . -1042) 151459) ((-897 . -319) T) ((-1324 . -1314) 151443) ((-793 . -816) T) ((-793 . -821) T) ((-723 . -38) 151430) ((-560 . -240) T) ((-509 . -250) T) ((-509 . -240) T) ((-1313 . -503) 151414) ((-1296 . -1249) T) ((-1183 . -242) 151364) ((-1119 . -940) 151343) ((-118 . -38) 151330) ((-212 . -824) T) ((-211 . -824) T) ((-210 . -824) T) ((-209 . -824) T) ((-897 . -1052) 151308) ((-686 . -1249) T) ((-667 . -1249) T) ((-803 . -940) 151287) ((-802 . -940) 151266) ((-1221 . -1249) T) ((-368 . -1249) T) ((-366 . -1249) T) ((-358 . -1249) T) ((-275 . -1249) T) ((-255 . -1249) T) ((-468 . -940) 151245) ((-758 . -503) 151229) ((-1119 . -670) 151118) ((-721 . -635) 151053) ((-803 . -670) 150942) ((-642 . -1088) 150929) ((-493 . -1249) T) ((-357 . -381) T) ((-143 . -503) 150911) ((-802 . -670) 150800) ((-1173 . -1249) T) ((-564 . -872) T) ((-475 . -670) 150771) ((-275 . -912) 150630) ((-255 . -912) NIL) ((-119 . -1088) 150575) ((-468 . -670) 150464) ((-686 . -1070) 150441) ((-642 . -111) 150426) ((-404 . -1083) 150410) ((-368 . -1070) 150394) ((-366 . -1070) 150378) ((-358 . -1070) 150362) ((-275 . -1070) 150206) ((-255 . -1070) 150082) ((-936 . -1249) T) ((-119 . -111) 150011) ((-58 . -1249) T) ((-404 . -662) 149995) ((-638 . -1083) 149979) ((-533 . -1249) T) ((-530 . -1249) T) ((-511 . -1249) T) ((-510 . -1249) T) ((-450 . -632) 149961) ((-448 . -632) 149943) ((-638 . -662) 149927) ((-3 . -102) T) ((-1059 . -1244) 149896) ((-856 . -102) T) ((-711 . -57) 149854) ((-721 . -1081) T) ((-652 . -668) 149823) ((-620 . -668) 149792) ((-50 . -670) 149766) ((-301 . -466) T) ((-490 . -1244) 149735) ((0 . -102) T) ((-595 . -670) 149700) ((-532 . -670) 149645) ((-49 . -102) T) ((-936 . -1070) 149632) ((-721 . -250) T) ((-1111 . -424) 149611) ((-753 . -660) 149559) ((-1028 . -1133) T) ((-734 . -175) 149450) ((-642 . -635) 149345) ((-501 . -1023) 149327) ((-419 . -236) 149272) ((-275 . -390) 149256) ((-255 . -390) 149240) ((-413 . -1133) T) ((-1058 . -102) 149218) ((-352 . -38) 149202) ((-221 . -1023) 149184) ((-119 . -635) 149114) ((-177 . -38) 149046) ((-1285 . -319) 149025) ((-1264 . -319) 149004) ((-676 . -748) T) ((-99 . -632) 148986) ((-491 . -1083) 148951) ((-1200 . -660) 148903) ((-491 . -662) 148868) ((-663 . -875) 148847) ((-499 . -25) T) ((-499 . -21) T) ((-1264 . -1052) 148799) ((-1090 . -1249) T) ((-1 . -1249) T) ((-642 . -1081) T) ((-391 . -418) T) ((-404 . -102) T) ((-1137 . -637) 148714) ((-275 . -928) 148660) ((-255 . -928) 148637) ((-119 . -1081) T) ((-1119 . -748) T) ((-840 . -1144) T) ((-843 . -875) T) ((-642 . -240) 148616) ((-638 . -102) T) ((-526 . -1249) T) ((-521 . -1249) T) ((-803 . -748) T) ((-802 . -748) T) ((-1255 . -872) T) ((-427 . -1144) T) ((-119 . -250) T) ((-40 . -381) NIL) ((-119 . -240) NIL) ((-400 . -875) 148595) ((-468 . -748) T) ((-840 . -23) T) ((-753 . -25) T) ((-753 . -21) T) ((-692 . -922) 148516) ((-1109 . -298) 148495) ((-75 . -411) T) ((-75 . -410) T) ((-547 . -789) 148477) ((-229 . -875) T) ((-716 . -1088) 148427) ((-1325 . -102) T) ((-1289 . -133) T) ((-1280 . -133) T) ((-1259 . -133) T) ((-1207 . -25) T) ((-1174 . -426) 148411) ((-652 . -380) 148343) ((-620 . -380) 148275) 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-1133) 145971) ((-1257 . -868) T) ((-331 . -1005) 145933) ((-105 . -102) T) ((-48 . -1088) 145898) ((-896 . -875) NIL) ((-1324 . -102) T) ((-395 . -102) T) ((-1286 . -632) 145880) ((-1165 . -1166) 145864) ((-1036 . -660) 145846) ((-901 . -1249) T) ((-48 . -111) 145802) ((-703 . -1249) T) ((-698 . -1249) T) ((-674 . -1249) T) ((-839 . -922) 145669) ((-492 . -1249) T) ((-252 . -1249) T) ((-545 . -102) T) ((-514 . -102) T) ((-154 . -1307) 145653) ((-140 . -1249) T) ((-139 . -1249) T) ((-135 . -1249) T) ((-1250 . -102) T) ((-1056 . -635) 145590) ((-841 . -239) T) ((-1203 . -1254) 145569) ((-218 . -381) T) ((-353 . -635) 145499) ((-1157 . -1254) 145478) ((-246 . -25) 145311) ((-246 . -21) 145222) ((-129 . -121) 145206) ((-123 . -121) 145190) ((-44 . -766) 145174) ((-1203 . -571) 145085) ((-1157 . -571) 145016) ((-1257 . -1133) T) ((-561 . -875) T) ((-1067 . -298) 144991) ((-1199 . -1115) T) ((-1026 . -1115) T) ((-840 . -133) T) ((-119 . -821) NIL) ((-119 . -816) NIL) ((-368 . -319) T) 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. -133) T) ((-1135 . -1133) T) ((-1035 . -1133) T) ((-63 . -632) 142001) ((-1111 . -922) 141870) ((-1056 . -816) T) ((-1056 . -821) T) ((-1289 . -25) T) ((-1289 . -21) T) ((-1280 . -21) T) ((-1280 . -25) T) ((-894 . -670) 141857) ((-1259 . -21) T) ((-1259 . -25) T) ((-1059 . -153) 141841) ((-1036 . -236) 141828) ((-897 . -844) 141807) ((-897 . -951) T) ((-734 . -298) 141734) ((-610 . -21) T) ((-352 . -668) 141693) ((-108 . -922) NIL) ((-610 . -25) T) ((-609 . -21) T) ((-177 . -668) 141610) ((-40 . -748) T) ((-226 . -528) 141543) ((-609 . -25) T) ((-490 . -153) 141527) ((-477 . -153) 141511) ((-187 . -1249) T) ((-949 . -818) T) ((-949 . -748) T) ((-793 . -817) T) ((-793 . -818) T) ((-520 . -1133) T) ((-516 . -1133) T) ((-793 . -748) T) ((-229 . -376) T) ((-1321 . -1083) 141495) ((-1320 . -1083) 141479) ((-1321 . -662) 141449) ((-1187 . -1133) 141427) ((-896 . -1254) T) ((-1320 . -662) 141397) ((-1120 . -875) T) ((-678 . -632) 141379) ((-896 . -571) T) ((-716 . -381) NIL) ((-44 . -1083) 141363) ((-1329 . -635) 141345) ((-1323 . -1133) T) ((-692 . -102) T) ((-372 . -1307) 141329) ((-367 . -1307) 141313) ((-44 . -662) 141297) ((-359 . -1307) 141281) ((-563 . -102) T) ((-1242 . -1249) T) ((-534 . -872) 141260) ((-733 . -1249) T) ((-988 . -875) 141239) ((-873 . -875) T) ((-501 . -239) T) ((-221 . -239) T) ((-1078 . -1133) T) ((-841 . -466) 141218) ((-154 . -1083) 141202) ((-1078 . -1103) 141131) ((-1059 . -1008) 141100) ((-843 . -1144) T) ((-1035 . -739) 141045) ((-154 . -662) 141029) ((-400 . -1144) T) ((-490 . -1008) 140998) ((-477 . -1008) 140967) ((-1216 . -875) T) ((-110 . -153) 140949) ((-73 . -632) 140931) ((-919 . -632) 140913) ((-1215 . -875) T) ((-1111 . -746) 140892) ((-1329 . -1081) T) ((-840 . -660) 140840) ((-305 . -1089) 140782) ((-171 . -1254) 140687) ((-229 . -1144) T) ((-336 . -23) T) ((-1200 . -1023) 140639) ((-1286 . -1088) 140544) ((-866 . -1133) T) ((-131 . -875) T) ((-1158 . -762) 140523) ((-1285 . -951) 140502) ((-1264 . -951) 140481) ((-894 . 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137321) ((-1119 . -1249) T) ((-1067 . -300) 137296) ((-594 . -748) T) ((-560 . -818) T) ((-171 . -376) 137247) ((-560 . -814) T) ((-560 . -748) T) ((-509 . -748) T) ((-803 . -1249) T) ((-802 . -1249) T) ((-1178 . -503) 137231) ((-475 . -1249) T) ((-468 . -1249) T) ((-1321 . -1322) 137207) ((-1119 . -912) NIL) ((-896 . -1144) T) ((-119 . -940) NIL) ((-1320 . -1322) 137186) ((-671 . -1249) T) ((-803 . -912) NIL) ((-802 . -912) 137045) ((-1315 . -25) T) ((-1315 . -21) T) ((-1247 . -102) 137023) ((-1138 . -410) T) ((-642 . -670) 137010) ((-468 . -912) NIL) ((-697 . -102) 136960) ((-1119 . -1070) 136787) ((-896 . -23) T) ((-803 . -1070) 136646) ((-802 . -1070) 136503) ((-119 . -670) 136448) ((-468 . -1070) 136324) ((-286 . -1249) T) ((-326 . -635) 135888) ((-325 . -635) 135771) ((-50 . -1249) T) ((-404 . -668) 135740) ((-671 . -1070) 135724) ((-646 . -102) T) ((-595 . -1249) T) ((-532 . -1249) T) ((-226 . -503) 135708) ((-1299 . -34) T) ((-638 . -668) 135667) ((-301 . -1083) 135654) ((-137 . -635) 135638) ((-301 . -662) 135625) ((-652 . -739) 135609) ((-620 . -739) 135593) ((-692 . -38) 135553) ((-331 . -102) T) ((-1152 . -1088) 135540) ((-86 . -632) 135522) ((-50 . -1070) 135506) ((-1119 . -390) 135490) ((-803 . -390) 135474) ((-721 . -748) T) ((-721 . -818) T) ((-721 . -814) T) ((-60 . -57) 135436) ((-595 . -1070) 135423) ((-532 . -1070) 135400) ((-174 . -1249) T) ((-336 . -133) T) ((-326 . -1081) 135290) ((-325 . -1081) T) ((-171 . -1144) T) ((-802 . -390) 135274) ((-45 . -153) 135224) ((-1036 . -1023) 135206) ((-468 . -390) 135190) ((-421 . -175) T) ((-326 . -250) 135169) ((-325 . -250) T) ((-325 . -240) NIL) ((-305 . -1133) 134951) ((-229 . -133) T) ((-1152 . -111) 134936) ((-171 . -23) T) ((-822 . -149) 134915) ((-822 . -147) 134894) ((-260 . -660) 134800) ((-259 . -660) 134706) ((-331 . -296) 134672) ((-1187 . -528) 134605) ((-491 . -668) 134555) ((-657 . -868) T) ((-496 . -922) 134422) ((-1165 . -1133) T) ((-229 . -1092) T) ((-839 . -321) 134360) ((-1119 . -928) 134295) ((-803 . -928) 134238) ((-802 . -928) 134222) ((-1321 . -38) 134192) ((-1320 . -38) 134162) ((-1268 . -1144) T) ((-880 . -1144) T) ((-468 . -928) 134139) ((-883 . -1133) T) ((-1268 . -23) T) ((-1152 . -635) 134111) ((-1094 . -133) T) ((-880 . -23) T) ((-585 . -1144) T) ((-642 . -748) T) ((-525 . -875) T) ((-368 . -951) T) ((-366 . -951) T) ((-301 . -102) T) ((-358 . -951) T) ((-1002 . -1115) T) ((-976 . -133) T) ((-840 . -236) 134056) ((-119 . -818) NIL) ((-119 . -814) NIL) ((-119 . -748) T) ((-1078 . -528) 133957) ((-716 . -940) NIL) ((-585 . -23) T) ((-495 . -133) T) ((-419 . -239) 133908) ((-697 . -321) 133846) ((-227 . -1249) T) ((-657 . -1133) T) ((-652 . -783) T) ((-620 . -783) T) ((-1259 . -872) NIL) ((-1111 . -1083) 133756) ((-1035 . -302) T) ((-716 . -670) 133706) ((-260 . -25) T) ((-365 . -1133) T) ((-260 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-154 . -38) 133690) ((-2 . -102) T) ((-936 . -951) T) ((-1111 . -662) 133558) ((-496 . -1307) 133528) ((-1152 . -1081) T) ((-733 . -319) T) ((-723 . -1089) T) ((-372 . -1083) 133480) ((-367 . -1083) 133432) ((-359 . -1083) 133384) ((-372 . -662) 133336) ((-227 . -1070) 133313) ((-367 . -662) 133265) ((-108 . -1083) 133215) ((-359 . -662) 133167) ((-305 . -739) 133109) ((-661 . -1249) T) ((-501 . -466) T) ((-421 . -528) 133021) ((-108 . -662) 132971) ((-221 . -466) T) ((-1152 . -240) T) ((-307 . -153) 132921) ((-1028 . -633) 132882) ((-1028 . -632) 132864) ((-1021 . -632) 132846) ((-118 . -1089) T) ((-678 . -1088) 132830) ((-229 . -507) T) ((-413 . -632) 132812) ((-413 . -633) 132789) ((-1086 . -1307) 132759) ((-678 . -111) 132738) ((-692 . -930) 132661) ((-1174 . -503) 132645) ((-1324 . -668) 132604) ((-395 . -668) 132573) ((-64 . -455) T) ((-64 . -410) T) ((-1192 . -102) T) ((-896 . -133) T) ((-498 . -102) 132523) ((-1147 . -1249) T) ((-1256 . -875) T) ((-1329 . -381) T) ((-1111 . -102) T) ((-1093 . -102) T) ((-365 . -739) 132468) ((-897 . -875) 132419) ((-753 . -149) 132398) ((-753 . -147) 132377) 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-872) 127355) ((-734 . -338) 127332) ((-495 . -660) 127280) ((-40 . -1070) 127168) ((-734 . -240) T) ((-723 . -739) 127155) ((-352 . -1133) T) ((-177 . -1133) T) ((-343 . -872) T) ((-419 . -466) 127105) ((-391 . -23) T) ((-372 . -38) 127070) ((-367 . -38) 127035) ((-359 . -38) 127000) ((-80 . -455) T) ((-80 . -410) T) ((-229 . -25) T) ((-229 . -21) T) ((-858 . -1144) T) ((-108 . -38) 126950) ((-852 . -1144) T) ((-795 . -1133) T) ((-118 . -739) 126937) ((-694 . -1070) 126921) ((-630 . -102) T) ((-858 . -23) T) ((-852 . -23) T) ((-1187 . -298) 126873) ((-1145 . -321) 126811) ((-496 . -1083) 126712) ((-1129 . -242) 126696) ((-61 . -411) T) ((-61 . -410) T) ((-1185 . -102) T) ((-110 . -102) T) ((-496 . -662) 126618) ((-40 . -390) 126595) ((-96 . -102) T) ((-677 . -877) 126579) ((-1203 . -236) 126566) ((-1167 . -1115) T) ((-1094 . -21) T) ((-1094 . -25) T) ((-1086 . -1083) 126550) ((-839 . -274) 126519) ((-839 . -234) 126488) ((-976 . -25) T) ((-976 . -21) T) ((-1152 . -381) T) ((-1086 . 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-670) 121450) ((-325 . -670) 121379) ((-488 . -571) 121330) ((-352 . -528) 121296) ((-565 . -153) 121246) ((-40 . -319) T) ((-866 . -632) 121228) ((-723 . -302) T) ((-897 . -23) T) ((-391 . -507) T) ((-1111 . -274) 121198) ((-1111 . -234) 121168) ((-524 . -102) T) ((-421 . -633) 120975) ((-421 . -632) 120957) ((-270 . -632) 120939) ((-118 . -302) T) ((-1286 . -748) T) ((-642 . -1249) T) ((-1325 . -1133) T) ((-1285 . -376) 120918) ((-1264 . -376) 120897) ((-1313 . -34) T) ((-1258 . -1133) T) ((-119 . -1249) T) ((-108 . -274) 120879) ((-108 . -234) 120861) ((-1211 . -102) T) ((-491 . -1133) T) ((-537 . -503) 120845) ((-758 . -34) T) ((-677 . -1083) 120829) ((-677 . -662) 120799) ((-896 . -236) NIL) ((-143 . -34) T) ((-119 . -910) 120776) ((-119 . -912) NIL) ((-1312 . -102) T) ((-1289 . -239) 120735) ((-642 . -1070) 120618) ((-625 . -102) T) ((-624 . -102) T) ((-622 . -102) T) ((-663 . -872) 120597) ((-1280 . -239) 120549) ((-1259 . -239) 120372) ((-307 . -102) T) ((-734 . -381) 120351) 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T) ((-659 . -133) T) ((-488 . -376) 118985) ((-372 . -363) 118964) ((-367 . -363) 118943) ((-359 . -363) 118922) ((-326 . -487) 118901) ((-1285 . -23) T) ((-1264 . -23) T) ((-740 . -1144) T) ((-736 . -133) T) ((-677 . -102) T) ((-491 . -739) 118866) ((-674 . -875) 118845) ((-45 . -294) 118795) ((-105 . -1133) T) ((-68 . -632) 118777) ((-252 . -875) 118756) ((-1002 . -102) T) ((-889 . -102) T) ((-642 . -928) 118715) ((-1324 . -1133) T) ((-395 . -1133) T) ((-1) T) ((-1268 . -236) 118702) ((-1250 . -1133) T) ((-83 . -1249) T) ((-1145 . -274) 118671) ((-1094 . -872) T) ((-119 . -928) NIL) ((-803 . -951) 118650) ((-735 . -872) T) ((-545 . -1133) T) ((-514 . -1133) T) ((-368 . -1254) T) ((-366 . -1254) T) ((-358 . -1254) T) ((-275 . -1254) 118629) ((-255 . -1254) 118608) ((-547 . -886) T) ((-1145 . -234) 118577) ((-1191 . -845) T) ((-1174 . -1088) 118561) ((-404 . -783) T) ((-716 . -1249) T) ((-713 . -1070) 118545) ((-368 . -571) T) ((-366 . -571) T) ((-358 . -571) T) ((-275 . -571) 118476) 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. -319) T) ((-560 . -319) T) ((-509 . -319) T) ((-1324 . -739) 116675) ((-716 . -390) 116657) ((-716 . -351) 116639) ((-491 . -175) T) ((-395 . -739) 116609) ((-891 . -635) 116544) ((-896 . -872) NIL) ((-560 . -1052) T) ((-509 . -1052) T) ((-1165 . -632) 116526) ((-1145 . -245) 116505) ((-217 . -102) T) ((-1183 . -102) T) ((-71 . -632) 116487) ((-1056 . -1249) T) ((-1174 . -1081) T) ((-1211 . -38) 116384) ((-883 . -632) 116366) ((-560 . -559) T) ((-692 . -1089) T) ((-753 . -980) 116319) ((-1174 . -240) 116298) ((-353 . -1249) T) ((-1114 . -1133) T) ((-1066 . -25) T) ((-1066 . -21) T) ((-1035 . -1088) 116243) ((-339 . -875) 116222) ((-932 . -102) T) ((-891 . -1081) T) ((-716 . -928) NIL) ((-368 . -341) 116206) ((-368 . -376) T) ((-366 . -341) 116190) ((-366 . -376) T) ((-358 . -341) 116174) ((-358 . -376) T) ((-501 . -102) T) ((-1312 . -38) 116144) ((-561 . -872) T) ((-537 . -708) 116094) ((-221 . -102) T) ((-1056 . -1070) 115974) ((-1035 . -111) 115903) ((-657 . -632) 115885) ((-1207 . 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112348) ((-1200 . -1261) 112332) ((-529 . -25) T) ((-509 . -310) T) ((-526 . -23) T) ((-525 . -25) T) ((-522 . -25) T) ((-521 . -23) T) ((-421 . -1081) T) ((-419 . -1083) 112306) ((-331 . -1089) T) ((-716 . -319) T) ((-419 . -662) 112280) ((-108 . -871) T) ((-734 . -748) T) ((-421 . -250) T) ((-421 . -240) 112259) ((-391 . -236) 112246) ((-501 . -38) 112196) ((-221 . -38) 112146) ((-488 . -507) 112112) ((-659 . -21) T) ((-659 . -25) T) ((-1257 . -381) T) ((-1191 . -1176) T) ((-1134 . -102) T) ((-852 . -236) 112085) ((-723 . -632) 112067) ((-723 . -633) 111982) ((-736 . -21) T) ((-736 . -25) T) ((-1167 . -102) T) ((-496 . -668) 111761) ((-246 . -922) 111628) ((-136 . -632) 111610) ((-118 . -632) 111592) ((-159 . -25) T) ((-1321 . -1133) T) ((-897 . -660) 111540) ((-1320 . -1133) T) ((-890 . -1249) T) ((-986 . -102) T) ((-757 . -102) T) ((-737 . -102) T) ((-467 . -102) T) ((-840 . -466) 111491) ((-44 . -1133) T) ((-1120 . -872) T) ((-1095 . -321) 111342) ((-686 . -133) T) ((-1086 . -668) 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. |RecordCategory|) T) ((-1145 . -1089) 105375) ((-856 . -632) 105357) ((-1094 . -239) T) ((-594 . -951) T) ((-560 . -844) T) ((-560 . -951) T) ((-509 . -951) T) ((-137 . -1070) 105341) ((-229 . -95) T) ((-171 . -149) 105320) ((-76 . -455) T) ((0 . -632) 105302) ((-76 . -410) T) ((-171 . -147) 105253) ((-229 . -35) T) ((-49 . -632) 105235) ((-491 . -1089) T) ((-501 . -274) 105217) ((-501 . -234) 105199) ((-498 . -1000) 105183) ((-221 . -274) 105165) ((-221 . -234) 105147) ((-81 . -455) T) ((-81 . -410) T) ((-1178 . -34) T) ((-753 . -102) T) ((-677 . -668) 105106) ((-1058 . -632) 105073) ((-514 . -298) 105023) ((-326 . -390) 104992) ((-325 . -390) 104953) ((-325 . -351) 104914) ((-1117 . -632) 104896) ((-840 . -980) 104843) ((-674 . -133) T) ((-1268 . -147) 104822) ((-1268 . -149) 104801) ((-1207 . -102) T) ((-1206 . -102) T) ((-1200 . -102) T) ((-1192 . -1133) T) ((-1158 . -102) T) ((-1108 . -1249) T) ((-226 . -34) T) ((-301 . -739) 104788) ((-1289 . -1292) 104772) ((-1192 . -629) 104748) ((-607 . -321) NIL) ((-1289 . -1278) 104725) ((-1183 . -233) 104675) ((-498 . -1133) 104653) ((-452 . -1249) T) ((-404 . -632) 104635) ((-525 . -872) T) ((-1152 . -1249) T) ((-1280 . -1284) 104596) ((-1280 . -1278) 104566) ((-1280 . -1282) 104550) ((-1259 . -1263) 104511) ((-1259 . -1278) 104488) ((-1259 . -1261) 104472) ((-1207 . -296) 104438) ((-638 . -632) 104420) ((-1206 . -296) 104386) ((-721 . -951) T) ((-1200 . -296) 104352) ((-1158 . -296) 104318) ((-1152 . -912) 104300) ((-1111 . -1133) T) ((-1093 . -1133) T) ((-48 . -310) T) ((-326 . -928) 104266) ((-325 . -928) NIL) ((-1093 . -1100) 104245) ((-822 . -38) 104229) ((-275 . -660) 104177) ((-114 . -875) T) ((-255 . -660) 104125) ((-723 . -1088) 104112) ((-609 . -1278) 104089) ((-1152 . -1070) 104071) ((-331 . -175) 104002) ((-372 . -1133) T) ((-367 . -1133) T) ((-359 . -1133) T) ((-514 . -19) 103984) ((-1129 . -153) 103968) ((-896 . -239) NIL) ((-108 . -1133) T) ((-118 . -1088) 103955) ((-733 . -376) T) ((-514 . -618) 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. -47) 98844) ((-372 . -175) T) ((-367 . -175) T) ((-533 . -57) 98818) ((-511 . -57) 98768) ((-365 . -1318) 98745) ((-229 . -466) T) ((-331 . -302) 98696) ((-359 . -175) T) ((-177 . -250) T) ((-1264 . -872) 98595) ((-108 . -175) T) ((-897 . -1023) 98579) ((-676 . -1144) T) ((-595 . -376) T) ((-595 . -341) 98566) ((-532 . -341) 98543) ((-532 . -376) T) ((-326 . -319) 98522) ((-325 . -319) T) ((-616 . -872) 98501) ((-1145 . -739) 98443) ((-623 . -1249) T) ((-534 . -294) 98427) ((-676 . -23) T) ((-419 . -234) 98411) ((-419 . -274) 98395) ((-325 . -1052) NIL) ((-346 . -23) T) ((-103 . -1042) 98379) ((-657 . -381) T) ((-45 . -36) 98358) ((-630 . -1133) T) ((-365 . -381) T) ((-538 . -102) T) ((-509 . -27) T) ((-246 . -321) 98296) ((-1119 . -1144) T) ((-1323 . -670) 98270) ((-803 . -1144) T) ((-802 . -1144) T) ((-1211 . -426) 98254) ((-468 . -1144) T) ((-1094 . -466) T) ((-1185 . -1133) T) ((-976 . -466) 98205) ((-1148 . -1115) T) ((-110 . -1133) T) ((-1119 . -23) T) ((-1192 . -528) 97988) 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-1254) T) ((-1036 . -274) 86640) ((-331 . -632) 86622) ((-1036 . -234) 86604) ((-171 . -168) 86588) ((-594 . -571) T) ((-560 . -571) T) ((-509 . -571) T) ((-793 . -23) T) ((-1285 . -149) 86567) ((-1285 . -147) 86546) ((-1192 . -618) 86522) ((-1264 . -147) 86447) ((-1059 . -503) 86431) ((-1257 . -1249) T) ((-1264 . -149) 86356) ((-1315 . -1322) 86335) ((-896 . -922) NIL) ((-490 . -503) 86319) ((-477 . -503) 86303) ((-537 . -34) T) ((-677 . -739) 86273) ((-1289 . -930) 86186) ((-1280 . -930) 86092) ((-1259 . -930) 85853) ((-114 . -999) T) ((-1211 . -175) 85804) ((-674 . -872) 85783) ((-377 . -102) T) ((-609 . -930) 85696) ((-246 . -245) 85675) ((-260 . -102) T) ((-259 . -102) T) ((-1268 . -980) 85644) ((-252 . -872) 85623) ((-1056 . -875) T) ((-840 . -38) 85472) ((-45 . -528) 85264) ((-1191 . -298) 85214) ((-217 . -1133) T) ((-1183 . -1133) T) ((-897 . -239) 85165) ((-1183 . -629) 85144) ((-597 . -25) T) ((-597 . -21) T) ((-1129 . -321) 85082) ((-986 . -426) 85066) ((-721 . -1254) T) 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83947) ((-1203 . -1083) 83770) ((-1174 . -1249) T) ((-1157 . -1083) 83613) ((-879 . -1083) 83597) ((-651 . -618) 83572) ((-1285 . -95) 83538) ((-1285 . -239) 83490) ((-1266 . -102) 83468) ((-1203 . -662) 83297) ((-1157 . -662) 83146) ((-879 . -662) 83116) ((-1264 . -1235) 83082) ((-1119 . -25) T) ((-564 . -1133) T) ((-1119 . -21) T) ((-986 . -1089) T) ((-545 . -816) T) ((-545 . -821) T) ((-119 . -1254) T) ((-891 . -1249) T) ((-642 . -571) T) ((-803 . -25) T) ((-803 . -21) T) ((-802 . -21) T) ((-802 . -25) T) ((-757 . -1089) T) ((-737 . -1089) T) ((-692 . -1088) 83066) ((-531 . -1115) T) ((-475 . -25) T) ((-119 . -571) T) ((-475 . -21) T) ((-468 . -25) T) ((-468 . -21) T) ((-1264 . -1238) 83032) ((-1185 . -93) T) ((-1174 . -1070) 82928) ((-841 . -302) 82907) ((-1264 . -239) 82766) ((-848 . -1133) T) ((-996 . -999) T) ((-692 . -111) 82745) ((-636 . -1249) T) ((-307 . -528) 82537) ((-1259 . -234) 82489) ((-1259 . -274) 82441) ((-1258 . -381) T) ((-260 . -321) 82379) ((-259 . -321) 82317) 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. -503) 37533) ((-697 . -1249) T) ((-492 . -102) T) ((-252 . -102) 37463) ((-561 . -868) T) ((-140 . -102) T) ((-139 . -102) T) ((-135 . -102) T) ((-1119 . -922) 37358) ((-896 . -1133) T) ((-1203 . -528) 37305) ((-1094 . -739) 37292) ((-803 . -922) 37195) ((-753 . -1088) 37038) ((-802 . -922) 37020) ((-976 . -739) 36869) ((-1157 . -528) 36821) ((-1311 . -1133) T) ((-1310 . -1133) T) ((-468 . -922) 36796) ((-495 . -739) 36645) ((-67 . -632) 36627) ((-646 . -1249) T) ((-753 . -111) 36456) ((-973 . -503) 36440) ((-1312 . -670) 36400) ((-1207 . -1088) 36283) ((-841 . -748) T) ((-1206 . -1088) 36118) ((-1200 . -1088) 35908) ((-331 . -1249) T) ((-1158 . -1088) 35791) ((-1035 . -1254) T) ((-1121 . -102) 35769) ((-839 . -390) 35738) ((-593 . -632) 35720) ((-561 . -1133) T) ((-1035 . -571) T) ((-1207 . -111) 35589) ((-1206 . -111) 35410) ((-1200 . -111) 35179) ((-1158 . -111) 35048) ((-1137 . -1136) 35012) ((-391 . -871) T) ((-1289 . -632) 34994) ((-1280 . -632) 34976) ((-897 . -668) 34913) 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. -668) 25814) ((-255 . -668) 25724) ((-1315 . -397) 25696) ((-531 . -1133) T) ((-119 . -466) T) ((-1229 . -102) T) ((-1124 . -1133) 25666) ((-1066 . -1133) T) ((-1148 . -93) T) ((-919 . -872) T) ((-1289 . -111) 25535) ((-365 . -1254) T) ((-1289 . -1088) 25418) ((-1145 . -390) 25387) ((-1280 . -1088) 25222) ((-1259 . -1088) 25012) ((-1280 . -111) 24833) ((-1259 . -111) 24602) ((-1242 . -321) 24589) ((-1035 . -133) T) ((-936 . -668) 24539) ((-377 . -632) 24521) ((-365 . -571) T) ((-301 . -319) T) ((-610 . -1088) 24481) ((-609 . -1088) 24364) ((-595 . -1083) 24329) ((-532 . -1083) 24274) ((-374 . -1133) T) ((-334 . -1133) T) ((-260 . -632) 24235) ((-259 . -632) 24196) ((-595 . -662) 24161) ((-532 . -662) 24106) ((-716 . -424) 24073) ((-652 . -23) T) ((-620 . -23) T) ((-40 . -922) 23980) ((-676 . -102) T) ((-610 . -111) 23933) ((-609 . -111) 23802) ((-391 . -1133) T) ((-346 . -102) T) ((-171 . -302) 23713) ((-1264 . -871) 23666) ((-736 . -1089) T) ((-630 . -1249) T) ((-1180 . -528) 23599) 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19523) ((-227 . -102) T) ((-496 . -390) 19492) ((-529 . -1133) T) ((-525 . -1133) T) ((-522 . -1133) T) ((-822 . -670) 19466) ((-1056 . -466) T) ((-988 . -528) 19399) ((-365 . -23) T) ((-652 . -133) T) ((-620 . -133) T) ((-353 . -466) T) ((-246 . -381) 19378) ((-391 . -175) T) ((-1285 . -1089) T) ((-1264 . -1089) T) ((-229 . -1034) T) ((-840 . -635) 19115) ((-721 . -401) T) ((-419 . -748) T) ((-723 . -1254) T) ((-1174 . -660) 19063) ((-659 . -1133) T) ((-661 . -102) T) ((-594 . -895) 19047) ((-1315 . -1088) 19031) ((-1192 . -1226) 19007) ((-723 . -571) T) ((-128 . -1133) 18985) ((-736 . -1133) T) ((-676 . -38) 18955) ((-496 . -928) 18887) ((-257 . -1133) T) ((-186 . -1133) T) ((-353 . -416) T) ((-326 . -149) 18866) ((-326 . -147) 18845) ((-118 . -571) T) ((-131 . -528) NIL) ((-325 . -149) 18801) ((-325 . -147) 18757) ((-48 . -466) T) ((-163 . -1133) T) ((-159 . -1133) T) ((-1192 . -107) 18704) ((-803 . -1184) 18682) ((-1315 . -111) 18661) ((-711 . -34) T) ((-606 . -1249) T) ((-565 . -34) T) ((-498 . -107) 18645) ((-260 . -300) 18622) ((-259 . -300) 18599) ((-1256 . -868) T) ((-896 . -298) 18550) ((-45 . -1249) T) ((-1242 . -930) 18531) ((-841 . -1249) T) ((-840 . -1081) T) ((-638 . -875) 18510) ((-674 . -668) 18479) ((-1211 . -47) 18455) ((-840 . -338) 18417) ((-1119 . -38) 18266) ((-840 . -240) 18245) ((-803 . -38) 18074) ((-802 . -38) 17923) ((-1148 . -504) 17904) ((-468 . -38) 17753) ((-1148 . -632) 17719) ((-1147 . -102) T) ((-663 . -633) 17680) ((-663 . -632) 17592) ((-595 . -1184) T) ((-532 . -1184) T) ((-1180 . -503) 17576) ((-357 . -1083) 17521) ((-1236 . -1133) 17499) ((-1174 . -25) T) ((-1174 . -21) T) ((-357 . -662) 17444) ((-1315 . -635) 17393) ((-342 . -1249) T) ((-488 . -1089) T) ((-1256 . -1133) T) ((-1259 . -816) NIL) ((-1259 . -821) NIL) ((-1028 . -872) 17372) ((-891 . -21) T) ((-862 . -1133) T) ((-843 . -632) 17354) ((-891 . -25) T) ((-822 . -748) T) ((-659 . -739) 17338) ((-177 . -1254) T) ((-595 . -38) 17303) ((-532 . -38) 17268) ((-400 . -632) 17250) ((-345 . -102) T) ((-336 . -632) 17232) ((-171 . -298) 17190) ((-1258 . -875) T) ((-64 . -1249) T) ((-114 . -102) T) ((-897 . -1133) T) ((-524 . -1249) T) ((-177 . -571) T) ((-736 . -739) 17160) ((-305 . -133) 17043) ((-229 . -632) 17025) ((-229 . -633) 16955) ((-1035 . -660) 16894) ((-1315 . -1081) T) ((-1211 . -1249) T) ((-1152 . -149) T) ((-651 . -1226) 16869) ((-753 . -940) 16848) ((-607 . -34) T) ((-669 . -107) 16832) ((-651 . -107) 16778) ((-625 . -1249) T) ((-624 . -1249) T) ((-622 . -1249) T) ((-1312 . -1249) T) ((-642 . -922) 16699) ((-1268 . -298) 16626) ((-753 . -670) 16515) ((-307 . -1249) T) ((-1211 . -1070) 16411) ((-973 . -637) 16388) ((-591 . -590) T) ((-591 . -541) T) ((-543 . -541) T) ((-119 . -922) NIL) ((-1200 . -940) NIL) ((-1094 . -633) 16303) ((-1094 . -632) 16285) ((-976 . -632) 16267) ((-735 . -504) 16217) ((-357 . -102) T) ((-260 . -1088) 16138) ((-259 . -1088) 16059) ((-407 . -102) T) ((-31 . -1133) T) ((-976 . -633) 15920) ((-735 . -632) 15855) 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-102) T) ((-894 . -1083) 13250) ((-1158 . -748) T) ((-793 . -102) T) ((-694 . -102) T) ((-894 . -662) 13237) ((-561 . -632) 13219) ((-488 . -1133) T) ((-352 . -1144) T) ((-177 . -1144) T) ((-331 . -951) 13198) ((-1285 . -739) 13039) ((-897 . -175) T) ((-1264 . -739) 12853) ((-866 . -21) 12805) ((-866 . -25) 12757) ((-252 . -1182) 12741) ((-128 . -528) 12674) ((-421 . -25) T) ((-421 . -21) T) ((-352 . -23) T) ((-171 . -633) 12435) ((-171 . -632) 12417) ((-177 . -23) T) ((-663 . -300) 12394) ((-534 . -34) T) ((-636 . -684) T) ((-926 . -632) 12376) ((-89 . -1249) T) ((-865 . -632) 12358) ((-832 . -632) 12340) ((-791 . -632) 12322) ((-699 . -632) 12304) ((-246 . -670) 12137) ((-636 . -113) T) ((-1209 . -1133) T) ((-1203 . -1088) 11960) ((-217 . -1249) T) ((-1183 . -1249) T) ((-1157 . -1088) 11803) ((-879 . -1088) 11787) ((-1114 . -875) T) ((-1266 . -637) 11771) ((-1203 . -111) 11580) ((-1157 . -111) 11409) ((-879 . -111) 11388) ((-1257 . -872) T) ((-1268 . -633) NIL) ((-1268 . -632) 11370) 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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 a081d63c..dab21f9b 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3514591830) +(30 . 3514823547) (4513 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -489,671 +489,673 @@ |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| - |Enumeration| |Mapping| |Record| |Union| |li| |zero?| |rk4qc| - |subresultantVector| |edf2fi| |lyndon?| |hostByteOrder| |dimensionsOf| - |nthRoot| |traceMatrix| |stopTableGcd!| |realElementary| |difference| - |hermiteH| |atanIfCan| |notelem| |erf| |width| |clearTable!| - |diagonals| |OMlistCDs| |setAdaptive3D| |makeRecord| |readByte!| - |compound?| |linear| |setlast!| |shanksDiscLogAlgorithm| - |clearTheFTable| |inverseIntegralMatrix| |linkToFortran| |redPol| - |numberOfFactors| |diagonal| |constructor| |jvmSynchronized| - |rationalApproximation| |e01saf| |c06fqf| |normFactors| |splitLinear| - |minPoly| |corrPoly| |safeFloor| |ideal| |returns| |plus!| - |printInfo!| |completeHermite| |polynomial| |dilog| - |expandTrigProducts| |shiftRoots| |numberOfNormalPoly| - |subresultantSequence| |putProperty| |d01asf| |simpleBounds?| - |trueEqual| |nsqfree| |coth2trigh| |sin| |wholePart| |case| |e02agf| - |numberOfComponents| |iiasinh| |atanhIfCan| |functionIsOscillatory| - |primlimitedint| |jvmPublic| |property| |lowerCase!| |cos| |Zero| - |nor| |critMonD1| |f07adf| |unitVector| |generate| |neglist| - |LyndonCoordinates| |rk4| |irreducibleFactors| |tan| |upperCase!| - |One| |hasPredicate?| |dequeue!| |jvmFinal| |symmetric?| |nthExpon| - |solveLinearPolynomialEquation| |divide| - |removeRoughlyRedundantFactorsInContents| |cot| |qqq| |incrementBy| - |optional| |closed| |linearDependenceOverZ| |explicitlyEmpty?| - |llprop| |basisOfLeftAnnihilator| |computePowers| |push!| - |RemainderList| |monicLeftDivide| |sec| |carriageReturn| - |numericalOptimization| |inconsistent?| |OMputEndBVar| |expand| - |log10| |e01bgf| |errorKind| |Lazard2| |partitions| |csc| - |characteristic| |LazardQuotient| |factorSquareFree| |hdmpToP| |list?| - |filterWhile| |bezoutDiscriminant| |unitNormal| |cSech| |asin| - |viewWriteAvailable| |definingEquations| |bitand| |PollardSmallFactor| - |jacobian| |errorInfo| |radicalEigenvectors| |insert!| |filterUntil| - |doublyTransitive?| |setleft!| |FormatArabic| |acos| |denominator| - |symFunc| |bitior| |elt| |rootBound| |exprex| |e04fdf| |generalSqFr| - |stoseIntegralLastSubResultant| |select| |basisOfRightNucleus| - |coerceP| |heapSort| |e01sff| |outputFloating| |atan| |exp| - |setColumn!| |magnitude| |useSingleFactorBound?| |fmecg| |padecf| - |second| |say| |symmetricRemainder| |stoseInvertible?reg| |imagi| - |particularSolution| |acot| |viewport3D| |outputMeasure| - |branchPointAtInfinity?| |check| |plenaryPower| |third| |permutation| - |prinb| |totalGroebner| |splitDenominator| |appendPoint| |asec| - |iroot| |augment| |c06gcf| |omError| |linearAssociatedLog| - |completeEchelonBasis| |dual| |numFunEvals| |acsc| |addiag| - |binarySearchTree| |zeroSetSplitIntoTriangularSystems| |f2st| - |mainForm| |primextintfrac| |ScanArabic| |showTheRoutinesTable| - |fixedPoints| |sinh| |karatsubaDivide| |functorData| |sumOfDivisors| - |selectsecond| |idealSimplify| |distdfact| |OMgetString| |isPower| - |prepareDecompose| |mesh| |cosh| |prinpolINFO| |algebraicDecompose| - |minGbasis| |transcendentalDecompose| |setLength!| |makeVariable| - |iisech| |subNode?| |perfectNthRoot| |tanh| |finiteBasis| - |positiveRemainder| |setEpilogue!| |upperBound| |level| - |reducedContinuedFraction| |divisor| |genericLeftNorm| |rowEchLocal| - |numeric| |createZechTable| |coth| |tail| |leftScalarTimes!| - |companionBlocks| |lfextlimint| |extractClosed| |measure2Result| - |gcdprim| |radical| |thetaCoord| |primitivePart| |key| - |matrixConcat3D| |sech| |perfectSqrt| |ridHack1| |hdmpToDmp| |member?| - |properties| |union| |s18adf| |computeCycleLength| |nextPartition| - |e02dff| |csch| |iiexp| |showClipRegion| |OMconnOutDevice| - |internalLastSubResultant| |translate| |leftRankPolynomial| - |lazyEvaluate| |diagonal?| |radicalEigenvector| |asinh| |npcoef| - |diagonalProduct| |brillhartIrreducible?| |zerosOf| |low| |expr| - |cycleSplit!| |clikeUniv| |colorFunction| |acosh| |raisePolynomial| - |vertConcat| |solid?| |scopes| |cons| |mkcomm| |doubleRank| - |drawCurves| |palgLODE0| |atanh| |multinomial| |filename| |quoted?| - |length| |inverseIntegralMatrixAtInfinity| |unit| |leader| |drawStyle| - |sncndn| |tab| |presuper| |acoth| |balancedBinaryTree| - |getExplanations| |scripts| |mapBivariate| |lifting| - |validExponential| |rightNorm| |coefficients| |newline| |asech| - |parse| |basisOfLeftNucloid| |stoseInvertible?| |parseString| - |collectQuasiMonic| |f2df| |aQuartic| |repeating?| |coefChoose| - |iiacsc| |e02baf| |computeBasis| |LyndonWordsList1| |source| |cycles| - |minimize| |setVariableOrder| |jvmNative| |multiple| |tanhIfCan| - |maxRowIndex| |build| |numberOfMonomials| |reduceBasisAtInfinity| - |leftRegularRepresentation| |identification| |d02gaf| |applyQuote| - |extractProperty| |isPlus| |rationalFunction| |ScanFloatIgnoreSpaces| - |reduced?| |sayLength| |scanOneDimSubspaces| |newReduc| - |doubleComplex?| |createPrimitivePoly| |super| |headAst| |axes| - |iiacsch| |UP2ifCan| |target| |jvmProtected| |child?| |s14abf| - |boundOfCauchy| |laguerre| |lowerPolynomial| |OMputObject| - |numberOfFractionalTerms| |rightMult| |rules| |datalist| |resetNew| - |uncouplingMatrices| |univariatePolynomial| |s21baf| |ruleset| - |iiacosh| |mesh?| |euclideanSize| |zeroDimPrimary?| - |factorGroebnerBasis| |infinityNorm| |LiePolyIfCan| - |numericalIntegration| |simplify| |c06ebf| |s17aef| |coord| |pushdown| - |controlPanel| |rightTraceMatrix| |definingInequation| - |divideExponents| |curve| |physicalLength!| |internal?| |bothWays| - |janko2| |normalize| |univariatePolynomials| |lastSubResultant| - |OMputEndApp| |suchThat| |localIntegralBasis| |basisOfCenter| |f04mbf| - |fixedPoint| |decomposeFunc| |s14baf| |pleskenSplit| |reduction| - |fortranLinkerArgs| |position| |getSyntaxFormsFromFile| |csc2sin| - |oneDimensionalArray| |cAcoth| |readUInt8!| |solve| |unknown| - |reducedDiscriminant| |OMwrite| |options| |insert| |realEigenvalues| - |log| |zCoord| |OMUnknownSymbol?| |subSet| |traverse| |bits| |iiabs| - |parent| |innerSolve| |subst| |asinhIfCan| |integer?| |reorder| - |swap!| |setrest!| |setRealSteps| |pdct| |wholeRadix| |string| - |goodPoint| |genericLeftTrace| |epilogue| |graphs| |setIntersection| - |sh| |iCompose| |dominantTerm| |intPatternMatch| |entries| |algint| - |univariatePolynomialsGcds| |basisOfMiddleNucleus| |isImplies| |size| - |shellSort| |stoseLastSubResultant| |transcendenceDegree| - |normalizedAssociate| |nullity| |close!| |euclideanGroebner| |conical| - |zeroSetSplit| |removeCosSq| |squareFreeFactors| |bipolarCylindrical| - |someBasis| |getOperator| |car| |systemCommand| |objects| |upperCase?| - |makeSin| |totolex| |primPartElseUnitCanonical!| |seriesToOutputForm| - |OMgetError| |cschIfCan| |range| |specialTrigs| |base| - |clipWithRanges| |d01amf| |signatureAst| |consnewpol| |deepExpand| - |f04maf| |readInt16!| |spherical| |lieAlgebra?| |normal| - |linearAssociatedOrder| |row| |completeEval| |makeCos| |OMgetApp| - |supersub| |denomRicDE| |algebraicOf| |predicate| |nextPrime| - |weighted| |hexDigit| |minimumDegree| |fortranLogical| - |normInvertible?| |rename| |fixedPointExquo| |close| |acscIfCan| - |roughUnitIdeal?| |front| |reseed| |rewriteIdealWithHeadRemainder| - |float?| |submod| |permutationGroup| |init| |arrayStack| - |readLineIfCan!| |OMgetEndBVar| |loadNativeModule| |OMputEndError| - |logGamma| |sumOfKthPowerDivisors| |palgextint| |trigs| |display| - |isConnected?| |pr2dmp| |revert| |less?| |wholeRagits| - |mainPrimitivePart| |node| |leftCharacteristicPolynomial| |ParCond| - |updateStatus!| |formula| |putColorInfo| - |purelyAlgebraicLeadingMonomial?| |upperCase| |associator| - |evenInfiniteProduct| |delta| |leftNorm| |f04qaf| |s17aff| |normalise| - |nextsousResultant2| |shallowExpand| |initiallyReduce| |polygon| - |rootDirectory| |pmComplexintegrate| |deepestTail| |approxSqrt| - |argument| |sum| |mainDefiningPolynomial| |f01bsf| |returnType!| |is?| - |cot2trig| |LiePoly| |upDateBranches| |c06ecf| |mainCharacterization| - |cAcosh| |entry?| |leftLcm| |f01ref| |last| |input| |externalList| - |diag| |s21bbf| |assoc| |cRationalPower| |previous| |nrows| - |parameters| |delete| |coerceL| |OMopenString| |normalDeriv| - |cyclicEntries| |library| |alternative?| |title| |exp1| |s17ajf| - |possiblyNewVariety?| |ncols| |eq?| |extract!| |stopTableInvSet!| - |separate| |inverseLaplace| |ranges| |lexico| |figureUnits| |gethi| - |viewPosDefault| |complexSolve| |bumptab1| |twist| - |resetAttributeButtons| |removeSuperfluousCases| |OMputEndBind| |eq| - |diff| |quadraticForm| |setPoly| |empty| |cap| |swapColumns!| - |setStatus| |lazyIntegrate| |indices| |iter| |radicalEigenvalues| - |twoFactor| |homogeneous?| |typeLists| |complexEigenvectors| |message| - |unprotectedRemoveRedundantFactors| |log2| |listOfLists| - |standardBasisOfCyclicSubmodule| |generalizedEigenvector| - |jordanAdmissible?| |e04ycf| |collectUpper| |absolutelyIrreducible?| - |create3Space| |f02ajf| |signAround| |packageCall| - |subQuasiComponent?| |fortranLiteralLine| |rangeIsFinite| - |endSubProgram| |coth2tanh| |cubic| |OMputBVar| |recoverAfterFail| - |unitCanonical| |contractSolve| |linearAssociatedExp| |f04adf| - |polygamma| |collectUnder| |bezoutResultant| |palgint| |jvmAbstract| - |rightExactQuotient| |categoryMode| |infiniteProduct| |reduceLODE| - |cartesian| |setEmpty!| |crest| |c06fpf| |leftQuotient| |redpps| - |simplifyLog| |jvmTransient| |string?| |maxdeg| |crushedSet| - |stosePrepareSubResAlgo| |LazardQuotient2| |asimpson| |cTanh| |root| - |d02bbf| |constDsolve| |partition| |orthonormalBasis| |inspect| - |const| |unexpand| |iiasin| |iExquo| |modifyPointData| |intcompBasis| - |tRange| |midpoint| |eulerE| |drawComplex| |tubeRadiusDefault| - |rightUnit| |rightMinimalPolynomial| |acschIfCan| |leftReducedSystem| - |generalTwoFactor| |innerint| |fortranCompilerName| |jvmStatic| - |hasTopPredicate?| |internalSubPolSet?| |internalSubQuasiComponent?| - |taylorRep| |dictionary| |whileLoop| |removeRedundantFactors| - |withPredicates| |elementary| |showTheSymbolTable| |OMgetVariable| - |binaryTree| |commutativeEquality| |delay| |integralLastSubResultant| - |varList| |associatedSystem| |jvmInterface| |number?| |f02wef| - |internalInfRittWu?| |rischNormalize| |hitherPlane| |lazy?| - |cyclePartition| |irreducible?| |f04mcf| |legendreP| |changeBase| - |f04faf| |chineseRemainder| |OMgetEndApp| |wordInGenerators| - |realZeros| |invmultisect| |writeUInt8!| |constantOpIfCan| |rk4f| - |exponential| |write| |jokerMode| |rspace| |leftMult| |pair?| - |realEigenvectors| |linGenPos| |cylindrical| |nextItem| - |integralDerivationMatrix| |save| |simplifyPower| |decompose| - |pushuconst| |messagePrint| |mapExponents| |characteristicPolynomial| - |addPoint| |order| |green| |d01anf| |headReduced?| |laurentRep| - |viewport2D| |SturmHabichtSequence| |topPredicate| |iidprod| - |leadingTerm| |ode| |leftUnits| |polyred| |removeSquaresIfCan| - |repeating| |s14aaf| |rem| |associative?| |f04asf| |s15aef| |elliptic| - |iiasech| |c06gqf| |subResultantChain| |vedf2vef| |elem?| - |aspFilename| |quo| |rightOne| |makeop| |leftDivide| |blue| - |convergents| |bitTruth| |f02abf| |factorSFBRlcUnit| |partialFraction| - |contains?| |yCoord| |componentUpperBound| |truncate| |ksec| - |extractBottom!| |regularRepresentation| |noKaratsuba| |explogs2trigs| - |setPredicates| |optional?| |div| |binomial| |moduloP| |tanh2coth| - |interpolate| |getRef| |d02bhf| |complexEigenvalues| |sts2stst| - |symmetricDifference| |exquo| |triangular?| |setErrorBound| |s01eaf| - |setButtonValue| |OMreceive| |leftFactor| |tracePowMod| |iomode| - |space| ~= |setProperties| |cycleElt| |coerceS| |depth| |s17def| - |weakBiRank| |patternVariable| |weight| |expandPower| |gensym| |#| - |iiatan| |sturmVariationsOf| |lazyIrreducibleFactors| |biRank| - |genericLeftTraceForm| |OMputApp| |domainTemplate| |makeEq| - |realSolve| ~ |read!| |critBonD| |randnum| |oblateSpheroidal| - |OMputInteger| |maxrank| |unit?| |d01ajf| |generalPosition| |pastel| - |powmod| |s17dhf| |multMonom| |support| |scripted?| - |topFortranOutputStack| |ptFunc| |setUnion| |splitSquarefree| |recur| - |invertIfCan| |e02dcf| |palgintegrate| |tanh2trigh| |f02bbf| |rotate| - |deleteProperty!| |/\\| |setLabelValue| |abelianGroup| |roughBase?| - |critT| |hconcat| |fractRagits| |setClipValue| |fortranDoubleComplex| - |quadraticNorm| |\\/| |eigenMatrix| |squareFreeLexTriangular| - |getBadValues| |symbolIfCan| |cAcot| |Is| FG2F |evaluate| |content| - |numberOfIrreduciblePoly| |variable| |cycleTail| |mainExpression| - |numberOfComposites| |arg1| |cAsin| |merge| - |genericRightMinimalPolynomial| |setref| |listRepresentation| - |pointLists| |iterators| |algSplitSimple| |algebraicCoefficients?| - |pair| |gcdPolynomial| |arg2| |connectTo| |assign| |curry| |getMatch| - |seed| |var1Steps| |semiResultantEuclidean2| |graphStates| - |makeViewport3D| |charthRoot| |makeprod| |extractTop!| - |degreeSubResultantEuclidean| |monicDivide| |fortranReal| |e02def| - |fixedDivisor| |leadingIndex| |conditions| |goto| |sqfrFactor| - |basisOfRightAnnihilator| |iitanh| |setFieldInfo| |characteristicSet| - |gderiv| |newSubProgram| |OMputAtp| |match| |youngGroup| - |selectSumOfSquaresRoutines| |expenseOfEvaluationIF| |isExpt| |plot| - |zeroDimensional?| |rightRemainder| |tableau| - |createNormalPrimitivePoly| |cAtanh| |isAbsolutelyIrreducible?| - |anfactor| |asecIfCan| |patternMatchTimes| |prepareSubResAlgo| - |jvmStringConstantTag| |cos2sec| |palgRDE| |constantLeft| |connect| - |swap| |removeRedundantFactorsInContents| |commutator| |true| - |OMclose| |makeYoungTableau| |nativeModuleExtension| - |genericLeftMinimalPolynomial| |zeroOf| |resultantEuclideannaif| - |cCosh| |toseSquareFreePart| |asinIfCan| |idealiserMatrix| |printInfo| - |OMputEndAtp| |Frobenius| |e02ddf| |deepestInitial| |cycleEntry| - |part?| |lowerBound| |checkForZero| |solveRetract| |lflimitedint| - |insertionSort!| |quasiAlgebraicSet| |rightTrim| |constantOperator| - |pointColor| |isOpen?| |extractIfCan| |jvmPrivate| - |jvmUTF8ConstantTag| |environment| |mix| |newLine| |leftTrim| - |associatorDependence| |constantRight| |elements| |simplifyExp| - |halfExtendedSubResultantGcd2| |ListOfTerms| |quasiMonicPolynomials| - |antiAssociative?| |inc| |singleFactorBound| |palgLODE| |select!| - |dimensionOfIrreducibleRepresentation| |binary| |univariate?| - |createNormalElement| |fortranInteger| |moduleSum| |update| - |cyclotomic| |rewriteSetByReducingWithParticularGenerators| - |tryFunctionalDecomposition?| |B1solve| |times!| |radicalSimplify| - |iisinh| |LyndonWordsList| |duplicates| |byteBuffer| - |symmetricProduct| |conjugates| |euler| |inputBinaryFile| |legendre| - |rootOf| |setright!| |primeFactor| |removeDuplicates!| |headRemainder| - |invertible?| |outputBinaryFile| |shade| |f02aff| |leviCivitaSymbol| - |subResultantsChain| |airyBi| |module| |f04jgf| |getIdentifier| - |setOrder| |attributeData| |multiset| |leastAffineMultiple| - |youngDiagram| |superHeight| |mantissa| |mainKernel| |autoReduced?| - |antiCommutative?| |localAbs| |e04ucf| |diophantineSystem| |e02ajf| - |s19aaf| |definingPolynomial| |factors| |SturmHabichtCoefficients| - |ratPoly| |s19acf| |isEquiv| |set| |makeSeries| |cCoth| |debug| - |deepCopy| |pointColorDefault| |linearMatrix| |cCos| |nullary?| - |rightZero| |open| |OMUnknownCD?| |precision| |debug3D| |besselI| - |graphImage| D |doubleDisc| |irCtor| |jvmClassConstantTag| |child| - |reduceByQuasiMonic| |radix| |contours| |palglimint0| |rootKerSimp| - |d03faf| |multiEuclidean| |vectorise| |lexGroebner| |exponents| |isOr| - |edf2efi| |leftRemainder| |physicalLength| |sdf2lst| |plotPolar| - |birth| |escape| |transpose| |quasiRegular?| |factorials| - |totalDifferential| |s17akf| |imaginary| |adjoint| |leftExactQuotient| - |operations| |semiSubResultantGcdEuclidean2| |infix| |acosIfCan| - |constantIfCan| |match?| |decrease| |showArrayValues| |primaryDecomp| - |enqueue!| |usingTable?| |normalizeIfCan| |splitNodeOf!| |cfirst| - |halfExtendedResultant1| |unparse| |laurentIfCan| |rightUnits| - |OMsend| |factorSquareFreeByRecursion| |bitCoef| |indicialEquation| - |solveLinear| |script| |primintegrate| |symmetricGroup| |every?| - |ODESolve| |rewriteIdealWithQuasiMonicGenerators| |stop| |pquo| - |HermiteIntegrate| |coHeight| |leftPower| |rowEchelonLocal| - |resultantReduit| |wordsForStrongGenerators| |round| |signature| - |complexNormalize| |singularAtInfinity?| |partialNumerators| - |exprHasLogarithmicWeights| |lazyResidueClass| |sumSquares| |null| - |deleteRoutine!| |radicalSolve| |sample| |central?| |pmintegrate| - |nextPrimitivePoly| |bubbleSort!| |selectPolynomials| |tanAn| |tex| - |setClosed| |horizontalTab| |integralRepresents| |not| |exists?| - |print| |extension| |selectODEIVPRoutines| |iiperm| |isQuotient| - |delete!| |torsion?| |factorByRecursion| |unravel| |and| - |retractIfCan| |resolve| |removeSinhSq| |exprToGenUPS| - |fortranCarriageReturn| |beauzamyBound| |sequence| |resetBadValues| - |curve?| |setfirst!| |or| |exprHasWeightCosWXorSinWX| |sorted?| - |taylorQuoByVar| |prime?| |sylvesterSequence| |ramified?| |laplace| - |bumptab| |rightFactorIfCan| |xor| |rotatez| |subHeight| - |setScreenResolution3D| |ode1| |dihedral| |any| |iterationVar| - |semicolonSeparate| |even?| |UpTriBddDenomInv| |computeCycleEntry| - |torsionIfCan| |firstSubsetGray| |jvmInterfaceMethodConstantTag| - |s13acf| |split| |subtractIfCan| |medialSet| |iicos| |polCase| - |rightExtendedGcd| |shape| |comp| |totalfract| |singularitiesOf| - |identity| |height| |headReduce| |listLoops| |vconcat| |numer| |hclf| - |minimalPolynomial| |setsubMatrix!| |dark| |rk4a| |assert| - |pointColorPalette| |lSpaceBasis| |just| |table| |besselK| |denom| - |ParCondList| |semiResultantEuclidean1| |besselY| |coefficient| - |failed| |rischDE| |readInt8!| |secIfCan| |toseInvertible?| |iicsch| - |basisOfCommutingElements| |inf| |binaryTournament| |startTableGcd!| - |findBinding| |squareFreePart| |genericRightTraceForm| |getGraph| - |e04mbf| |pi| |categoryFrame| |cond| |bitLength| |measure| - |lastSubResultantElseSplit| |branchPoint?| |saturate| |positive?| - |newTypeLists| |new| |createMultiplicationMatrix| |infinity| - |integral?| |prime| |digit| |rectangularMatrix| |capacity| |qPot| - |clipBoolean| |bernoulli| |intensity| |createIrreduciblePoly| - |roughBasicSet| |tubePointsDefault| |dimension| |condition| |simpson| - |directory| |bracket| |deriv| |bat1| |minus!| |normalForm| |inverse| - |flexibleArray| |s20adf| |dualSignature| |tube| |iicosh| |quartic| - |kernel| |normalDenom| |lift| |graeffe| |mirror| |polarCoordinates| - |rightPower| |exptMod| |jvmNameAndTypeConstantTag| |eigenvalues| - |setMinPoints3D| |inGroundField?| |functionIsContinuousAtEndPoints| - |list| |reduce| |getConstant| |members| |primitiveElement| - |chainSubResultants| |ellipticCylindrical| |genericPosition| |draw| - |cCsc| |option?| |rightDiscriminant| |f02axf| |continuedFraction| - |symbolTable| |has?| |shallowCopy| |df2ef| |OMsetEncoding| |checkRur| - |tower| |moreAlgebraic?| |size?| |tanIfCan| |component| |nextColeman| - |formfeed| ** |pToHdmp| |intersect| |rightQuotient| |lowerCase| - |operators| |exprToUPS| |semiLastSubResultantEuclidean| - |LowTriBddDenomInv| |genericRightDiscriminant| |host| - |pushFortranOutputStack| |pointData| |initiallyReduced?| |bfEntry| - |jvmVolatile| |explimitedint| |monicModulo| |left| |coordinates| - |viewDeltaXDefault| |primintfldpoly| |popFortranOutputStack| - |bombieriNorm| |primextendedint| |mergeDifference| |hspace| |constant| - |mapSolve| |jvmSuper| |removeZeroes| |matrixDimensions| |right| - |makeObject| |transform| |ratDenom| |outputAsFortran| |rightDivide| - |units| |SFunction| |stopTable!| |getOperands| |voidMode| |normal?| - |listOfMonoms| |OMputBind| |coef| |zero| |lowerCase?| |pushup| - |critMTonD1| |s17dgf| |generic?| |numerators| |double| |Vectorise| - |eyeDistance| |tValues| |iiasec| |makeGraphImage| |lifting1| |powern| - |nil?| |showSummary| |createLowComplexityNormalBasis| |nil| - |complexNumeric| |cosSinInfo| |OMgetInteger| |subCase?| |f01brf| - |integralMatrixAtInfinity| |And| |meshPar2Var| |multiplyExponents| - |expIfCan| |removeSinSq| |qualifier| |matrix| |increment| - |showFortranOutputStack| |scale| |constant?| |fortranComplex| |Or| - |concat| |rangePascalTriangle| |conjug| |sPol| |writeBytes!| - |systemSizeIF| |kernels| |showAttributes| |firstDenom| |bigEndian| - |matrixGcd| |laplacian| |ravel| |code| |Not| |fglmIfCan| - |LagrangeInterpolation| |curveColorPalette| |cosIfCan| |polyPart| - |operator| |approximate| |next| |lazyPremWithDefault| |e01daf| - |algDsolve| |OMputVariable| |reshape| |rightRecip| |regime| - |semiDegreeSubResultantEuclidean| |collect| |complex| - |innerEigenvectors| |univariate| |substring?| |weights| - |sizePascalTriangle| |polyRDE| |d01alf| |d02raf| |opeval| - |lexTriangular| |createGenericMatrix| |expint| |complement| - |fullDisplay| |preprocess| |continue| |OMgetBVar| |byte| |result| - |overbar| |quotientByP| |s18aff| |slash| F2FG |suffix?| |listBranches| - |declare!| |unknownEndian| |rarrow| |equiv| |parts| |setprevious!| - |iiacot| |PDESolve| |quasiComponent| |selectFiniteRoutines| |factor| - |nary?| |integralAtInfinity?| |minPol| |rdHack1| |vector| - |removeRoughlyRedundantFactorsInPols| |KrullNumber| |paraboloidal| - |cyclic?| |cTan| |sqrt| |prefix?| |imagJ| |solveInField| |triangSolve| - |conditionsForIdempotents| |prefix| |differentiate| |f02agf| - |geometric| |cyclicEqual?| |clipSurface| |discriminantEuclidean| - |real| |integralBasis| |rationalIfCan| |symbol| - |countRealRootsMultiple| |degree| |maxPoints3D| |selectPDERoutines| - |noncommutativeJordanAlgebra?| |factorList| |tanQ| |imag| - |coercePreimagesImages| |OMgetAtp| |leftGcd| |expression| |imagj| - |d01aqf| |numericIfCan| |gramschmidt| |monicDecomposeIfCan| - |getMultiplicationTable| |directProduct| |jacobi| |oddlambert| - |nthRootIfCan| |integer| |extendedEuclidean| |char| - |complexElementary| |viewpoint| |chvar| |universe| |redPo| |gbasis| - |bipolar| |bytes| |problemPoints| |int| |hyperelliptic| |prindINFO| - |semiDiscriminantEuclidean| |tab1| |one?| |brace| |ratDsolve| - |segment| |denominators| |decimal| |element?| |sup| |subTriSet?| - |irreducibleFactor| |nullary| |An| |infix?| |destruct| |dom| - |putProperties| |subscriptedVariables| |untab| |s13adf| |postfix| - |dmpToHdmp| |changeMeasure| |BumInSepFFE| |frobenius| |mask| |obj| - |scan| |leadingIdeal| |rubiksGroup| |pushNewContour| |morphism| - |randomLC| |isNot| |float| |atrapezoidal| |rCoord| |e04jaf| - |curryRight| |tensorProduct| |e01bef| |contract| |cyclicSubmodule| - |OMgetEndAttr| |subspace| |flagFactor| |op| |OMputAttr| |outputFixed| - |trigs2explogs| |ricDsolve| |cyclic| |squareFreePolynomial| - |tableForDiscreteLogarithm| |endOfFile?| |setMaxPoints| |monomial| - |power!| |octon| |alternating| |nothing| |acotIfCan| |unvectorise| - |df2fi| |adaptive| |lagrange| |numberOfOperations| |multivariate| |sn| - |monomialIntPoly| |constantKernel| |open?| |nextPrimitiveNormalPoly| - |stoseInvertible?sqfreg| |mapUnivariate| |mapUnivariateIfCan| |iidsum| - |normalized?| |variables| |branchIfCan| |Hausdorff| - |associatedEquations| |zeroSquareMatrix| |red| |polynomialZeros| - |status| |sech2cosh| |replace| |computeInt| |mathieu11| |mapDown!| - |changeName| |bsolve| |optimize| |commaSeparate| |isList| - |getMultiplicationMatrix| |create| |ffactor| |getZechTable| - |henselFact| |relationsIdeal| |interval| |color| |lfunc| |wreath| - |makeFR| |writeLine!| |outputGeneral| |leaves| |argscript| |iiacoth| - |s19abf| GE |monic?| |viewThetaDefault| |infieldint| |routines| - |f01qef| |groebnerIdeal| |lfextendedint| |returnTypeOf| |sizeLess?| GT - |center| |quotedOperators| |cPower| |isobaric?| |taylor| - |enterPointData| |qfactor| |meshFun2Var| |outputForm| |binaryFunction| - LE |chebyshevT| |basis| |bivariate?| |laurent| |makeFloatFunction| - |completeSmith| |leftUnit| |clipPointsDefault| |c02agf| |c06ekf| - |mainMonomial| |f02bjf| LT |probablyZeroDim?| |cscIfCan| |sinh2csch| - |puiseux| |brillhartTrials| |var1StepsDefault| |totalLex| |Beta| - |leadingExponent| |vspace| |enumerate| |modTree| |distribute| - |moebiusMu| |mindegTerm| |kmax| |bivariateSLPEBR| |localUnquote| - |OMencodingUnknown| |selectAndPolynomials| |terms| |commonDenominator| - |orbit| |inv| |integralBasisAtInfinity| |axesColorDefault| |direction| - |summation| |mapMatrixIfCan| |rombergo| |iteratedInitials| |Gamma| - |droot| |ground?| |typeList| |ratpart| |groebner| |polygon?| |binding| - |categories| |OMputSymbol| |hasHi| |setProperty| |updatF| - |minimumExponent| |ground| |internalZeroSetSplit| |makeSketch| |mvar| - |graphCurves| |pol| |rightRank| |outputAsTex| |disjunction| |tan2cot| - |exQuo| |output| |radPoly| |leadingMonomial| |primeFrobenius| - |showScalarValues| |realRoots| |associates?| |showTheFTable| |cycle| - |test| |s21bcf| |lastSubResultantEuclidean| |arity| - |leadingCoefficient| UTS2UP |hash| |tryFunctionalDecomposition| - |OMencodingXML| |lazyGintegrate| |quasiRegular| |mainValue| - |halfExtendedSubResultantGcd1| |setRow!| |nthCoef| |count| - |primitiveMonomials| |splitConstant| |listexp| |increase| |alphabetic| - |pushucoef| |smith| |square?| |quoByVar| |f07aef| |froot| |reductum| - |useSingleFactorBound| |setScreenResolution| |nonSingularModel| - |overset?| |search| |c05adf| |resize| |drawComplexVectorField| - |isTimes| |OMReadError?| |distance| |lllip| |approxNthRoot| |e01baf| - |OMmakeConn| |characteristicSerie| |invmod| |region| |complexZeros| - |dec| |finite?| |iisqrt3| |rur| |lazyPquo| |stronglyReduced?| |dflist| - |acothIfCan| |startTable!| |fortranTypeOf| |function| |psolve| - |points| |divergence| |roman| |sylvesterMatrix| |lookupFunction| - |derivative| |solid| |nonQsign| |accuracyIF| |monomials| |putGraph| - |primitive?| |addBadValue| |zoom| |partialQuotients| |f01qcf| - |mergeFactors| |jvmMethodrefConstantTag| |pop!| |solve1| |csch2sinh| - |lazyVariations| |genericLeftDiscriminant| |leftOne| |nodeOf?| - |rightAlternative?| |SturmHabichtMultiple| |doubleResultant| |primes| - |karatsuba| |leftZero| |elseBranch| |countRealRoots| - |nextsubResultant2| |expenseOfEvaluation| |backOldPos| - |clipParametric| |quotient| |c05nbf| |expt| |blankSeparate| - |subPolSet?| |sinhIfCan| |shiftLeft| |HenselLift| |intChoose| - |createPrimitiveNormalPoly| |OMgetBind| |maxint| |maxrow| |zeroVector| - |retractable?| |initTable!| |bit?| |ddFact| |palglimint| |negative?| - |rewriteIdealWithRemainder| |plusInfinity| |repSq| |fixPredicate| - |pdf2ef| |linears| |elaborate| |getButtonValue| |goodnessOfFit| - |squareTop| |rename!| |graphState| |minusInfinity| |quickSort| - |minset| |copies| |getCode| |predicates| |printStatement| - |complexLimit| |duplicates?| |d01fcf| |e04naf| |leftDiscriminant| - |quote| |identityMatrix| |chiSquare| |belong?| |character?| |makeTerm| - |cyclicCopy| |countable?| |shufflein| |rowEch| |determinant| - |readUInt16!| |multiplyCoefficients| |irVar| |coerceListOfPairs| - |moebius| |middle| |qinterval| |RittWuCompare| |lp| - |exteriorDifferential| |setImagSteps| |infieldIntegrate| |real?| - |setMinPoints| |label| |factorOfDegree| |e02adf| |stFunc2| |ran| - |mappingAst| |integralCoordinates| |lfintegrate| |cup| - |leadingBasisTerm| |pdf2df| |lcm| |type| |e01bhf| - |setLegalFortranSourceExtensions| |recip| |useEisensteinCriterion| - |monicRightFactorIfCan| |critpOrder| |compactFraction| |cdr| - |subResultantGcd| |jvmFieldrefConstantTag| |gcdPrimitive| |writable?| - |cSinh| |knownInfBasis| |curryLeft| |principalAncestors| |rightLcm| - |getMeasure| |push| |divideIfCan!| |currentEnv| |gcd| - |leftMinimalPolynomial| |OMunhandledSymbol| |limitPlus| |bottom!| - |updatD| |freeOf?| |reducedForm| |stFunc1| |finiteBound| |cAcos| - |e01sbf| |false| |horizConcat| |highCommonTerms| |nilFactor| - |OMputString| |uniform| |Nul| |createPrimitiveElement| |optAttributes| - |mapExpon| |btwFact| |recolor| |overlabel| |minRowIndex| - |removeDuplicates| |getProperty| |unitNormalize| |clip| - |restorePrecision| |f01rdf| |Lazard| |maximumExponent| EQ |option| - |unrankImproperPartitions0| |wordInStrongGenerators| |exactQuotient| - |pade| |permanent| |generators| |startTableInvSet!| |df2st| |head| - |integralMatrix| |fortran| |linearlyDependentOverZ?| - |structuralConstants| |children| |diagonalMatrix| |closedCurve?| - |concat!| |alphanumeric| |readIfCan!| |stiffnessAndStabilityOfODEIF| - |cAcsch| |ramifiedAtInfinity?| |f02akf| |getProperties| - |jordanAlgebra?| |cAsec| |extractSplittingLeaf| |setStatus!| |iicoth| - |decreasePrecision| |linearPart| |lazyPseudoDivide| |addPointLast| - |firstNumer| |maxIndex| |linearPolynomials| |palgRDE0| |rational?| - |interpret| |retract| |testModulus| |makeMulti| |keys| |patternMatch| - |discriminant| |setAdaptive| |fi2df| |prod| |getOrder| - |nthFractionalTerm| |xCoord| |reflect| |antiCommutator| |commutative?| - |virtualDegree| |monomial?| |mainVariable?| |socf2socdf| |tanSum| - |sinhcosh| |dimensions| |groebnerFactorize| |s17dlf| |mdeg| - |replaceKthElement| |tubePlot| |explicitlyFinite?| |d01gaf| - |principalIdeal| |findConstructor| |f07fdf| |critM| - |currentSubProgram| |radicalRoots| |elliptic?| |iprint| - |generalizedContinuumHypothesisAssumed| |entry| |ef2edf| - |lfinfieldint| |d02ejf| 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|f07fef| - |createNormalPoly| |linearDependence| |mapGen| |getPickedPoints| - |setOfMinN| |cot2tan| |charClass| |hcrf| |abs| |insertBottom!| |eof?| - |clearFortranOutputStack| |rotate!| |palginfieldint| |OMputError| - |ord| |limitedIntegrate| |c05pbf| |e02bdf| |showTheIFTable| - |palgextint0| |cross| |defineProperty| |powerAssociative?| |tablePow| - |selectMultiDimensionalRoutines| |d02cjf| |f01maf| |exprToXXP| - |integrate| |digit?| |kovacic| |quasiMonic?| |top| |BasicMethod| - |internalIntegrate0| |wrregime| |padicFraction| |ReduceOrder| |ipow| - |rationalPoint?| |bringDown| |node?| |subscript| |initials| |reify| - |f04axf| |fortranLiteral| |unitsColorDefault| |safeCeiling| - |pseudoQuotient| |iisqrt2| |makeCrit| |firstUncouplingMatrix| - |att2Result| |imagk| |squareFreePrim| |rootProduct| |monomRDE| - |lieAdmissible?| |trivialIdeal?| |hermite| |shiftRight| |linefeed| - |mathieu24| |atoms| |fracPart| |linearlyDependent?| |multiple?| - |limit| |f02adf| |linearForm| |nextSublist| |parabolic| - |pointSizeDefault| |compile| |UnVectorise| |floor| |innerSolve1| - |anticoord| |redmat| |exprHasAlgebraicWeight| |rightGcd| |copyInto!| - |resultant| |kroneckerDelta| |removeZero| |f02fjf| |evenlambert| - |eisensteinIrreducible?| |subResultantGcdEuclidean| |style| - |setleaves!| |safetyMargin| |mappingMode| |jacobiIdentity?| |f04arf| - |sortConstraints| |mainCoefficients| |cCot| |nullSpace| |randomR| - |f01qdf| |qelt| |bfKeys| |backspace| |reciprocalPolynomial| - |singular?| |lazyPseudoQuotient| |equality| |extendedint| - |euclideanNormalForm| |linearElement| |qsetelt| |extensionDegree| - |index| |mightHaveRoots| |d03edf| |SturmHabicht| |position!| |pack!| - |cAsech| |norm| |hex| |divisors| |e02ahf| |bag| |xRange| |inR?| - |outlineRender| |tanNa| |viewDeltaYDefault| |adaptive3D?| - |closeComponent| |shuffle| |hexDigit?| |yRange| |fill!| - |currentCategoryFrame| |stirling2| |rationalPoints| |hessian| |trunc| - |before?| |implies| |stoseInvertibleSetreg| |setFormula!| |zRange| - |OMconnectTCP| |selectIntegrationRoutines| |nthFactor| - |fractionFreeGauss!| |reducedQPowers| |squareFree| |e04gcf| - |denomLODE| |name| |point?| |map!| |s17ahf| |integerBound| |addMatch| - |extractPoint| |bumprow| |construct| |fTable| |changeVar| |mkIntegral| - |reverseLex| |body| |meatAxe| |qsetelt!| |complexForm| - |fullPartialFraction| |expandLog| |thenBranch| |mainVariable| - |iiatanh| |iflist2Result| |singRicDE| |badValues| |in?| |sort!| - |surface| |monicRightDivide| |karatsubaOnce| |differentialVariables| - |squareMatrix| |inrootof| |rst| |resultantnaif| |lprop| - |unrankImproperPartitions1| |leadingSupport| |modularGcdPrimitive| - |readBytes!| |fractionPart| |d01akf| |ScanRoman| |expintfldpoly| - |adaptive?| |makeResult| |comment| |subMatrix| |imagI| - |useEisensteinCriterion?| |lllp| |pomopo!| |encodingDirectory| SEGMENT - |padicallyExpand| UP2UTS |e02zaf| |invertibleSet| |charpol| |nthr| - |s15adf| |subNodeOf?| |nlde| |var2StepsDefault| |getVariableOrder| - |comparison| |printHeader| |cycleRagits| |imports| |acsch| - |composites| |triangularSystems| |mkAnswer| |setMaxPoints3D| - |basisOfRightNucloid| |initial| |tanintegrate| |expextendedint| - |intermediateResultsIF| |cardinality| |stack| |rootPower| |iiacos| - |e02daf| |hostPlatform| |qroot| |whitePoint| |alphabetic?| |htrigs| - |createThreeSpace| |s17adf| |s18def| |partialDenominators| |pureLex| - |alphanumeric?| |presub| |bandedJacobian| |normal01| |localReal?| - |trapezoidal| |port| |satisfy?| |unary?| |lazyPseudoRemainder| - |setValue!| |iipow| |representationType| |tree| |dn| - |monicCompleteDecompose| |find| |midpoints| |numberOfComputedEntries| - |clearCache| |seriesSolve| |leftExtendedGcd| |dmp2rfi| |zeroDim?| - |ceiling| |ocf2ocdf| |optpair| |iisin| |addPoint2| |compose| - |rationalPower| |GospersMethod| |fintegrate| |cyclotomicDecomposition| - |irDef| |harmonic| |alternatingGroup| |represents| |tan2trig| - |pascalTriangle| |lighting| |isOp| |ptree| |d01apf| |prem| |error| - |rational| |extendIfCan| |logical?| |inHallBasis?| - |identitySquareMatrix| |lepol| |verticalTab| |integers| |iisec| - |outputArgs| |f01rcf| |more?| |viewWriteDefault| |laguerreL| - |strongGenerators| |readInt32!| |selectNonFiniteRoutines| - |basisOfCentroid| |gcdcofactprim| |approximants| |maxColIndex| - |idealiser| |s17dcf| |stoseInternalLastSubResultant| |gcdcofact| - |internalAugment| |conditionP| |polyRicDE| |numberOfPrimitivePoly| - |powers| |OMgetAttr| |toseLastSubResultant| |multiEuclideanTree| - |rightRegularRepresentation| |extendedSubResultantGcd| |aLinear| - |f01mcf| |allRootsOf| |irForm| |df2mf| |c06eaf| |setTopPredicate| - |cyclicGroup| |sin2csc| |chiSquare1| |cycleLength| |modulus| |move| - |dioSolve| |changeThreshhold| |ref| |f02xef| |largest| |generic| - |startStats!| |fractRadix| |userOrdered?| |iitan| |variable?| - |myDegree| |top!| |dihedralGroup| |s18dcf| |skewSFunction| |point| - |split!| |getDatabase| |pointPlot| |elRow2!| |primitivePart!| |rule| - |generalizedEigenvectors| |edf2ef| |sizeMultiplication| |s18acf| - |OMencodingSGML| |internalDecompose| |curveColor| |OMputFloat| |cAcsc| - |mainMonomials| |sequences| |bivariatePolynomials| |OMsupportsSymbol?| - |stoseInvertibleSetsqfreg| |write!| |expressIdealMember| |setPosition| - |typeForm| |expPot| |extend| |getStream| |variationOfParameters| - |gradient| |whatInfinity| |eval| |indiceSubResultantEuclidean| - |removeRoughlyRedundantFactorsInPol| |completeHensel| |inRadical?| - |nodes| |lambda| |OMreadStr| |lazyPrem| |series| |coshIfCan| - |numberOfImproperPartitions| |listConjugateBases| |quadratic| |reset| - |numberOfVariables| |symbolTableOf| |groebner?| |trailingCoefficient| - |generalInfiniteProduct| |rootNormalize| |totalDegree| |pushdterm| - |over| |fortranCharacter| |derivationCoordinates| |equation| |makeSUP| - |transcendent?| |Ei| |prefixRagits| |iifact| |leadingCoefficientRicDE| - |cotIfCan| |orbits| |univariateSolve| |insertRoot!| |setnext!| - |oddintegers| |viewPhiDefault| |musserTrials| |c06gsf| |tubePoints| - |aCubic| |root?| |s17acf| |relativeApprox| |readUInt32!| |modularGcd| - |solveLinearPolynomialEquationByFractions| |lineColorDefault| - |modularFactor| |factorset| |forLoop| |wronskianMatrix| |map| |min| - |toseInvertibleSet| |stirling1| |symbol?| |mapCoef| |f02aaf| - |arguments| |antisymmetricTensors| |cosh2sech| |sumOfSquares| - |infLex?| |stripCommentsAndBlanks| |createLowComplexityTable| - |symmetricTensors| |iicsc| |mathieu23| |scaleRoots| |clearTheIFTable| - |drawToScale| |mindeg| |rightScalarTimes!| |trim| - |factorsOfCyclicGroupSize| |nextIrreduciblePoly| |positiveSolve| - |complete| |removeCoshSq| |groebSolve| |s19adf| |show| |cn| |rank| - |interactiveEnv| |ScanFloatIgnoreSpacesIfCan| |genericRightNorm| - |mainContent| |relerror| |void| |reindex| |critB| |scalarTypeOf| - |supRittWu?| |prinshINFO| |unaryFunction| |startPolynomial| |distFact| - |extendedResultant| |OMconnInDevice| |perfectSquare?| - |screenResolution3D| |colorDef| |OMgetFloat| |sub| |rotatex| - |rightRankPolynomial| |trace| |setAttributeButtonStep| |macroExpand| - |clearDenominator| |semiIndiceSubResultantEuclidean| - |numberOfChildren| |setchildren!| |convert| |stopMusserTrials| - |showAll?| |frst| |stFuncN| |d01gbf| |areEquivalent?| |acoshIfCan| - |viewSizeDefault| |queue| |extractIndex| |viewDefaults| - |hypergeometric0F1| |cAsinh| |dot| |pow| |aromberg| - |incrementKthElement| BY |normDeriv2| |factorFraction| |minPoints3D| - |sec2cos| |coleman| |leftTraceMatrix| |components| |mulmod| |d03eef| - |OMbindTCP| |interpretString| |isAtom| |weierstrass| |makingStats?| - |getCurve| |symmetricSquare| |calcRanges| |rischDEsys| |yCoordinates| - |composite| |radicalOfLeftTraceForm| |selectfirst| |s21bdf| - |initializeGroupForWordProblem| |s18aef| |OMgetEndObject| - |perspective| |complex?| |d01bbf| |parametersOf| |plus| |imagE| - |permutations| LODO2FUN |bindings| |lists| |balancedFactorisation| - |rewriteSetWithReduction| |ldf2vmf| |selectOptimizationRoutines| - |bandedHessian| |getGoodPrime| |exponential1| |coerce| |leftRecip| - |inverseColeman| |nextNormalPoly| |resultantEuclidean| - |checkPrecision| |OMputEndAttr| |algebraicSort| |iibinom| |powerSum| - |OMsupportsCD?| |degreePartition| |reverse| |possiblyInfinite?| - |mapmult| |degreeSubResultant| |mainSquareFreePart| |complexIntegrate| - |exactQuotient!| |cache| |generalizedInverse| |paren| |lintgcd| - |choosemon| |numFunEvals3D| |combineFeatureCompatibility| |reverse!| - |jvmFloatConstantTag| |times| |factorSquareFreePolynomial| - |interReduce| |jvmIntegerConstantTag| |indicialEquationAtInfinity| - |apply| |minIndex| |indiceSubResultant| |any?| |eulerPhi| NOT - |taylorIfCan| |toroidal| |fortranDouble| |Ci| |leftFactorIfCan| |cLog| - |roughEqualIdeals?| |first| |binomThmExpt| |heap| |perfectNthPower?| - |repeatUntilLoop| F |tubeRadius| OR |append| |swapRows!| |isAnd| - |sin?| |unmakeSUP| |mathieu12| |listYoungTableaus| |rest| |insertTop!| - |setCondition!| |normalizedDivide| |resetVariableOrder| - |evaluateInverse| AND |sqfree| |latex| |symmetricPower| |schema| |po| - |baseRDEsys| |generateIrredPoly| |cothIfCan| |coordinate| - |stronglyReduce| |argumentListOf| |constantToUnaryFunction| - |FormatRoman| |loopPoints| |poisson| |monom| |setvalue!| - |changeNameToObjf| |mapdiv| |trapezoidalo| |screenResolution| - |rootOfIrreduciblePoly| |product| |elaborateFile| |schwerpunkt| - |eigenvectors| |substitute| |c06gbf| |constantCoefficientRicDE| |back| - |high| |divisorCascade| |clearTheSymbolTable| |stoseInvertibleSet| - |prologue| |rotatey| |imagK| |factorial| - |generalizedContinuumHypothesisAssumed?| |separateDegrees| - |quadratic?| |lquo| |conjugate| |indicialEquations| |testDim| - |removeIrreducibleRedundantFactors| |parabolicCylindrical| - |prolateSpheroidal| |halfExtendedResultant2| |common| |bernoulliB| - |readable?| |double?| |setDifference| |mr| |bounds| |generalLambert| - |monomialIntegrate| |linear?| |normalizeAtInfinity| |null?| - |underscore| |infRittWu?| |leastPower| |printTypes| |littleEndian| - |yellow| |pToDmp| |setelt| |fillPascalTriangle| |d02gbf| |OMgetObject| - |showRegion| |value| |exportedOperators| |logpart| |key?| |rdregime| - |digits| |OMgetEndError| |odd?| |copy| |showAllElements| - |printingInfo?| |linSolve| |atom?| |findCycle| |modifyPoint| |edf2df| - |lyndon| |complexNumericIfCan| |Aleph| |chebyshevU| |pole?| - |autoCoerce| |factorAndSplit| |varselect| |flatten| |printStats!| - |zeroMatrix| |leaf?| GF2FG |OMreadFile| |viewZoomDefault| |remove| - |power| |setTex!| |bezoutMatrix| |showIntensityFunctions| |ip4Address| - |OMgetEndAtp| |numberOfHues| |category| |f04atf| |box| |light| - |digamma| |enterInCache| * |parents| |toScale| |lex| - |stiffnessAndStabilityFactor| |genus| |supDimElseRittWu?| |besselJ| - |domain| |sparsityIF| |eigenvector| |nextNormalPrimitivePoly| |Si| - |bright| |scalarMatrix| |elColumn2!| |sign| |leftTrace| - |createRandomElement| |getlo| |argumentList!| |package| |hue| - |nextLatticePermutation| |nthFlag| |iFTable| |setPrologue!| |index?| - |e02bef| |printCode| |e01sef| |rootPoly| |phiCoord| |rowEchelon| - |csubst| |c06frf| = |OMParseError?| |sort| |airyAi| |hMonic| - |permutationRepresentation| |fibonacci| |logIfCan| |discreteLog| - |pseudoRemainder| |e02aef| |reducedSystem| |lambert| |flexible?| - |mathieu22| |hasSolution?| |e02akf| |badNum| |t| |outputAsScript| - |failed?| < |OMgetType| |random| |empty?| |copy!| |d02kef| |OMserve| - |maxPoints| |polar| > |zag| |shrinkable| |generator| |ode2| |cAtan| - |cyclicParents| |dfRange| |explicitEntries?| |e04dgf| |rightTrace| <= - |sincos| |operation| |elRow1!| |closed?| |OMgetEndBind| - |rightFactorCandidate| |addmod| |OMlistSymbols| - |solveLinearPolynomialEquationByRecursion| |asechIfCan| >= - |pseudoDivide| |outputSpacing| |readLine!| |basisOfNucleus| |e02gaf| - |basisOfLeftNucleus| |nextSubsetGray| |remove!| |mpsode| - |makeViewport2D| |doubleFloatFormat| |max| |algebraic?| - |functionIsFracPolynomial?| |changeWeightLevel| |OMopenFile| - |extendedIntegrate| |writeByte!| |cSin| |outerProduct| - |solveLinearlyOverQ| |dAndcExp| |lyndonIfCan| |closedCurve| - |algebraicVariables| + |f02awf| |OMcloseConn| |mat| |deref| |mkPrim| - |jvmStrict| |prevPrime| |purelyTranscendental?| |e02bcf| - |rootsOf| - |baseRDE| |compBound| |subset?| |sinIfCan| |lookup| - |resultantReduitEuclidean| / |limitedint| |expintegrate| |e01bff| - |minPoints| |exponent| |solveid| |groebgen| |cSec| |integral| - |certainlySubVariety?| |block| |removeRedundantFactorsInPols| - |romberg| |credPol| |bat| |minColIndex| |lhs| |nand| |xn| |s13aaf| - |semiResultantReduitEuclidean| |complexRoots| - |createMultiplicationTable| |stoseSquareFreePart| |rootRadius| |rhs| - |arbitrary| |roughSubIdeal?| |incr| |numberOfDivisors| |integerIfCan| - |simpsono| |internalIntegrate| |e| |selectOrPolynomials| |OMgetSymbol| - |basicSet| |currentScope| |hi| |kind| |complexExpand| |univcase| - |infinite?| |rightCharacteristicPolynomial| |compdegd| |f02aef| - |callForm?| |inputOutputBinaryFile| |iiGamma| |leftRank| - |cyclotomicFactorization| |iilog| |c06fuf| |numerator| |insertMatch| - |parametric?| |reopen!| |semiResultantEuclideannaif| |s20acf| - |normalElement| |rroot| |noLinearFactor?| - |removeSuperfluousQuasiComponents| |purelyAlgebraic?| RF2UTS |cCsch| - |jvmDoubleConstantTag| |var2Steps| |declare| |nonLinearPart| - |remainder| |iicot| |zeroDimPrime?| |OMputEndObject| |pile| |rootSimp| - |algintegrate| |conjunction| |trace2PowMod| |dim| |call| |cExp| - |monomRDEsys| |noValueMode| |divideIfCan| |factorsOfDegree| |se2rfi| - |vark| |antisymmetric?| |factorPolynomial| |primPartElseUnitCanonical| - |LyndonBasis| |nil| |infinite| |arbitraryExponent| |approximate| - |complex| |shallowMutable| |canonical| |noetherian| |central| + |Enumeration| |Mapping| |Record| |Union| |eof?| |roughSubIdeal?| + |mulmod| |delta| |port| |integerBound| |sinIfCan| |setStatus| + |showRegion| |asimpson| |optional?| |putColorInfo| |OMUnknownCD?| + |cycles| |OMopenString| |setsubMatrix!| |gcdprim| |nthRoot| |capacity| + |systemSizeIF| |leaves| |matrix| |limit| |modTree| |mapMatrixIfCan| + |intermediateResultsIF| |rationalPoints| |nextLatticePermutation| + |writable?| |subSet| |makeResult| |setTopPredicate| |ODESolve| + |e02ajf| |roughEqualIdeals?| |eigenvalues| + |jvmInterfaceMethodConstantTag| |recur| |complexNumeric| |aQuartic| + |euler| |box| |setleft!| |algintegrate| |c05adf| |s15aef| + |mainVariables| |algebraic?| |alphanumeric| |solveInField| + |semiSubResultantGcdEuclidean1| |lex| |zag| |minimumDegree| + |prindINFO| |indicialEquations| |combineFeatureCompatibility| + |subPolSet?| |e02dff| |goto| |or| |balancedFactorisation| |OMreadStr| + |ipow| |outputMeasure| |lineColorDefault| |prepareDecompose| + |ratDenom| |strongGenerators| |OMencodingBinary| |iicsc| |xor| + |horizontalTab| |cPower| |factorials| |lowerPolynomial| + |lazyIntegrate| |biRank| |previous| |d01apf| |eyeDistance| |lambda| + |halfExtendedSubResultantGcd2| |postfix| |case| |f04faf| + |mainCharacterization| |constantToUnaryFunction| |cCosh| |declare| + |setImagSteps| |cons| |iiGamma| |numberOfDivisors| |d03eef| |f02ajf| + |Zero| |f04arf| |imagi| |realRoots| |tanSum| |apply| |nthExpon| + |s18acf| |minimize| |totolex| |create| |dark| |One| + |exportedOperators| |representationType| |adaptive| |minset| |first| + |OMgetBVar| |distribute| |clearFortranOutputStack| |normalDeriv| + |addMatch| |pToHdmp| |roman| |binomial| |clearDenominator| |rest| + |linear| |purelyAlgebraicLeadingMonomial?| |directSum| |debug3D| + |cardinality| |nthFlag| |lookup| |cSinh| |cTanh| |firstDenom| + |stirling2| |f02adf| |source| |binomThmExpt| |s19aaf| |setMinPoints3D| + |point| |repeating?| |traceMatrix| |thetaCoord| |qPot| |cyclicGroup| + |firstSubsetGray| |polynomial| |rewriteIdealWithQuasiMonicGenerators| + |jvmFloatConstantTag| |rombergo| |functionIsFracPolynomial?| + |sqfrFactor| |invertIfCan| |traverse| |subMatrix| |conjunction| + |toScale| |testDim| |elliptic| |cubic| |iiexp| |readIfCan!| |elt| + |meshPar1Var| |plenaryPower| |totalDifferential| |shrinkable| |target| + |resize| |rightDivide| |sinhIfCan| |ffactor| |series| |mathieu23| |mr| + |legendre| |lazyPrem| |branchPointAtInfinity?| |fortranLogical| + |genericLeftTraceForm| |readInt32!| |prem| |OMbindTCP| |dmpToHdmp| + |isobaric?| |triangSolve| |rationalPoint?| |OMputObject| |mesh| + |integerIfCan| |tValues| |cyclicEntries| |signAround| |cAcosh| + |rewriteSetWithReduction| |associates?| |toseSquareFreePart| + |infieldIntegrate| |leftRank| |setVariableOrder| |rootPower| + |homogeneous?| |rk4a| |sortConstraints| |chineseRemainder| + |FormatRoman| |sinhcosh| |OMencodingSGML| |primPartElseUnitCanonical!| + |definingPolynomial| |jvmPublic| |inGroundField?| |min| |extractPoint| + |integralRepresents| |particularSolution| |bigEndian| + |semiIndiceSubResultantEuclidean| |flatten| |union| |overbar| + |rotate!| |invertibleElseSplit?| |iicos| |changeWeightLevel| |iFTable| + |sylvesterMatrix| |dn| |copies| |lagrange| |drawComplexVectorField| + |moebiusMu| |besselI| |updatD| |coefChoose| |logpart| |intersect| + |root| |moduloP| |precision| |upperCase| |heap| + |factorSquareFreePolynomial| |showClipRegion| + |basisOfRightAnnihilator| |knownInfBasis| |resultantReduitEuclidean| + |clipBoolean| |partitions| |linearForm| |OMputBVar| |iteratedInitials| + |fractRagits| |stiffnessAndStabilityOfODEIF| |bits| |primitivePart| + |imagI| |sin2csc| |pquo| |SFunction| |iiasech| |getZechTable| + |scaleRoots| |conditionsForIdempotents| |stopTableGcd!| |trace2PowMod| + |ode2| |rootBound| |rational| |shiftLeft| |interpretString| + |changeMeasure| |primlimintfrac| |e02dcf| |bringDown| + |numberOfFractionalTerms| |removeIrreducibleRedundantFactors| |iiasec| + |simpsono| |alternative?| |packageCall| |coshIfCan| |rootOf| + |normInvertible?| |asinIfCan| |prinpolINFO| |jvmNative| + |selectNonFiniteRoutines| |functionIsContinuousAtEndPoints| + |pointColorPalette| |ldf2vmf| |entry?| |showTheFTable| |dimensions| + |arguments| |OMputApp| |cyclotomicFactorization| |factors| |iiacos| + |bumprow| |exists?| |enterPointData| |numberOfOperations| |s17akf| + |numeric| |real?| |seriesToOutputForm| |superscript| |OMopenFile| + |OMgetEndApp| |mainCoefficients| |numberOfChildren| |loopPoints| + |prefix| |radical| |quotientByP| |graphImage| |interReduce| + |OMconnOutDevice| |lookupFunction| |viewport3D| |getCode| |d02bbf| + |match?| |internalDecompose| |palginfieldint| |mindegTerm| + |setClipValue| |key?| |rightQuotient| |useEisensteinCriterion?| + |matrixGcd| |outerProduct| |parabolicCylindrical| |perfectNthPower?| + |recoverAfterFail| |freeOf?| |matrixConcat3D| |monicCompleteDecompose| + |bernoulli| |tanh2coth| |stopTable!| |Gamma| |isAtom| |palgintegrate| + |limitedint| |cAtan| |chiSquare1| |karatsubaDivide| |HenselLift| + |extendIfCan| |henselFact| |charthRoot| |realElementary| |curryLeft| + |rightMult| |characteristic| |weakBiRank| |any| |internalIntegrate| + |c06gqf| |exp1| |mapCoef| |iiabs| |f02agf| |groebnerFactorize| |cExp| + |multiplyCoefficients| |basisOfCentroid| |tanhIfCan| |getConstant| + |sup| |idealiserMatrix| |rename| |d02raf| |makeGraphImage| |kmax| + |e02daf| |log2| |OMsetEncoding| |stronglyReduced?| |imaginary| + |monomialIntPoly| |split!| |compile| |iilog| |jvmIntegerConstantTag| + |extendedIntegrate| |nthFactor| |rowEchLocal| |normal01| + |setchildren!| |node?| |revert| |unitCanonical| |OMgetError| + |reducedForm| |totalfract| |multMonom| |prevPrime| |constDsolve| + |cycle| |factorSquareFreeByRecursion| |internalLastSubResultant| + |scalarMatrix| |readUInt8!| |monicRightFactorIfCan| |poisson| |lllp| + |shiftRight| |iCompose| |nextsubResultant2| |fortranDoubleComplex| + |rightNorm| |gradient| |zero?| |laplacian| |intensity| |imagK| |ode| + |rquo| |relationsIdeal| |bright| |makeprod| |dmpToP| |rdHack1| + |predicates| |cyclicParents| |quoByVar| |verticalTab| |youngDiagram| + |weierstrass| |head| |littleEndian| |radicalSimplify| |functorData| + |OMputBind| |mainSquareFreePart| |s17ajf| |f02aaf| |e01sff| |routines| + |extendedSubResultantGcd| |endOfFile?| |irVar| |PollardSmallFactor| + |sinh2csch| |writeByte!| |subTriSet?| |f01bsf| |perspective| + |rationalApproximation| |scale| |patternVariable| |primextendedint| + |removeCosSq| |quadraticNorm| |center| |listOfLists| |central?| + |localReal?| |nonLinearPart| |simplifyLog| |opeval| |cCoth| + |decompose| |singularitiesOf| |numberOfFactors| + |eisensteinIrreducible?| |physicalLength| |modularGcdPrimitive| + |getDatabase| |irDef| |getPickedPoints| |elementary| + |leftReducedSystem| |fractionFreeGauss!| |iiasinh| + |stoseInvertible?reg| |OMgetApp| |positive?| |less?| |zeroMatrix| + |s13aaf| |normalDenom| |qroot| |elColumn2!| |dflist| |hitherPlane| + |kovacic| |OMgetType| |brillhartTrials| |linefeed| |close| + |primitiveElement| |nodeOf?| |currentCategoryFrame| |composites| + |remove!| |iiacsch| |coefficients| |createZechTable| |checkRur| |po| + |script| |basisOfCenter| |expenseOfEvaluation| |bitCoef| |e02gaf| + |enterInCache| |dominantTerm| |loadNativeModule| |table| |extractTop!| + |critpOrder| |purelyTranscendental?| |reflect| |outputAsTex| + |basisOfRightNucleus| |factorial| |initial| |ldf2lst| |display| + |leftUnits| |length| |select!| |inverseIntegralMatrixAtInfinity| |cap| + |integralMatrix| |rk4qc| |support| |elaborate| |commutator| + |lowerCase?| |f07aef| |scripts| |superHeight| |overlap| + |rightTraceMatrix| |irreducibleFactor| |ksec| |torsionIfCan| + |whatInfinity| |solve| |setMaxPoints| |tex| |varList| |rotatey| + |sumOfDivisors| |complexIntegrate| |integers| |environment| |new| + |antisymmetricTensors| |iisinh| |removeRoughlyRedundantFactorsInPols| + |screenResolution3D| |aLinear| |weight| |pushuconst| + |squareFreeFactors| |square?| |minordet| + |standardBasisOfCyclicSubmodule| |yellow| |hasoln| |jvmTransient| + |constant?| |coerceListOfPairs| |harmonic| |setOfMinN| |mathieu11| + |showTheSymbolTable| |identity| |complex?| + |removeRoughlyRedundantFactorsInContents| |lhs| |e01saf| |remainder| + |input| |lexTriangular| |mergeDifference| |chainSubResultants| + |deepCopy| |factorFraction| |stoseInvertibleSetreg| |reducedQPowers| + |outputFloating| |f01qef| |rhs| |sdf2lst| |readBytes!| |plus| + |sparsityIF| |pointPlot| |backOldPos| |semiResultantReduitEuclidean| + |whitePoint| |generalTwoFactor| |e| |FormatArabic| |lazy?| + |returnType!| |supersub| |newTypeLists| + |generalizedContinuumHypothesisAssumed?| |graeffe| |mainKernel| + |polyred| |getExplanations| |setlast!| |sign| |pmintegrate| + |trapezoidal| |quasiMonic?| |empty?| |pointLists| |times| |unit| + |iisec| |wholeRagits| |formula| |intPatternMatch| |f04mbf| + |triangularSystems| |newline| |subResultantGcdEuclidean| + |moreAlgebraic?| |UP2ifCan| |disjunction| |irreducibleFactors| + |connectTo| |indicialEquation| |addMatchRestricted| |pushup| + |basisOfLeftNucleus| |palgint0| |degreeSubResultantEuclidean| + |acothIfCan| |diagonal| |antiCommutator| |baseRDEsys| |gbasis| + |message| |Lazard| |bipolarCylindrical| |mathieu24| |isMult| + |exactQuotient!| |dimensionOfIrreducibleRepresentation| |left| + |linearlyDependentOverZ?| |leftScalarTimes!| |e02bcf| |getButtonValue| + |OMclose| |nsqfree| |OMgetVariable| |cot2tan| |var1StepsDefault| |mix| + |right| |nullary| |groebnerIdeal| |compactFraction| |extractBottom!| + |power!| |monom| |level| |mapDown!| |froot| |messagePrint| + |pointColorDefault| |alphabetic?| |nrows| |cosh2sech| |scripted?| + |reducedDiscriminant| |fortranComplex| |colorDef| + |ellipticCylindrical| |elRow2!| |toroidal| |hspace| |minPoints3D| + |ncols| |generalizedEigenvector| |filename| |width| + |indiceSubResultantEuclidean| |subresultantVector| |c06fqf| |f01mcf| + |lp| |selectsecond| |orbit| |alternatingGroup| |iroot| + |shanksDiscLogAlgorithm| |headReduce| |LyndonWordsList| |KrullNumber| + |iicot| |string?| |common| |moebius| |clipParametric| |complexRoots| + |innerint| |fixedPoint| |stack| |style| |squareFree| |sechIfCan| + |parse| |createMultiplicationMatrix| |denomRicDE| |expandPower| + |readByte!| |removeSquaresIfCan| |useNagFunctions| |mkAnswer| + |leftTrace| |nextPrimitivePoly| |d01bbf| |BasicMethod| |fractionPart| + |createGenericMatrix| |critMTonD1| |entries| |binary| |mirror| + |denominator| |rootsOf| |qqq| |copy!| |plotPolar| |separateDegrees| + |toseInvertibleSet| |outputArgs| |triangulate| |wreath| + |nextSubsetGray| |basisOfLeftNucloid| |jvmSynchronized| |is?| + |generateIrredPoly| |jvmProtected| |hyperelliptic| + |useSingleFactorBound| |eq| |someBasis| |autoReduced?| |calcRanges| + |hdmpToDmp| |cyclePartition| |structuralConstants| |optional| |pToDmp| + |commutative?| |tan2cot| |binaryTree| |solveLinear| + |solveLinearPolynomialEquationByFractions| |iter| |property| + |charClass| |generalizedInverse| |changeName| |f01rdf| |arg1| + |monicDivide| |satisfy?| |startTable!| |regularRepresentation| + |makeYoungTableau| |newLine| |divide| |linearMatrix| + |mainPrimitivePart| |genericPosition| |totalLex| |gcdPolynomial| |key| + |log10| |fortran| |sumOfSquares| |arg2| |companionBlocks| |size?| + |octon| |goodnessOfFit| |dim| |problemPoints| |typeLists| |atoms| + |mapExponents| |integralBasisAtInfinity| |oddInfiniteProduct| |htrigs| + |bitand| |An| |shift| |edf2fi| |topFortranOutputStack| + |rangePascalTriangle| |OMgetFloat| |setFormula!| |hessian| + |represents| |coth2trigh| |fortranDouble| |clearTheFTable| |symbol| + |sec2cos| |bitior| |jordanAdmissible?| |conditions| |OMwrite| |cdr| + |allRootsOf| |maxdeg| |permutation| |polarCoordinates| |s13acf| |rem| + |idealSimplify| |quotient| |mapSolve| |expression| |expr| |e04gcf| + |match| |paraboloidal| |dequeue| |integral?| |zeroDimPrime?| + |stiffnessAndStabilityFactor| |createMultiplicationTable| |gensym| + |quo| |isQuotient| |fortranCompilerName| |repeating| |integer| + |decomposeFunc| |duplicates| |listLoops| |index| + |removeRoughlyRedundantFactorsInPol| |internalIntegrate0| |d01akf| + |middle| |antiCommutative?| |f01rcf| |processTemplate| + |setMaxPoints3D| |createRandomElement| |setleaves!| |lfextendedint| + |d02kef| |algebraicOf| |interpret| |div| |expint| |algint| |s17dgf| + |univariate?| |augment| |symFunc| |closed| |parametersOf| + |alternating| |exQuo| |rule| |exquo| |primitivePart!| |compound?| + |getOperator| |makeFR| |mpsode| |stoseInvertible?| |irreducible?| + |cot2trig| |virtualDegree| |birth| |quadratic?| |hcrf| ~= |s17agf| + |checkPrecision| |rischDEsys| |member?| |unary?| |fortranReal| + |fillPascalTriangle| |startTableInvSet!| |cothIfCan| |child?| + |leftCharacteristicPolynomial| |height| |#| |cCos| |paren| |returns| + |associatorDependence| |squareTop| |substring?| |children| |tanIfCan| + |bubbleSort!| |outputList| |nativeModuleExtension| |fracPart| ~ |Ci| + |Beta| |commutativeEquality| |compiledFunction| |putProperties| + |baseRDE| |fortranTypeOf| |sub| |noKaratsuba| |primintegrate| + |jvmSuper| |axesColorDefault| |cCsc| |bsolve| |suffix?| |infLex?| + |lfextlimint| |lyndon?| |irForm| |crushedSet| |size| + |setScreenResolution| |normFactors| |characteristicPolynomial| + |coleman| |createThreeSpace| |e04ycf| |ptFunc| |realEigenvalues| + |ScanRoman| |conjug| |/\\| |wholePart| |c05nbf| |tan2trig| + |basisOfRightNucloid| |prinb| |prefix?| |byteBuffer| |subResultantGcd| + |OMputEndObject| |prime| |distdfact| |\\/| |result| |s14aaf| + |stoseSquareFreePart| |jvmStatic| |s14baf| |increasePrecision| + |completeHensel| |OMserve| |nextPrime| |simpleBounds?| |separant| + |generic?| |createNormalElement| |rightPower| |imagE| |cyclic?| + |escape| |rotatex| |iiatan| |localAbs| |more?| |separateFactors| + |c06gcf| |LiePoly| |returnTypeOf| |s14abf| |wrregime| + |leadingExponent| |car| |yCoordinates| |makeViewport2D| |safetyMargin| + |f04mcf| |radPoly| |genericLeftMinimalPolynomial| |macroExpand| + |tensorProduct| |nullary?| |lintgcd| |s18adf| |writeLine!| |component| + |selectPolynomials| |coordinate| |monomial?| |OMputEndError| + |modularGcd| |abs| |addPoint| |constantRight| |plus!| |infix?| + |d02gbf| |lazyPseudoRemainder| |explogs2trigs| |acotIfCan| |imagk| + |pascalTriangle| |true| |solveLinearPolynomialEquation| |direction| + |uniform01| |delay| |mask| |rename!| |stosePrepareSubResAlgo| |node| + |splitNodeOf!| |swapColumns!| |removeZeroes| |leftFactorIfCan| + |option?| |leftTraceMatrix| |s18def| |setEpilogue!| |digit| |df2mf| + |fibonacci| |rootRadius| |splitLinear| |s17adf| |commaSeparate| + |pdf2df| |f02awf| |tail| |sPol| |expintfldpoly| |f2st| |associative?| + |computeBasis| |pleskenSplit| |tanintegrate| |reduction| |d01ajf| + |pile| |maxPoints| |iomode| |fortranInteger| |exptMod| |setPosition| + |moduleSum| |weighted| |insert!| |cyclicCopy| |jvmVolatile| + |linearElement| |setelt!| |omError| |buildSyntax| |quasiComponent| + |padicFraction| |boundOfCauchy| |genericRightNorm| |resetBadValues| + |removeRedundantFactorsInPols| |outputGeneral| |doubleFloatFormat| + |radicalOfLeftTraceForm| |pmComplexintegrate| |zeroOf| |transpose| + |goodPoint| |inputBinaryFile| |e01bef| |jvmMethodrefConstantTag| + |title| |computeCycleLength| |composite| |lazyResidueClass| |position| + |argscript| |logGamma| |f04jgf| |outputBinaryFile| + |complexNumericIfCan| |twoFactor| |minrank| |printInfo!| + |associatedSystem| |insert| |resultant| |retractIfCan| |e01bgf| + |selectMultiDimensionalRoutines| |doubleResultant| |squareFreePrim| + |OMread| |implies| |comp| |integralLastSubResultant| |elements| + |partialDenominators| |finite?| |cartesian| |vectorise| |powerSum| + |cfirst| |laurentRep| |medialSet| |rightDiscriminant| |isList| + |comment| |f02axf| |null?| |inrootof| |internalZeroSetSplit| |log| + |logIfCan| |tanQ| |c02agf| |OMcloseConn| |upperBound| |categoryFrame| + |resetVariableOrder| |mainForm| |explimitedint| + |derivationCoordinates| |firstUncouplingMatrix| |var2StepsDefault| + |generalPosition| |fortranLinkerArgs| |factorSFBRlcUnit| |mathieu22| + |countable?| |set| |normalizedAssociate| |realEigenvectors| + |solveLinearPolynomialEquationByRecursion| |usingTable?| |e01bhf| + |coerceImages| |trigs2explogs| |negative?| |space| |equation| |Aleph| + |addPoint2| |constantOperator| |c06gbf| |clip| |expPot| |cyclotomic| + |powers| |scanOneDimSubspaces| |options| |contract| |romberg| |pop!| + |internalSubPolSet?| |simplify| |algSplitSimple| |iiacoth| + |selectFiniteRoutines| |setAdaptive| |expIfCan| |computePowers| + |mainContent| |genericLeftTrace| |primes| |elliptic?| |regime| + |coerceP| |upperCase!| |selectfirst| |map| |purelyAlgebraic?| + |cos2sec| |cond| |mapExpon| |string| |getIdentifier| + |sumOfKthPowerDivisors| |categories| |viewport2D| |putProperty| + |list?| |jvmInterface| |deepestTail| |lieAlgebra?| |unaryFunction| + |mainExpression| |rootProduct| |writeInt8!| |coercePreimagesImages| + |cAsinh| |userOrdered?| |kroneckerDelta| |pureLex| |d02cjf| + |errorKind| |nthRootIfCan| |halfExtendedResultant1| |c06ekf| |makeSUP| + |bothWays| |red| |sumSquares| |continuedFraction| |lexGroebner| + |setEmpty!| |oddintegers| |discreteLog| |OMsupportsCD?| |nullity| + |drawComplex| |att2Result| |init| |underscore| |mat| |makeSketch| + |bitLength| |bumptab1| |primextintfrac| |ignore?| |linGenPos| + |nthCoef| |s20adf| |iisqrt3| |rst| |getSyntaxFormsFromFile| |convert| + |evaluateInverse| |ptree| |subHeight| |setProperties| |polCase| + |monicModulo| |SturmHabichtCoefficients| |normalizeIfCan| + |getVariableOrder| |reducedContinuedFraction| |nthExponent| |null| + |hasSolution?| |partialFraction| |inR?| |eigenvector| |shufflein| + |solve1| |compose| |constantCoefficientRicDE| |asechIfCan| + |setLegalFortranSourceExtensions| + |rewriteSetByReducingWithParticularGenerators| |not| |startPolynomial| + |rewriteIdealWithRemainder| |setTex!| |palgextint| |credPol| + |chebyshevU| |c06ebf| |internalSubQuasiComponent?| |s19abf| |pastel| + |and| |newReduc| |OMgetAttr| |vertConcat| |unparse| + |SturmHabichtSequence| |epilogue| |pointColor| |iitan| |nary?| + |s21bdf| |fi2df| |removeSinSq| |push!| |monomRDE| |refine| |karatsuba| + |iprint| |semiDegreeSubResultantEuclidean| |number?| |extend| + |palgRDE| RF2UTS |btwFact| |last| |pseudoRemainder| |OMgetAtp| + |setOrder| |polynomialZeros| |janko2| |unitVector| |fmecg| + |linearAssociatedOrder| |ricDsolve| |assoc| |numberOfComposites| + |ScanArabic| |degreePartition| |transcendent?| |splitConstant| |dot| + |has?| |approxSqrt| |exponents| |Lazard2| |extendedEuclidean| + |cycleElt| |close!| |mainMonomial| |back| |tubeRadiusDefault| + |alphanumeric?| |deleteRoutine!| |f01maf| |crest| |viewPhiDefault| + |rowEch| |ratPoly| |cylindrical| |comparison| |taylorRep| |deref| + |removeZero| |measure| |sqfree| |twist| |failed| |sizePascalTriangle| + |f07fef| |coordinates| |dualSignature| |variable?| |rur| |csc2sin| + |resultantnaif| |mvar| |setScreenResolution3D| |dihedralGroup| |pole?| + |rationalPower| |collect| |pseudoDivide| |tryFunctionalDecomposition?| + |infRittWu?| |repSq| |e02akf| |outlineRender| |trigs| |bat| + |csch2sinh| |s17aef| |normalize| |divisor| |fprindINFO| |eval| + |doubleComplex?| |contains?| |bezoutMatrix| |lieAdmissible?| + |leftZero| |graphs| |generalizedContinuumHypothesisAssumed| |makeUnit| + |powmod| |initializeGroupForWordProblem| |constantLeft| + |toseLastSubResultant| |solid?| |laurentIfCan| |elaboration| + |topPredicate| |isOpen?| |ListOfTerms| |monic?| |recip| |qualifier| + |prod| |recolor| |e02aef| |attributeData| |Ei| |pow| |listexp| + |integralAtInfinity?| |f02wef| |cyclic| |cCsch| |cAsin| |f02bjf| + |showTheRoutinesTable| |leftGcd| |variable| |high| |status| |cn| ** + |getStream| |presub| |distFact| |row| |musserTrials| + |createNormalPoly| |coerceS| |iterators| |possiblyInfinite?| + |dictionary| |rightUnit| |neglist| |shallowCopy| |exprToXXP| |c06fpf| + |complexElementary| |euclideanGroebner| |determinant| |GospersMethod| + |lists| |innerEigenvectors| |printHeader| |pair| |heapSort| |mkPrim| + |isOr| |lastSubResultantElseSplit| |resetAttributeButtons| |s18dcf| + |s19acf| |nextItem| |myDegree| |tube| |oneDimensionalArray| + |leastPower| |latex| |lprop| |tanNa| |factorAndSplit| |polyRDE| + |outputSpacing| |viewDeltaXDefault| |keys| |univariatePolynomials| + |argument| |c02aff| |badNum| |graphCurves| |ode1| |isConnected?| + |lazyVariations| |minColIndex| |coord| |numberOfCycles| |f02fjf| + |B1solve| |createPrimitivePoly| |fixPredicate| + |showIntensityFunctions| |rightUnits| |iidprod| |setIntersection| + |ef2edf| |quasiMonicPolynomials| |s18aef| |radicalSolve| |yCoord| + |getOrder| |scopes| |trivialIdeal?| |elseBranch| |multiset| |increase| + |extractIfCan| |e02agf| |viewThetaDefault| |multiEuclideanTree| + |connect| |overlabel| |reducedSystem| |nil| |conical| |quatern| + |divisorCascade| |aromberg| |padecf| |lazyPquo| |increment| + |extendedResultant| |merge| |properties| |whileLoop| |fixedPoints| + |linearDependence| |probablyZeroDim?| |sech2cosh| |numer| + |genericLeftNorm| |jvmDoubleConstantTag| |internalInfRittWu?| + |squareFreePolynomial| |radicalEigenvalues| |c06gsf| |weights| + |readUInt16!| |translate| |isEquiv| |mapmult| |rightMinimalPolynomial| + |denom| |before?| |df2ef| |useEisensteinCriterion| |completeEval| + |leftQuotient| |viewpoint| |s17def| |approximate| + |integralDerivationMatrix| |viewWriteAvailable| |top!| |iicosh| + |subtractIfCan| |bandedJacobian| |s17dhf| |edf2efi| |branchPoint?| + |removeSuperfluousCases| |complex| |skewSFunction| + |genericLeftDiscriminant| |primintfldpoly| |cycleRagits| + |lastSubResultant| |pi| |inc| |jvmStrict| |minPol| + |unrankImproperPartitions1| |integrate| |dihedral| |antiAssociative?| + |varselect| |d01alf| |besselJ| |fintegrate| |readLine!| |infinity| + |cAcoth| |variationOfParameters| |pol| |outputAsScript| + |viewDeltaYDefault| |balancedBinaryTree| |pr2dmp| |nand| |leadingTerm| + |lfinfieldint| |aQuadratic| |LyndonCoordinates| |factor1| |headAst| + |symmetricPower| |ip4Address| |var1Steps| |OMsend| |countRealRoots| + |sh| |alphabetic| |pushdown| |times!| |mainDefiningPolynomial| |swap| + |pdf2ef| |mkcomm| |leastAffineMultiple| |hermite| |lepol| |jvmPrivate| + |kernel| |clearTheSymbolTable| |infieldint| |numberOfComponents| + |nthFractionalTerm| |componentUpperBound| + |genericRightMinimalPolynomial| |genus| |external?| |listOfMonoms| + |removeRedundantFactors| |incrementKthElement| |list| |OMgetEndObject| + |printTypes| |tableForDiscreteLogarithm| |showFortranOutputStack| + |minRowIndex| |coefficient| |draw| |makeSeries| |degreeSubResultant| + |OMputEndApp| |replace| |tab| |rischNormalize| |sample| + |rightRegularRepresentation| |OMconnInDevice| |chvar| |currentEnv| + |rowEchelon| |applyRules| |cscIfCan| |zeroSetSplit| |getMatch| + |generalSqFr| |var2Steps| |symmetricRemainder| |evenlambert| |redpps| + |symbol?| |tubePoints| |linearAssociatedLog| |cyclotomicDecomposition| + |mapGen| |singleFactorBound| |corrPoly| |digit?| |saturate| + |supDimElseRittWu?| |unprotectedRemoveRedundantFactors| |OMputEndBind| + |selectSumOfSquaresRoutines| |simplifyPower| |definingEquations| + |pushucoef| |acschIfCan| |sequences| |makeCos| |leadingSupport| + |presuper| |selectIntegrationRoutines| |setStatus!| |makeObject| + |leftOne| |bombieriNorm| |imports| |stoseInvertibleSet| |double?| + |leftRemainder| |failed?| |seed| |randomLC| |xn| |printStats!| + |members| |quartic| |coef| |call| |normalise| |rightRank| |axes| + |positiveSolve| |basisOfNucleus| |withPredicates| |innerSolve1| + |schema| |removeRedundantFactorsInContents| |float?| |dmp2rfi| + |rationalIfCan| |computeInt| |hostPlatform| |wordsForStrongGenerators| + |linears| |xCoord| |rischDE| |unravel| |safeFloor| + |jvmUTF8ConstantTag| |localIntegralBasis| |e01baf| |perfectSquare?| + |truncate| |expandLog| |reciprocalPolynomial| |groebgen| + |exponentialOrder| |controlPanel| |iisech| |csubst| |primitive?| + |nextNormalPoly| |palgLODE| |d02ejf| |zeroVector| |mappingAst| + |rightTrim| |cAtanh| |print| |completeEchelonBasis| |swap!| |linSolve| + |normDeriv2| |smith| |resolve| |randnum| |leftTrim| |makeop| + |linearPolynomials| |expenseOfEvaluationIF| |optimize| + |OMunhandledSymbol| |diagonals| |stoseIntegralLastSubResultant| + |prologue| |palgint| |rarrow| |systemCommand| |OMgetInteger| |f04atf| + |iicoth| |f02aff| |roughBase?| |bivariatePolynomials| |sort!| + |stoseInternalLastSubResultant| |unitNormalize| |isNot| + |sturmSequence| |countRealRootsMultiple| |vark| |elRow1!| |super| + |anticoord| |semiResultantEuclideannaif| |startTableGcd!| |normal| + |palgLODE0| |complete| |makeViewport3D| |bivariate?| + |generalInfiniteProduct| |euclideanSize| |rootOfIrreduciblePoly| + |computeCycleEntry| |nextsousResultant2| + |rightCharacteristicPolynomial| |signatureAst| |generator| |element?| + |submod| |univariatePolynomialsGcds| |RemainderList| |constantIfCan| + |principalIdeal| |fill!| |OMmakeConn| |palgextint0| |extractProperty| + |thenBranch| |singular?| |host| |lowerBound| |unitsColorDefault| + |digamma| |datalist| |round| |palgRDE0| |contours| + |algebraicVariables| |rules| |readInt8!| |exponential| |removeSinhSq| + |iidsum| |OMencodingXML| |bounds| |OMputSymbol| + |isAbsolutelyIrreducible?| |brillhartIrreducible?| |c06frf| |ideal| + |addBadValue| |numericalOptimization| |acoshIfCan| |subNode?| + |relerror| |mathieu12| |nilFactor| |dual| |zeroDim?| |atom?| + |leftDiscriminant| |charpol| |oblateSpheroidal| |generators| + |leftDivide| |cyclicSubmodule| |Is| |atrapezoidal| |critT| |cSec| + |iExquo| |triangular?| |integralCoordinates| |jvmAbstract| + |retractable?| |numericIfCan| |condition| |removeCoshSq| |printInfo| + |output| |OMlistCDs| |limitPlus| |cSech| |f02xef| |unknown| + |OMsupportsSymbol?| |graphStates| |gcdcofact| |surface| + |leadingCoefficientRicDE| |test| |permutationGroup| |rootNormalize| + |setrest!| |lazyPremWithDefault| |deriv| |stirling1| |equiv| + |findBinding| |subCase?| |ranges| |adaptive3D?| |secIfCan| + |leviCivitaSymbol| |degree| |antisymmetric?| |closed?| |erf| |decimal| + |shallowExpand| |delete| |compdegd| |s17acf| |s20acf| |cAsech| + |expand| |mainVariable| |iterationVar| |basisOfMiddleNucleus| + |leftAlternative?| |zeroDimPrimary?| |definingInequation| |setPoly| + |redmat| |consnewpol| |isPlus| |incr| |sylvesterSequence| |decrease| + |filterWhile| |OMgetEndAtp| |OMParseError?| |exprToGenUPS| + |makeFloatFunction| |findConstructor| |li| |hexDigit?| |typeForm| + |complexNormalize| |anfactor| |palglimint0| |zerosOf| |hi| + |filterUntil| |doubleRank| |numFunEvals| |lazyPseudoQuotient| + |resultantEuclidean| |checkForZero| |safeCeiling| |dilog| |predicate| + |generalLambert| |rational?| |cross| FG2F |select| |setButtonValue| + |removeDuplicates| |monicLeftDivide| |atanhIfCan| |inconsistent?| + |normalized?| |sin| |characteristicSerie| |reindex| + |listYoungTableaus| |OMputString| |constant| |rk4| |chiSquare| + |dequeue!| |findCycle| |lazyGintegrate| |viewSizeDefault| |cos| + |lfintegrate| |OMgetEndAttr| |hasHi| |units| |cotIfCan| |groebSolve| + |setref| |jokerMode| |zoom| |modifyPointData| |product| |tan| + |perfectNthRoot| |zero| |rightExactQuotient| |blue| |gramschmidt| + |universe| |rCoord| |bottom!| |ceiling| |setErrorBound| |nthr| |cot| + |complexEigenvectors| |OMputInteger| |monicRightDivide| |initTable!| + |lexico| |arrayStack| |aCubic| |hconcat| |pointData| |quote| |bat1| + |sec| |setprevious!| |And| |lowerCase!| |f01brf| |squareFreePart| + |ramified?| |iiatanh| |diff| |maxPoints3D| |integral| |e01daf| + |OMgetEndBind| |csc| |OMconnectTCP| |stoseInvertibleSetsqfreg| |Or| + |f02aef| |internalAugment| |norm| |makeRecord| |semicolonSeparate| + |toseInvertible?| |setRealSteps| |totalDegree| |factorGroebnerBasis| + |largest| |asin| |code| |Not| |initiallyReduce| |normalElement| + |rationalFunction| |leaf?| |next| |airyAi| |closeComponent| + |setAdaptive3D| |isImplies| |f07fdf| |factorPolynomial| |acos| + |exprHasAlgebraicWeight| |deepExpand| |testModulus| |low| |assert| + |qelt| |numberOfHues| |addiag| |equality| |jvmLongConstantTag| + |solveRetract| |divideExponents| |atan| |parameters| + |singularAtInfinity?| |rootKerSimp| |asecIfCan| |evaluate| |qsetelt| + |belong?| |drawCurves| |functionIsOscillatory| |subResultantsChain| + |elaborateFile| |queue| |acot| |invmod| |critB| |defineProperty| + |uniform| |xRange| |getProperty| |OMreceive| |fortranCarriageReturn| + |OMputEndAttr| |showArrayValues| |branchIfCan| |continue| |asec| + |monomialIntegrate| |setProperty| |subspace| |generate| |orbits| + |yRange| |e04jaf| |listRepresentation| |partialQuotients| + |completeSmith| |intcompBasis| |pseudoQuotient| |acsc| + |carriageReturn| |finiteBasis| |insertTop!| |categoryMode| + |relativeApprox| |monicDecomposeIfCan| |say| |zRange| |redPo| |s19adf| + |minus!| |modifyPoint| |d01asf| |OMputEndBVar| |sinh| |rank| + |convergents| |cup| |genericRightTraceForm| |figureUnits| + |incrementBy| |empty| |map!| |root?| |readLineIfCan!| |jvmFinal| + |pushdterm| |s15adf| |quasiRegular| |split| |cosh| |drawStyle| + |maxrank| |bit?| |karatsubaOnce| |hex| |qsetelt!| EQ |iicsch| + |quadraticForm| |rspace| |selectPDERoutines| |generic| + |rightFactorCandidate| |tanh| |trunc| |maximumExponent| |iiacot| + |integralMatrixAtInfinity| |ScanFloatIgnoreSpaces| |laplace| + |iflist2Result| |ocf2ocdf| |shellSort| |infinityNorm| |identityMatrix| + |coth| |assign| |kernels| |write!| |makeMulti| |conditionP| GF2FG + |hMonic| |beauzamyBound| |initiallyReduced?| |critM| |s01eaf| |sech| + |polygon| |operator| |patternMatchTimes| |rroot| |cycleSplit!| + |binarySearchTree| |extendedint| |certainlySubVariety?| |lflimitedint| + |algDsolve| |csch| |partialNumerators| |flagFactor| |f04maf| + |univariate| |Nul| |character?| |primlimitedint| |pdct| + |totalGroebner| |extractIndex| |asinh| |rightGcd| |powerAssociative?| + |scalarTypeOf| |content| |acsch| |leftFactor| |edf2df| |leastMonomial| + |primPartElseUnitCanonical| |Hausdorff| |acosh| |linear?| |d03faf| + |infiniteProduct| |getMultiplicationTable| |interactiveEnv| |f01qcf| + |airyBi| |tRange| |curve| |atanh| |differentialVariables| |region| + |updatF| |factor| |univariateSolve| |curryRight| |leftUnit| + |rightAlternative?| |iisqrt2| |normalForm| |acoth| |leadingBasisTerm| + |sqrt| |setCondition!| |getGraph| |gethi| |OMgetEndBVar| |d01anf| + |algebraicSort| |primaryDecomp| |subNodeOf?| |asech| + |positiveRemainder| |bitTruth| |nothing| |real| |lambert| |divisors| + |schwerpunkt| |showSummary| |permutationRepresentation| + |noncommutativeJordanAlgebra?| |symmetric?| |addmod| |lift| |unit?| + |ddFact| |imag| |reduced?| |bumptab| |bfEntry| |leader| + |zeroSetSplitIntoTriangularSystems| |numberOfNormalPoly| |over| + |reduce| |mainValue| |multiple| |directProduct| |PDESolve| |concat| + |meshPar2Var| |patternMatch| |OMreadFile| |tracePowMod| + |showAttributes| |leftMult| |id| |stoseLastSubResultant| + |OMputVariable| |LiePolyIfCan| |applyQuote| |ravel| + |expressIdealMember| |polyRicDE| |prepareSubResAlgo| |clikeUniv| + |euclideanNormalForm| |makeTerm| |shuffle| |lo| |optpair| + |insertionSort!| |startStats!| |noLinearFactor?| |reshape| + |rootDirectory| |brace| |OMputAttr| |createPrimitiveElement| |block| + |ScanFloatIgnoreSpacesIfCan| |even?| |sequence| |step| + |currentSubProgram| |factorSquareFree| |exprHasLogarithmicWeights| + |readInt16!| |destruct| |supRittWu?| |numberOfIrreduciblePoly| + |mergeFactors| |wholeRadix| |associatedEquations| |splitDenominator| + |ruleset| |copyInto!| |multiEuclidean| |reduceLODE| |insertRoot!| + |setPrologue!| |module| |lyndon| |LyndonBasis| |viewDefaults| + |symbolTable| |complexZeros| |tablePow| |e04mbf| |jacobi| |iiacsc| + |removeConstantTerm| |SturmHabichtMultiple| |physicalLength!| + |midpoint| |normalizeAtInfinity| |minimumExponent| |squareMatrix| + |viewPosDefault| |iitanh| |iibinom| |makeCrit| |headReduced?| |second| + |nlde| |pushFortranOutputStack| |suchThat| |flexible?| + |normalizedDivide| |monomial| |e02ahf| |cAcsch| |fortranCharacter| + |clipPointsDefault| |third| |enqueue!| |inverse| + |popFortranOutputStack| |associator| |sayLength| |palglimint| + |multivariate| |rightFactorIfCan| |clearTheIFTable| |iisin| + |factorList| |eigenvectors| |OMlistSymbols| |outputAsFortran| + |HermiteIntegrate| |outputFixed| |f02abf| |variables| |sort| + |viewZoomDefault| |BumInSepFFE| |pair?| |transcendenceDegree| + |numericalIntegration| |halfExtendedSubResultantGcd1| |nextSublist| + |numberOfPrimitivePoly| |useSingleFactorBound?| + |basisOfLeftAnnihilator| |char| |directory| |subQuasiComponent?| + |hasTopPredicate?| |quasiAlgebraicSet| |exprex| |jvmStringConstantTag| + |random| |multiplyExponents| |colorFunction| |signature| |lSpaceBasis| + |setright!| |numberOfImproperPartitions| |appendPoint| |radicalRoots| + |isTimes| |value| |removeSuperfluousQuasiComponents| |discriminant| + |optAttributes| |fTable| |leftLcm| |slex| |byte| |rightRecip| + |subresultantSequence| |algebraicDecompose| |spherical| |prinshINFO| + |cycleTail| |index?| |extension| |qfactor| |hypergeometric0F1| + |hdmpToP| |domainTemplate| |taylor| |setnext!| |float| |e02baf| |cCot| + |selectOptimizationRoutines| |dom| |zeroSquareMatrix| |fractRadix| + |setMinPoints| |logical?| |OMputError| |laurent| |oddlambert| + |ramifiedAtInfinity?| |derivative| |find| |obj| |eulerE| |internal?| + |curveColor| |doubleDisc| |getOperands| |puiseux| |complexSolve| + |setFieldInfo| |wordInGenerators| |rdregime| |setRow!| |flexibleArray| + |s18aff| |droot| |selectOrPolynomials| |bag| |drawToScale| + |perfectSqrt| |lowerCase| |op| |parabolic| |repeatUntilLoop| + |maxRowIndex| |inv| |rotatez| |frobenius| |principalAncestors| + |expintegrate| |interpolate| |resetNew| |vector| |evenInfiniteProduct| + |decreasePrecision| |gcdcofactprim| |ground?| |power| + |fortranLiteralLine| |difference| |tanh2trigh| |s17dlf| + |LazardQuotient| |int| |differentiate| |prolateSpheroidal| |intChoose| + |isExpt| |ground| |raisePolynomial| |just| |listConjugateBases| + |parent| |OMputEndAtp| |cycleLength| |sum| |coHeight| + |indicialEquationAtInfinity| |subResultantChain| |leadingMonomial| + |changeVar| |primeFactor| |geometric| |stopMusserTrials| |monomRDEsys| + |e04fdf| |lifting1| |bivariateSLPEBR| |leftRankPolynomial| + |leadingCoefficient| GE |e02bef| |e02bbf| |f01ref| |constantKernel| + |s21bcf| |OMReadError?| |c06fuf| |contractSolve| |stFunc1| + |primitiveMonomials| |mapBivariate| GT |bandedHessian| |f02akf| + |wordInStrongGenerators| |nullSpace| |partition| |fixedPointExquo| + |minGbasis| |setColumn!| |inHallBasis?| |interval| |reductum| + |pomopo!| LE |label| |characteristicSet| |meshFun2Var| + |selectODEIVPRoutines| |adjoint| |factorset| |factorOfDegree| + |voidMode| |cschIfCan| |makingStats?| LT |solid| |scan| + |createIrreduciblePoly| |realZeros| |subscript| |tab1| |makeEq| |ord| + |OMgetSymbol| |possiblyNewVariety?| |mindeg| |operators| |digits| + |dfRange| |setvalue!| |OMputFloat| |build| |irCtor| |curve?| + |rangeIsFinite| |midpoints| |ridHack1| |uncouplingMatrices| + |printStatement| |slash| |tubeRadius| |linearPart| |extensionDegree| + |mkIntegral| |e01bff| |f02bbf| |getRef| |check| + |inverseIntegralMatrix| |plot| |typeList| |finiteBound| |besselK| + |innerSolve| |rightLcm| |fglmIfCan| |mdeg| |nor| |UpTriBddDenomInv| + |localUnquote| |vedf2vef| |cSin| |option| |printCode| |hermiteH| + |quadratic| |modulus| |Frobenius| |error| |leftNorm| |light| + |createPrimitiveNormalPoly| |minIndex| |lazyEvaluate| |getProperties| + |removeDuplicates!| |cyclicEqual?| |noValueMode| |showAll?| + |multinomial| |leftPower| |approximants| |linearAssociatedExp| + |linearDependenceOverZ| |gderiv| |column| |externalList| + |changeNameToObjf| |open?| |library| |pointSizeDefault| + |identitySquareMatrix| |powern| |eigenMatrix| |iiperm| |leadingIdeal| + |jacobian| |getGoodPrime| |coerce| |hash| |orthonormalBasis| |search| + |halfExtendedResultant2| |normal?| |numerator| |color| + |encodingDirectory| |rightScalarTimes!| |randomR| |outputForm| |count| + |acscIfCan| |distance| |range| |basicSet| |pade| |getCurve| + |endSubProgram| |OMgetEndError| |invmultisect| |leftExactQuotient| + |roughBasicSet| |retract| |transcendentalDecompose| |limitedIntegrate| + |numberOfMonomials| |eq?| |ratDsolve| |function| |reverseLex| + |exprToUPS| |nonQsign| |explicitEntries?| |initials| |e02adf| + |jvmClassConstantTag| |zeroDimensional?| |wronskianMatrix| + |mightHaveRoots| |rightExtendedGcd| |ParCondList| + |numberOfComputedEntries| |getMeasure| |e02ddf| + |lastSubResultantEuclidean| |realSolve| |lazyPseudoDivide| |magnitude| + |setfirst!| |nextNormalPrimitivePoly| |e01sef| |minPoints| |rotate| + |complexLimit| |univariatePolynomial| |cAcsc| |ratpart| + |OMencodingUnknown| |cAcos| |entry| |jordanAlgebra?| |pattern| + |atanIfCan| |numberOfVariables| |d02bhf| |replaceKthElement| F2FG + |cache| |swapRows!| |indiceSubResultant| |solveLinearlyOverQ| + |newSubProgram| |asinhIfCan| |clipSurface| |nextPrimitiveNormalPoly| + |LagrangeInterpolation| |linkToFortran| |elem?| |f04adf| + |explicitlyEmpty?| |rubiksGroup| |rootSplit| |diag| |frst| |move| + |critMonD1| |reset| |OMgetBind| |currentScope| |diagonal?| |lifting| + |trim| |delete!| |headRemainder| |inspect| |divideIfCan| + |plusInfinity| |f04qaf| |reduceBasisAtInfinity| |maxColIndex| + |squareFreeLexTriangular| |binaryFunction| |coth2tanh| |f01qdf| + |setelt| |reify| |padicallyExpand| |minusInfinity| |rowEchelonLocal| + |write| |rightRemainder| |nil?| |lfunc| |accuracyIF| + |semiResultantEuclidean1| |exponential1| |copy| |roughUnitIdeal?| + |tubePointsDefault| |save| |UnVectorise| |insertMatch| |addPointLast| + |symmetricSquare| |writeUInt8!| |meatAxe| |odd?| |autoCoerce| |e04dgf| + |errorInfo| |show| |specialTrigs| |bernoulliB| |any?| |exactQuotient| + |extract!| |rootPoly| |deleteProperty!| |seriesSolve| |tubePlot| + |semiSubResultantGcdEuclidean2| |forLoop| |lllip| |c05pbf| + |selectAndPolynomials| |exprHasWeightCosWXorSinWX| |lcm| |cAsec| + |push| |semiLastSubResultantEuclidean| |s21baf| |arity| BY |trace| + |setLength!| |one?| |polygamma| |child| |d03edf| |dec| |top| + |OMputAtp| |exponent| |discriminantEuclidean| |deepestInitial| + |mapdiv| |type| |read!| |basisOfCommutingElements| |groebner| + |parents| |dAndcExp| |gcd| |factorsOfCyclicGroupSize| |notelem| + |symbolTableOf| |duplicates?| |stoseInvertible?sqfreg| |exp| |stFunc2| + |singRicDE| |isAnd| |llprop| |false| |s21bbf| |pushNewContour| + |complexEigenvalues| |integer?| |depth| |stFuncN| |listBranches| + |complexExpand| |maxint| |radicalEigenvector| |bfKeys| + |complementaryBasis| |besselY| |update| |double| + |algebraicCoefficients?| |dioSolve| |const| |mainMonomials| + |leftRegularRepresentation| |aspFilename| |e01sbf| |readUInt32!| + |reverse| |complexForm| |torsion?| |invertible?| |curveColorPalette| + UP2UTS |redPol| |createLowComplexityNormalBasis| |firstNumer| + |getBadValues| |bytes| |reverse!| |phiCoord| |leftRecip| |monomials| + |factorsOfDegree| |dimension| |f07adf| |idealiser| |tableau| + |stopTableInvSet!| NOT |youngGroup| |chebyshevT| |showAllElements| + |rightTrace| |f04axf| |readable?| |eulerPhi| |parametric?| |sorted?| + |append| OR |mantissa| |extractSplittingLeaf| |constantOpIfCan| + |setLabelValue| |iiacosh| |front| |s17aff| |clipWithRanges| |terms| + |SturmHabicht| AND |morphism| |divideIfCan!| |leftExtendedGcd| |infix| + |explicitlyFinite?| |resultantReduit| |e02bdf| |collectUnder| F + |completeHermite| |nextIrreduciblePoly| |groebner?| + |LowTriBddDenomInv| |permanent| |radicalEigenvectors| |cycleEntry| + |bipolar| |floor| |inf| |reduceByQuasiMonic| |lyndonIfCan| |solveid| + |mapUnivariate| |substitute| |rewriteIdealWithHeadRemainder| + |declare!| |integralBasis| |trapezoidalo| |semiResultantEuclidean2| + |approxNthRoot| |sin?| |badValues| |npcoef| |denominators| + |fullPartialFraction| |reorder| |cRationalPower| |d01gbf| UTS2UP + |makeVariable| |univcase| |polygon?| |symbolIfCan| |setDifference| + |backspace| |clearTable!| |bezoutDiscriminant| |d01fcf| |rightOne| + |ran| |identification| |debug| |shape| |horizConcat| |denomLODE| + |principal?| |open| |factorByRecursion| |sts2stst| |unexpand| + |createNormalPrimitivePoly| |critBonD| |Si| D |maxrow| |imagj| + |vconcat| |shade| |printingInfo?| |e02zaf| |cosIfCan| |unknownEndian| + |validExponential| |maxIndex| |s17dcf| |void| |prefixRagits| |getlo| + |stop| |basis| |putGraph| |simpson| |changeThreshhold| |df2st| + |cosSinInfo| |taylorIfCan| |separate| |leftMinimalPolynomial| + |parseString| |parts| |remove| |inverseColeman| Y |se2rfi| |sincos| + |qinterval| |reopen!| |commonDenominator| |position!| |e02def| * + |operations| |rk4f| |abelianGroup| |segment| |fortranLiteral| |mesh?| + |generalizedEigenvectors| |bezoutResultant| |d01amf| |taylorQuoByVar| + |diagonalMatrix| |genericRightDiscriminant| |trailingCoefficient| + |d01gaf| |reseed| |complement| |binaryTournament| |showTheIFTable| + |category| |expandTrigProducts| |subscriptedVariables| + |tryFunctionalDecomposition| |part?| |linearlyDependent?| |in?| + |radix| |domain| |closedCurve| |compBound| |stripCommentsAndBlanks| + |psolve| = |mapUnivariateIfCan| |acosIfCan| |ParCond| |tree| |binding| + |infinite?| |package| |highCommonTerms| |clearCache| |collectUpper| + |zCoord| |extractClosed| |screenResolution| |areEquivalent?| + |bindings| |operation| |symmetricGroup| |d02gaf| |unmakeSUP| + |diagonalProduct| |hclf| |jvmFieldrefConstantTag| |hostByteOrder| < + |iiasin| |e04naf| |nonSingularModel| |cAcot| + |irreducibleRepresentation| |point?| |setUnion| > |unitNormal| + |symmetricDifference| |lquo| |e04ucf| |expt| |iifact| |sncndn| |t| + |inRadical?| |argumentList!| |symmetricProduct| <= |polyPart| + |bracket| |edf2ef| |numerators| |multisect| |sizeLess?| |d01aqf| + |curry| |collectQuasiMonic| |cTan| >= |ref| |invertibleSet| + |constructor| |trueEqual| |choosemon| |viewWriteDefault| + |inverseLaplace| |unrankImproperPartitions0| |fixedDivisor| + |permutations| |upDateBranches| |OMgetString| |callForm?| |vspace| + |restorePrecision| |pack!| |closedCurve?| |mappingMode| |nextColeman| + |primeFrobenius| |mainVariable?| |sturmVariationsOf| |upperCase?| + |order| |quoted?| |prime?| |createLowComplexityTable| |legendreP| + |tanAn| + |rightRankPolynomial| |stronglyReduce| |RittWuCompare| + |insertBottom!| |matrixDimensions| |hasPredicate?| |shiftRoots| + |OMgetObject| |untab| |setValue!| - |setPredicates| |unvectorise| + |fullDisplay| |rightZero| |lighting| |absolutelyIrreducible?| + |subset?| |points| / |LazardQuotient2| |graphState| |subst| |every?| + |arbitrary| |summation| |components| |name| |minimalPolynomial| + |measure2Result| |dimensionsOf| |c06eaf| |adaptive?| |updateStatus!| + |construct| |cLog| |LyndonWordsList1| |coerceL| |body| |s17ahf| + |splitSquarefree| |OMUnknownSymbol?| |writeBytes!| |rectangularMatrix| + |overset?| |mapUp!| |minPoly| |expextendedint| |hue| |conjugates| + |gcdPrimitive| |doublyTransitive?| |rootSimp| |multiple?| |f04asf| + |diophantineSystem| |jvmNameAndTypeConstantTag| |f2df| |modularFactor| + |merge!| |imagJ| |hexDigit| |polar| |conjugate| |objects| + |blankSeparate| |numFunEvals3D| |max| |sn| |leadingIndex| + |semiDiscriminantEuclidean| |nodes| |quotedOperators| |laguerre| + |ReduceOrder| |kind| |base| |isPower| SEGMENT |Vectorise| |enumerate| + |nextPartition| |indices| |concat!| |c06ecf| LODO2FUN |socf2socdf| + |quasiRegular?| |exteriorDifferential| |laguerreL| |green| + |genericRightTrace| |tower| |s13adf| |jacobiIdentity?| |changeBase| + |resultantEuclideannaif| |showScalarValues| |lazyIrreducibleFactors| + |inputOutputBinaryFile| |transform| |simplifyExp| |symmetricTensors| + |formfeed| |setClosed| |setAttributeButtonStep| |argumentListOf| + |sizeMultiplication| |makeSin| |isOp| |getMultiplicationMatrix| + |create3Space| |iipow| |divergence| |df2fi| |quickSort| |preprocess| + |nil| |infinite| |arbitraryExponent| |approximate| |complex| + |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 78dbd0da..92067434 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5480 +1,5480 @@ -(3472811 . 3514591848) -((-2535 (((-114) (-1 (-114) |#2| |#2|) $) 86 T ELT) (((-114) $) NIL T ELT)) (-3691 (($ (-1 (-114) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-4216 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-1266 (-560)) |#2|) 44 T ELT)) (-4106 (($ $) 80 T ELT)) (-2661 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-1742 (((-560) (-1 (-114) |#2|) $) 27 T ELT) (((-560) |#2| $) NIL T ELT) (((-560) |#2| $ (-560)) 96 T ELT)) (-2835 (((-663 |#2|) $) 13 T ELT)) (-2237 (($ (-1 (-114) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-3667 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3955 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -4133 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -4133 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1235)) ((-95) |has| |#1| (-1235)) ((-102) . T) ((-111 #0# #0#) -4133 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -4133 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -4133 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -4133 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-888)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1052)) ((-633 (-171 (-391))) |has| |#1| (-1052)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-916 (-391))) |has| |#1| (-633 (-916 (-391)))) ((-633 (-916 (-560))) |has| |#1| (-633 (-916 (-560)))) ((-633 #1=(-1203 |#1|)) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -4144 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1235)) ((-95) |has| |#1| (-1235)) ((-102) . T) ((-111 #0# #0#) -4144 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -4144 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -4144 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-888)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1052)) ((-633 (-171 (-391))) |has| |#1| (-1052)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-916 (-391))) |has| |#1| (-633 (-916 (-391)))) ((-633 (-916 (-560))) |has| |#1| (-633 (-916 (-560)))) ((-633 #1=(-1203 |#1|)) . T) ((-236 $) -4144 (|has| |#1| (-363)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) -4144 (|has| |#1| (-363)) (|has| |#1| (-240))) ((-239) -4144 (|has| |#1| (-363)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-250) -4144 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-296) |has| |#1| (-1235)) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) -4144 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-319) -4144 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-376) -4144 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-416) |has| |#1| (-363)) ((-381) -4144 (|has| |#1| (-381)) (|has| |#1| (-363))) ((-363) |has| |#1| (-363)) ((-383 |#1| #1#) . T) ((-424 |#1| #1#) . T) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-414 |#1|) . T) ((-426 |#1|) . T) ((-466) -4144 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-507) |has| |#1| (-1235)) ((-528 (-1209) |#1|) |has| |#1| (-528 (-1209) |#1|)) ((-528 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-571) -4144 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-668 #0#) -4144 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) -4144 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-670 #2=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) -4144 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-662 |#1|) . T) ((-662 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-660 #2#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) -4144 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-739 |#1|) . T) ((-739 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-746 |#1| #1#) . T) ((-748) . T) ((-922 $ #3=(-1209)) -4144 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #3#) -4144 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) |has| |#1| (-912 (-391))) ((-912 (-560)) |has| |#1| (-912 (-560))) ((-910 |#1|) . T) ((-940) -12 (|has| |#1| (-319)) (|has| |#1| (-940))) ((-951) -4144 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1034) -12 (|has| |#1| (-1034)) (|has| |#1| (-1235))) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1083 #0#) -4144 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1083 |#1|) . T) ((-1083 $) . T) ((-1088 #0#) -4144 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1088 |#1|) . T) ((-1088 $) . T) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-363)) ((-1235) |has| |#1| (-1235)) ((-1238) |has| |#1| (-1235)) ((-1249) . 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T) ((-102) -4144 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -4144 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -4144 (|has| |#2| (-1081)) (|has| |#2| (-817)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-635 #0=(-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ((-635 (-560)) -4144 (|has| |#2| (-1081)) (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133)))) ((-635 |#2|) |has| |#2| (-1133)) ((-632 (-888)) -4144 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-632 (-888))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-632 (-1299 |#2|)) . T) ((-236 $) -4144 (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1081)))) ((-234 |#2|) |has| |#2| (-1081)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1081))) ((-239) -4144 (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1081)))) ((-274 |#2|) |has| |#2| (-1081)) ((-298 #1=(-560) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1081)) ((-426 |#2|) |has| |#2| (-1133)) ((-503 |#2|) . T) ((-618 #1# |#2|) . T) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-668 (-560)) -4144 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-668 |#2|) -4144 (|has| |#2| (-1081)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1081)) ((-670 #2=(-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081))) ((-670 |#2|) -4144 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-670 $) |has| |#2| (-1081)) ((-662 |#2|) -4144 (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-660 #2#) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081))) ((-660 |#2|) |has| |#2| (-1081)) ((-739 |#2|) -4144 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-748) |has| |#2| (-1081)) ((-816) |has| |#2| (-817)) ((-817) |has| |#2| (-817)) ((-818) |has| |#2| (-817)) ((-821) |has| |#2| (-817)) ((-872) -4144 (|has| |#2| (-872)) (|has| |#2| (-817))) ((-875) -4144 (|has| |#2| (-872)) (|has| |#2| (-817))) ((-922 $ #3=(-1209)) -4144 (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081)))) ((-928 (-1209)) -12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081))) ((-930 #3#) -4144 (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081)))) ((-1070 #0#) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ((-1070 (-560)) -12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) ((-1070 |#2|) |has| |#2| (-1133)) ((-1083 |#2|) -4144 (|has| |#2| (-1081)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1088 |#2|) -4144 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1081) |has| |#2| (-1081)) ((-1089) |has| |#2| (-1081)) ((-1144) |has| |#2| (-1081)) ((-1133) -4144 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1249) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -4133 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-888)) . T) ((-175) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-633 (-916 (-391)))) (|has| |#3| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-633 (-916 (-560)))) (|has| |#3| (-633 (-916 (-560))))) ((-236 $) -4133 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -4133 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -4133 (|has| |#1| (-940)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-922 $ #2=(-1209)) -4133 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-922 $ |#3|) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-928 |#3|) . T) ((-930 #2#) -4133 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-930 |#3|) . T) ((-912 (-391)) -12 (|has| |#1| (-912 (-391))) (|has| |#3| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-912 (-560))) (|has| |#3| (-912 (-560)))) ((-980 |#1| |#4| |#3|) . T) ((-940) |has| |#1| (-940)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1070 |#2|) . T) ((-1070 |#3|) . T) ((-1083 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1088 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -4144 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-888)) . T) ((-175) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-633 (-916 (-391)))) (|has| |#3| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-633 (-916 (-560)))) (|has| |#3| (-633 (-916 (-560))))) ((-236 $) -4144 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -4144 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -4144 (|has| |#1| (-940)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-922 $ #2=(-1209)) -4144 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-922 $ |#3|) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-928 |#3|) . T) ((-930 #2#) -4144 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-930 |#3|) . T) ((-912 (-391)) -12 (|has| |#1| (-912 (-391))) (|has| |#3| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-912 (-560))) (|has| |#3| (-912 (-560)))) ((-980 |#1| |#4| |#3|) . T) ((-940) |has| |#1| (-940)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1070 |#2|) . T) ((-1070 |#3|) . T) ((-1083 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1088 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . 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T) ((-310) . T) ((-376) |has| |#1| (-571)) ((-390 |#1|) |has| |#1| (-1081)) ((-414 |#1|) . T) ((-426 |#1|) . T) ((-466) |has| |#1| (-571)) ((-487) |has| |#1| (-487)) ((-528 (-630 $) $) . T) ((-528 $ $) . 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T) ((-310) . T) ((-376) |has| |#1| (-571)) ((-390 |#1|) |has| |#1| (-1081)) ((-414 |#1|) . T) ((-426 |#1|) . T) ((-466) |has| |#1| (-571)) ((-487) |has| |#1| (-487)) ((-528 (-630 $) $) . T) ((-528 $ $) . 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T) ((-951) |has| |#1| (-571)) ((-1070 (-421 (-560))) -4144 (|has| |#1| (-1070 (-421 (-560)))) (-12 (|has| |#1| (-571)) (|has| |#1| (-1070 (-560))))) ((-1070 #1#) |has| |#1| (-571)) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 #3#) |has| |#1| (-1081)) ((-1070 #4#) . T) ((-1070 |#1|) . T) ((-1083 #0#) |has| |#1| (-571)) ((-1083 |#1|) |has| |#1| (-175)) ((-1083 $) |has| |#1| (-571)) ((-1088 #0#) |has| |#1| (-571)) ((-1088 |#1|) |has| |#1| (-175)) ((-1088 $) |has| |#1| (-571)) ((-1081) -4144 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1089) -4144 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1144) -4144 (|has| |#1| (-1144)) (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-487)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1133) . T) ((-1249) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) . T) ((-38 |#1|) . T) ((-38 $) . T) ((-102) . T) ((-111 #0# #0#) . T) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) . T) ((-635 (-560)) . T) ((-635 #1=(-1209)) |has| |#1| (-1070 (-1209))) ((-635 |#1|) . T) ((-635 $) . T) ((-632 (-888)) . T) ((-175) . T) ((-633 (-229)) |has| |#1| (-1052)) ((-633 (-391)) |has| |#1| (-1052)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-916 (-391))) |has| |#1| (-633 (-916 (-391)))) ((-633 (-916 (-560))) |has| |#1| (-633 (-916 (-560)))) ((-236 $) -4144 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -4144 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-250) . T) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) . T) ((-319) . T) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-376) . T) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-414 |#1|) . T) ((-466) . T) ((-528 (-1209) |#1|) |has| |#1| (-528 (-1209) |#1|)) ((-528 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-571) . T) ((-668 #0#) . T) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) . T) ((-670 #2=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) . T) ((-662 |#1|) . T) ((-662 $) . T) ((-660 #2#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) . T) ((-739 |#1|) . T) ((-739 $) . T) ((-748) . 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -4133 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -4133 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -4133 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -4133 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -4133 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -4133 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -4133 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1209)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -4133 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -4133 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-549)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-560))))) ((-236 $) -4133 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -4133 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-239) -4133 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1144)) ((-302) -4133 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -4133 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -4133 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -4133 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -4133 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -4133 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -4133 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -4133 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-818) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-821) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-844) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-871) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-872) -4133 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-875) -4133 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-922 $ #4=(-1209)) -4133 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-928 (-1209)) -4133 (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-930 #4#) -4133 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-912 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-560)))) ((-910 |#2|) |has| |#1| (-376)) ((-940) -12 (|has| |#1| (-376)) (|has| |#2| (-940))) ((-1005 |#1| #0# (-1114)) . T) ((-951) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1052) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-1070 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-1070 |#2|) . T) ((-1083 #1#) -4133 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 |#2|) |has| |#1| (-376)) ((-1083 $) -4133 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -4133 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 |#2|) |has| |#1| (-376)) ((-1088 $) -4133 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) -12 (|has| |#1| (-376)) (|has| |#2| (-1184))) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1261 |#1|) . T) ((-1278 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1209)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -4144 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-549)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-560))))) ((-236 $) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-239) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1144)) ((-302) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . 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T) ((-951) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1052) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-1070 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-1070 |#2|) . T) ((-1083 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 |#2|) |has| |#1| (-376)) ((-1083 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 |#2|) |has| |#1| (-376)) ((-1088 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) -12 (|has| |#1| (-376)) (|has| |#2| (-1184))) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1261 |#1|) . T) ((-1278 |#1| #0#) . 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T) ((-175) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1114) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| (-1114) (-633 (-916 (-391)))) (|has| |#1| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| (-1114) (-633 (-916 (-560)))) (|has| |#1| (-633 (-916 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -4133 (|has| |#1| (-940)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2#) . T) ((-922 $ #4=(-1209)) -4133 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #2#) . T) ((-930 #4#) -4133 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) -12 (|has| (-1114) (-912 (-391))) (|has| |#1| (-912 (-391)))) ((-912 (-560)) -12 (|has| (-1114) (-912 (-560))) (|has| |#1| (-912 (-560)))) ((-980 |#1| #0# #2#) . T) ((-940) |has| |#1| (-940)) ((-951) |has| |#1| (-376)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 |#1|) . T) ((-1083 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4133 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-1184)) ((-1249) . T) ((-1254) |has| |#1| (-940))) -((-3955 ((|#4| (-1 |#3| |#1|) |#2|) 22 T ELT))) -(((-1276 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -3955 (|#4| (-1 |#3| |#1|) |#2|))) (-1081) (-1275 |#1|) (-1081) (-1275 |#3|)) (T -1276)) -((-3955 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1081)) (-4 *6 (-1081)) (-4 *2 (-1275 *6)) (-5 *1 (-1276 *5 *4 *6 *2)) (-4 *4 (-1275 *5))))) -(-10 -7 (-15 -3955 (|#4| (-1 |#3| |#1|) |#2|))) -((-2985 (((-663 (-1114)) $) 34 T ELT)) (-3147 (($ $) 31 T ELT)) (-2963 (($ |#2| |#3|) NIL T ELT) (($ $ (-1114) |#3|) 28 T ELT) (($ $ (-663 (-1114)) (-663 |#3|)) 27 T ELT)) (-3113 (($ $) 14 T ELT)) (-3124 ((|#2| $) 12 T ELT)) (-2870 ((|#3| $) 10 T ELT))) -(((-1277 |#1| |#2| |#3|) (-10 -8 (-15 -2985 ((-663 (-1114)) |#1|)) (-15 -2963 (|#1| |#1| (-663 (-1114)) (-663 |#3|))) (-15 -2963 (|#1| |#1| (-1114) |#3|)) (-15 -3147 (|#1| |#1|)) (-15 -2963 (|#1| |#2| |#3|)) (-15 -2870 (|#3| |#1|)) (-15 -3113 (|#1| |#1|)) (-15 -3124 (|#2| |#1|))) (-1278 |#2| |#3|) (-1081) (-816)) (T -1277)) -NIL -(-10 -8 (-15 -2985 ((-663 (-1114)) |#1|)) (-15 -2963 (|#1| |#1| (-663 (-1114)) (-663 |#3|))) (-15 -2963 (|#1| |#1| (-1114) |#3|)) (-15 -3147 (|#1| |#1|)) (-15 -2963 (|#1| |#2| |#3|)) (-15 -2870 (|#3| |#1|)) (-15 -3113 (|#1| |#1|)) (-15 -3124 (|#2| |#1|))) -((-2161 (((-114) $ $) 7 T ELT)) (-1335 (((-114) $) 21 T ELT)) (-2985 (((-663 (-1114)) $) 92 T ELT)) (-2231 (((-1209) $) 126 T ELT)) (-1461 (((-2 (|:| -1629 $) (|:| -4497 $) (|:| |associate| $)) $) 68 (|has| |#1| (-571)) ELT)) (-1983 (($ $) 69 (|has| |#1| (-571)) ELT)) (-2189 (((-114) $) 71 (|has| |#1| (-571)) ELT)) (-2133 (($ $ |#2|) 121 T ELT) (($ $ |#2| |#2|) 120 T ELT)) (-3075 (((-1187 (-2 (|:| |k| |#2|) (|:| |c| |#1|))) $) 127 T ELT)) (-2560 (((-3 $ "failed") $ $) 25 T ELT)) (-2500 (($) 22 T CONST)) (-3147 (($ $) 77 T ELT)) (-3300 (((-3 $ "failed") $) 42 T ELT)) (-4241 (((-114) $) 91 T ELT)) (-2093 ((|#2| $) 123 T ELT) ((|#2| $ |#2|) 122 T ELT)) (-2908 (((-114) $) 40 T ELT)) (-2761 (($ $ (-949)) 124 T ELT)) (-3410 (((-114) $) 79 T ELT)) (-2963 (($ |#1| |#2|) 78 T ELT) (($ $ (-1114) |#2|) 94 T ELT) (($ $ (-663 (-1114)) (-663 |#2|)) 93 T ELT)) (-3955 (($ (-1 |#1| |#1|) $) 80 T ELT)) (-3113 (($ $) 82 T ELT)) (-3124 ((|#1| $) 83 T ELT)) (-4149 (((-1191) $) 11 T ELT)) (-3126 (((-1152) $) 12 T ELT)) (-3895 (($ $ |#2|) 118 T ELT)) (-2151 (((-3 $ "failed") $ $) 67 (|has| |#1| (-571)) ELT)) (-3900 (((-1187 |#1|) $ |#1|) 117 (|has| |#1| (-15 ** (|#1| |#1| |#2|))) ELT)) (-1480 ((|#1| $ |#2|) 128 T ELT) (($ $ $) 104 (|has| |#2| (-1144)) ELT)) (-2859 (($ $ (-1209)) 116 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-663 (-1209))) 114 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-1209) (-793)) 113 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-663 (-1209)) (-663 (-793))) 112 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $) 108 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT) (($ $ (-793)) 106 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT)) (-2870 ((|#2| $) 81 T ELT)) (-3981 (($ $) 90 T ELT)) (-4080 (((-888) $) 13 T ELT) (($ (-560)) 38 T ELT) (($ (-421 (-560))) 74 (|has| |#1| (-38 (-421 (-560)))) ELT) (($ $) 66 (|has| |#1| (-571)) ELT) (($ |#1|) 64 (|has| |#1| (-175)) ELT)) (-2590 ((|#1| $ |#2|) 76 T ELT)) (-2257 (((-713 $) $) 65 (|has| |#1| (-147)) ELT)) (-1454 (((-793)) 37 T CONST)) (-3031 ((|#1| $) 125 T ELT)) (-3652 (((-114) $ $) 6 T ELT)) (-3117 (((-114) $ $) 70 (|has| |#1| (-571)) ELT)) (-2793 ((|#1| $ |#2|) 119 (-12 (|has| |#1| (-15 ** (|#1| |#1| |#2|))) (|has| |#1| (-15 -4080 (|#1| (-1209))))) ELT)) (-1408 (($) 23 T CONST)) (-1420 (($) 39 T CONST)) (-2421 (($ $ (-1209)) 115 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-663 (-1209))) 111 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-1209) (-793)) 110 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-663 (-1209)) (-663 (-793))) 109 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $) 107 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT) (($ $ (-793)) 105 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT)) (-4302 (((-114) $ $) 8 T ELT)) (-4398 (($ $ |#1|) 75 (|has| |#1| (-376)) ELT)) (-4390 (($ $) 28 T ELT) (($ $ $) 27 T ELT)) (-4380 (($ $ $) 18 T ELT)) (** (($ $ (-949)) 33 T ELT) (($ $ (-793)) 41 T ELT)) (* (($ (-949) $) 17 T ELT) (($ (-793) $) 20 T ELT) (($ (-560) $) 29 T ELT) (($ $ $) 32 T ELT) (($ $ |#1|) 85 T ELT) (($ |#1| $) 84 T ELT) (($ (-421 (-560)) $) 73 (|has| |#1| (-38 (-421 (-560)))) ELT) (($ $ (-421 (-560))) 72 (|has| |#1| (-38 (-421 (-560)))) ELT))) +((-2448 (*1 *2 *1 *3) (-12 (-5 *3 (-793)) (-4 *1 (-1275 *4)) (-4 *4 (-1081)) (-5 *2 (-1299 *4)))) (-2547 (*1 *2 *1) (-12 (-4 *1 (-1275 *3)) (-4 *3 (-1081)) (-5 *2 (-1203 *3)))) (-4307 (*1 *1 *2) (-12 (-5 *2 (-1203 *3)) (-4 *3 (-1081)) (-4 *1 (-1275 *3)))) (-3668 (*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-3342 (*1 *1 *1 *2) (|partial| -12 (-5 *2 (-793)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-2106 (*1 *2 *1 *1) (-12 (-4 *3 (-1081)) (-5 *2 (-2 (|:| -2162 *1) (|:| -1913 *1))) (-4 *1 (-1275 *3)))) (-1683 (*1 *2 *1 *3) (-12 (-5 *3 (-793)) (-4 *4 (-1081)) (-5 *2 (-2 (|:| -2162 *1) (|:| -1913 *1))) (-4 *1 (-1275 *4)))) (-1744 (*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-1604 (*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-2634 (*1 *1 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)))) (-3757 (*1 *1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-3679 (*1 *2 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-175)))) (-2434 (*1 *2 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-175)))) (-1497 (*1 *2 *2 *2) (-12 (-5 *2 (-421 *1)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)) (-4 *3 (-571)))) (-4367 (*1 *2 *1 *1) (-12 (-4 *1 (-1275 *3)) (-4 *3 (-1081)) (-4 *3 (-571)) (-5 *2 (-793)))) (-2289 (*1 *1 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-571)))) (-2421 (*1 *1 *1 *1) (|partial| -12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-571)))) (-2421 (*1 *2 *2 *1) (|partial| -12 (-5 *2 (-421 *1)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)) (-4 *3 (-571)))) (-3381 (*1 *1 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-571)))) (-2690 (*1 *2 *1 *1) (-12 (-4 *3 (-571)) (-4 *3 (-1081)) (-5 *2 (-2 (|:| -3002 *3) (|:| -2162 *1) (|:| -1913 *1))) (-4 *1 (-1275 *3)))) (-4242 (*1 *2 *1 *1) (-12 (-4 *3 (-466)) (-4 *3 (-1081)) (-5 *2 (-2 (|:| |primePart| *1) (|:| |commonPart| *1))) (-4 *1 (-1275 *3)))) (-1497 (*1 *2 *3 *2) (-12 (-5 *3 (-421 *1)) (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-376)))) (-2884 (*1 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-38 (-421 (-560))))))) +(-13 (-980 |t#1| (-793) (-1114)) (-298 |t#1| |t#1|) (-298 $ $) (-240) (-234 |t#1|) (-10 -8 (-15 -2448 ((-1299 |t#1|) $ (-793))) (-15 -2547 ((-1203 |t#1|) $)) (-15 -4307 ($ (-1203 |t#1|))) (-15 -3668 ($ $ (-793))) (-15 -3342 ((-3 $ "failed") $ (-793))) (-15 -2106 ((-2 (|:| -2162 $) (|:| -1913 $)) $ $)) (-15 -1683 ((-2 (|:| -2162 $) (|:| -1913 $)) $ (-793))) (-15 -1744 ($ $ (-793))) (-15 -1604 ($ $ (-793))) (-15 -2634 ($ $ $)) (-15 -3757 ($ $ (-1 |t#1| |t#1|) $)) (IF (|has| |t#1| (-1184)) (-6 (-1184)) |%noBranch|) (IF (|has| |t#1| (-175)) (PROGN (-15 -3679 (|t#1| $)) (-15 -2434 (|t#1| $ $))) |%noBranch|) (IF (|has| |t#1| (-571)) (PROGN (-6 (-298 (-421 $) (-421 $))) (-15 -1497 ((-421 $) (-421 $) (-421 $))) (-15 -4367 ((-793) $ $)) (-15 -2289 ($ $ $)) (-15 -2421 ((-3 $ "failed") $ $)) (-15 -2421 ((-3 (-421 $) "failed") (-421 $) $)) (-15 -3381 ($ $ $)) (-15 -2690 ((-2 (|:| -3002 |t#1|) (|:| -2162 $) (|:| -1913 $)) $ $))) |%noBranch|) (IF (|has| |t#1| (-466)) (-15 -4242 ((-2 (|:| |primePart| $) (|:| |commonPart| $)) $ $)) |%noBranch|) (IF (|has| |t#1| (-376)) (PROGN (-6 (-319)) (-6 -4506) (-15 -1497 (|t#1| (-421 $) |t#1|))) |%noBranch|) (IF (|has| |t#1| (-38 (-421 (-560)))) (-15 -2884 ($ $)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -4144 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1114)) . T) ((-635 |#1|) . T) ((-635 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1114) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| (-1114) (-633 (-916 (-391)))) (|has| |#1| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| (-1114) (-633 (-916 (-560)))) (|has| |#1| (-633 (-916 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -4144 (|has| |#1| (-940)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2#) . T) ((-922 $ #4=(-1209)) -4144 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #2#) . T) ((-930 #4#) -4144 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) -12 (|has| (-1114) (-912 (-391))) (|has| |#1| (-912 (-391)))) ((-912 (-560)) -12 (|has| (-1114) (-912 (-560))) (|has| |#1| (-912 (-560)))) ((-980 |#1| #0# #2#) . T) ((-940) |has| |#1| (-940)) ((-951) |has| |#1| (-376)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 |#1|) . T) ((-1083 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-1184)) ((-1249) . T) ((-1254) |has| |#1| (-940))) +((-2518 ((|#4| (-1 |#3| |#1|) |#2|) 22 T ELT))) +(((-1276 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -2518 (|#4| (-1 |#3| |#1|) |#2|))) (-1081) (-1275 |#1|) (-1081) (-1275 |#3|)) (T -1276)) +((-2518 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1081)) (-4 *6 (-1081)) (-4 *2 (-1275 *6)) (-5 *1 (-1276 *5 *4 *6 *2)) (-4 *4 (-1275 *5))))) +(-10 -7 (-15 -2518 (|#4| (-1 |#3| |#1|) |#2|))) +((-3648 (((-663 (-1114)) $) 34 T ELT)) (-3806 (($ $) 31 T ELT)) (-3625 (($ |#2| |#3|) NIL T ELT) (($ $ (-1114) |#3|) 28 T ELT) (($ $ (-663 (-1114)) (-663 |#3|)) 27 T ELT)) (-3772 (($ $) 14 T ELT)) (-3782 ((|#2| $) 12 T ELT)) (-3182 ((|#3| $) 10 T ELT))) +(((-1277 |#1| |#2| |#3|) (-10 -8 (-15 -3648 ((-663 (-1114)) |#1|)) (-15 -3625 (|#1| |#1| (-663 (-1114)) (-663 |#3|))) (-15 -3625 (|#1| |#1| (-1114) |#3|)) (-15 -3806 (|#1| |#1|)) (-15 -3625 (|#1| |#2| |#3|)) (-15 -3182 (|#3| |#1|)) (-15 -3772 (|#1| |#1|)) (-15 -3782 (|#2| |#1|))) (-1278 |#2| |#3|) (-1081) (-816)) (T -1277)) +NIL 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-571)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4133 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) |has| |#1| (-38 (-421 (-560)))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 $) |has| |#1| (-571)) ((-632 (-888)) . T) ((-175) -4133 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-240) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-239) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-298 |#2| |#1|) . T) ((-298 $ $) |has| |#2| (-1144)) ((-302) |has| |#1| (-571)) ((-571) |has| |#1| (-571)) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) |has| |#1| (-571)) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) |has| |#1| (-571)) ((-748) . T) ((-922 $ #1=(-1209)) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-928 (-1209)))) ((-928 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-928 (-1209)))) ((-930 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-928 (-1209)))) ((-1005 |#1| |#2| (-1114)) . T) ((-1083 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -4133 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1088 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4133 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . 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WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1308 3414913 3415376 3415838 "WEIER" 3416617 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1307 3413837 3414395 3414437 "VSPACE" 3414573 NIL VSPACE (NIL T) -9 NIL 3414647 NIL) (-1306 3413669 3413702 3413793 "VSPACE-" 3413798 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1305 3413466 3413520 3413588 "VOID" 3413623 T VOID (NIL) -8 NIL NIL NIL) (-1304 3409734 3410529 3411266 "VIEWDEF" 3412751 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1303 3398678 3401282 3403455 "VIEW3D" 3407583 T VIEW3D (NIL) -8 NIL NIL NIL) (-1302 3390695 3392589 3394168 "VIEW2D" 3397121 T VIEW2D (NIL) -8 NIL NIL NIL) (-1301 3388795 3389190 3389596 "VIEW" 3390311 T VIEW (NIL) -7 NIL NIL NIL) (-1300 3387348 3387631 3387949 "VECTOR2" 3388525 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1299 3382254 3387118 3387210 "VECTOR" 3387291 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1298 3375199 3379958 3380001 "VECTCAT" 3380996 NIL VECTCAT (NIL T) -9 NIL 3381583 NIL) (-1297 3374141 3374467 3374857 "VECTCAT-" 3374862 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1296 3373547 3373792 3373912 "VARIABLE" 3374056 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1295 3373480 3373485 3373515 "UTYPE" 3373520 T UTYPE (NIL) -9 NIL NIL NIL) (-1294 3372288 3372464 3372726 "UTSODETL" 3373306 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1293 3369680 3370188 3370712 "UTSODE" 3371829 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1292 3359690 3365613 3365656 "UTSCAT" 3366768 NIL UTSCAT (NIL T) -9 NIL 3367526 NIL) (-1291 3356816 3357760 3358749 "UTSCAT-" 3358754 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1290 3356437 3356486 3356619 "UTS2" 3356767 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1289 3347754 3354198 3354678 "UTS" 3356015 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1288 3341621 3344564 3344607 "URAGG" 3346677 NIL URAGG (NIL T) -9 NIL 3347400 NIL) (-1287 3338344 3339423 3340546 "URAGG-" 3340551 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1286 3333720 3336979 3337444 "UPXSSING" 3338008 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1285 3326149 3333624 3333696 "UPXSCONS" 3333701 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1284 3314907 3322351 3322413 "UPXSCCA" 3322987 NIL UPXSCCA (NIL T T) -9 NIL 3323220 NIL) (-1283 3314527 3314630 3314804 "UPXSCCA-" 3314809 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1282 3303185 3310354 3310397 "UPXSCAT" 3311045 NIL UPXSCAT (NIL T) -9 NIL 3311654 NIL) (-1281 3302609 3302694 3302873 "UPXS2" 3303100 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1280 3294101 3301991 3302255 "UPXS" 3302403 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1279 3292737 3293008 3293359 "UPSQFREE" 3293844 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1278 3285568 3289003 3289058 "UPSCAT" 3290138 NIL UPSCAT (NIL T T) -9 NIL 3290904 NIL) (-1277 3284724 3284979 3285306 "UPSCAT-" 3285311 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1276 3284345 3284394 3284527 "UPOLYC2" 3284675 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1275 3268493 3277472 3277515 "UPOLYC" 3279616 NIL UPOLYC (NIL T) -9 NIL 3280837 NIL) (-1274 3259362 3262261 3265401 "UPOLYC-" 3265406 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1273 3258683 3258808 3258972 "UPMP" 3259251 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1272 3258230 3258317 3258456 "UPDIVP" 3258596 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1271 3256768 3257047 3257363 "UPDECOMP" 3257979 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1270 3255981 3256111 3256297 "UPCDEN" 3256652 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1269 3255494 3255569 3255718 "UP2" 3255906 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1268 3246090 3255177 3255306 "UP" 3255413 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1267 3245295 3245432 3245637 "UNISEG2" 3245933 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1266 3243648 3244499 3244776 "UNISEG" 3245053 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1265 3242690 3242888 3243114 "UNIFACT" 3243464 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1264 3229421 3242594 3242666 "ULSCONS" 3242671 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1263 3209238 3222501 3222563 "ULSCCAT" 3223201 NIL ULSCCAT (NIL T T) -9 NIL 3223490 NIL) (-1262 3208234 3208533 3208921 "ULSCCAT-" 3208926 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3196689 3203780 3203823 "ULSCAT" 3204686 NIL ULSCAT (NIL T) -9 NIL 3205417 NIL) (-1260 3196113 3196198 3196377 "ULS2" 3196604 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1259 3177944 3195425 3195667 "ULS" 3195929 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1258 3176863 3177563 3177677 "UINT8" 3177788 T UINT8 (NIL) -8 NIL NIL 3177880) (-1257 3175781 3176481 3176595 "UINT64" 3176706 T UINT64 (NIL) -8 NIL NIL 3176798) (-1256 3174699 3175399 3175513 "UINT32" 3175624 T UINT32 (NIL) -8 NIL NIL 3175716) (-1255 3173617 3174317 3174431 "UINT16" 3174542 T UINT16 (NIL) -8 NIL NIL 3174634) (-1254 3171696 3172863 3172893 "UFD" 3173105 T UFD (NIL) -9 NIL 3173219 NIL) (-1253 3171478 3171536 3171631 "UFD-" 3171636 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1252 3170536 3170743 3170959 "UDVO" 3171284 T UDVO (NIL) -7 NIL NIL NIL) (-1251 3168302 3168761 3169232 "UDPO" 3170100 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1250 3168014 3168257 3168288 "TYPEAST" 3168293 T TYPEAST (NIL) -8 NIL NIL NIL) (-1249 3167947 3167952 3167982 "TYPE" 3167987 T TYPE (NIL) -9 NIL NIL NIL) (-1248 3166900 3167120 3167360 "TWOFACT" 3167741 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1247 3165875 3166309 3166544 "TUPLE" 3166700 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1246 3163512 3164085 3164624 "TUBETOOL" 3165358 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1245 3162318 3162559 3162801 "TUBE" 3163305 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1244 3150453 3155075 3155172 "TSETCAT" 3160441 NIL TSETCAT (NIL T T T T) -9 NIL 3161973 NIL) (-1243 3144921 3146785 3148676 "TSETCAT-" 3148681 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1242 3139107 3143893 3144176 "TS" 3144673 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3133580 3134593 3135522 "TRMANIP" 3138243 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1240 3133009 3133084 3133247 "TRIMAT" 3133512 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1239 3130821 3131112 3131469 "TRIGMNIP" 3132758 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1238 3130305 3130454 3130484 "TRIGCAT" 3130697 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1237 3129950 3130053 3130194 "TRIGCAT-" 3130199 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1236 3126564 3128808 3129089 "TREE" 3129704 NIL TREE (NIL T) -8 NIL NIL NIL) (-1235 3125670 3126366 3126396 "TRANFUN" 3126431 T TRANFUN (NIL) -9 NIL 3126497 NIL) (-1234 3124889 3125140 3125420 "TRANFUN-" 3125425 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1233 3124687 3124725 3124786 "TOPSP" 3124850 T TOPSP (NIL) -7 NIL NIL NIL) (-1232 3124017 3124150 3124304 "TOOLSIGN" 3124568 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1231 3122531 3123194 3123433 "TEXTFILE" 3123800 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1230 3122306 3122343 3122415 "TEX1" 3122494 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1229 3120110 3120759 3121188 "TEX" 3121899 T TEX (NIL) -8 NIL NIL NIL) (-1228 3119746 3119821 3119911 "TEMUTL" 3120042 T TEMUTL (NIL) -7 NIL NIL NIL) (-1227 3117840 3118180 3118505 "TBCMPPK" 3119469 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1226 3109160 3115926 3115982 "TBAGG" 3116382 NIL TBAGG (NIL T T) -9 NIL 3116593 NIL) (-1225 3104044 3105718 3107472 "TBAGG-" 3107477 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1224 3103410 3103535 3103680 "TANEXP" 3103933 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1223 3102861 3103185 3103275 "TALGOP" 3103355 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1222 3102255 3102372 3102510 "TABLEAU" 3102758 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1221 3095269 3102112 3102205 "TABLE" 3102210 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1220 3089799 3091097 3092345 "TABLBUMP" 3094055 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1219 3089009 3089168 3089349 "SYSTEM" 3089640 T SYSTEM (NIL) -8 NIL NIL NIL) (-1218 3085414 3086167 3086950 "SYSSOLP" 3088260 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1217 3085176 3085369 3085400 "SYSPTR" 3085405 T SYSPTR (NIL) -8 NIL NIL NIL) (-1216 3084015 3084707 3084833 "SYSNNI" 3085019 NIL SYSNNI (NIL NIL) -8 NIL NIL 3085111) (-1215 3083222 3083777 3083856 "SYSINT" 3083916 NIL SYSINT (NIL NIL) -8 NIL NIL 3083961) (-1214 3079320 3080500 3081210 "SYNTAX" 3082534 T SYNTAX (NIL) -8 NIL NIL NIL) (-1213 3076400 3077080 3077712 "SYMTAB" 3078710 T SYMTAB (NIL) -8 NIL NIL NIL) (-1212 3071499 3072551 3073534 "SYMS" 3075439 T SYMS (NIL) -8 NIL NIL NIL) (-1211 3068405 3070950 3071183 "SYMPOLY" 3071301 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1210 3067910 3067997 3068120 "SYMFUNC" 3068317 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1209 3063708 3065222 3066035 "SYMBOL" 3067119 T SYMBOL (NIL) -8 NIL NIL NIL) (-1208 3057181 3058936 3060656 "SWITCH" 3062010 T SWITCH (NIL) -8 NIL NIL NIL) (-1207 3049942 3056137 3056431 "SUTS" 3056945 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1206 3041434 3049324 3049588 "SUPXS" 3049736 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3040581 3040720 3040937 "SUPFRACF" 3041302 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1204 3040196 3040261 3040374 "SUP2" 3040516 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1203 3030740 3039814 3039940 "SUP" 3040105 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3029164 3029462 3029818 "SUMRF" 3030439 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1201 3028487 3028565 3028757 "SUMFS" 3029085 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1200 3010353 3027799 3028041 "SULS" 3028303 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1199 3009901 3010175 3010245 "SUCHTAST" 3010305 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1198 3009142 3009426 3009566 "SUCH" 3009809 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1197 3002781 3004048 3005007 "SUBSPACE" 3008230 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1196 3002201 3002301 3002465 "SUBRESP" 3002669 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1195 2996212 2997494 2998641 "STTFNC" 3001101 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1194 2989406 2990877 2992188 "STTF" 2994948 NIL STTF (NIL T) -7 NIL NIL NIL) (-1193 2980522 2982588 2984382 "STTAYLOR" 2987647 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1192 2973276 2980386 2980469 "STRTBL" 2980474 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1191 2967673 2972985 2973084 "STRING" 2973199 T STRING (NIL) -8 NIL NIL NIL) (-1190 2967177 2967260 2967404 "STREAM3" 2967590 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1189 2966141 2966342 2966577 "STREAM2" 2966990 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1188 2965823 2965881 2965974 "STREAM1" 2966083 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1187 2957937 2963442 2964053 "STREAM" 2965247 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2956929 2957134 2957365 "STINPROD" 2957753 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1185 2956044 2956418 2956566 "STEPAST" 2956803 T STEPAST (NIL) -8 NIL NIL NIL) (-1184 2955540 2955785 2955815 "STEP" 2955909 T STEP (NIL) -9 NIL 2955980 NIL) (-1183 2948596 2955439 2955516 "STBL" 2955521 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1182 2943146 2947759 2947802 "STAGG" 2947955 NIL STAGG (NIL T) -9 NIL 2948044 NIL) (-1181 2940698 2941450 2942322 "STAGG-" 2942327 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1180 2938670 2940468 2940560 "STACK" 2940641 NIL STACK (NIL T) -8 NIL NIL NIL) (-1179 2937987 2938500 2938530 "SRING" 2938535 T SRING (NIL) -9 NIL 2938555 NIL) (-1178 2929995 2936128 2936584 "SREGSET" 2937617 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1177 2922342 2923789 2925302 "SRDCMPK" 2928601 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1176 2914642 2919701 2919731 "SRAGG" 2921034 T SRAGG (NIL) -9 NIL 2921642 NIL) (-1175 2913593 2913914 2914293 "SRAGG-" 2914298 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1174 2907177 2912540 2912961 "SQMATRIX" 2913219 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1173 2900589 2903895 2904622 "SPLTREE" 2906522 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1172 2896414 2897245 2897891 "SPLNODE" 2900015 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1171 2895389 2895694 2895724 "SPFCAT" 2896168 T SPFCAT (NIL) -9 NIL NIL NIL) (-1170 2894084 2894336 2894600 "SPECOUT" 2895147 T SPECOUT (NIL) -7 NIL NIL NIL) (-1169 2884730 2887048 2887078 "SPADXPT" 2891756 T SPADXPT (NIL) -9 NIL 2893922 NIL) (-1168 2884485 2884531 2884600 "SPADPRSR" 2884683 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1167 2882088 2884440 2884471 "SPADAST" 2884476 T SPADAST (NIL) -8 NIL NIL NIL) (-1166 2873689 2875792 2875835 "SPACEC" 2880208 NIL SPACEC (NIL T) -9 NIL 2882024 NIL) (-1165 2871489 2873621 2873670 "SPACE3" 2873675 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1164 2870221 2870412 2870703 "SORTPAK" 2871294 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1163 2868283 2868616 2869028 "SOLVETRA" 2869885 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1162 2867321 2867555 2867816 "SOLVESER" 2868056 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1161 2862553 2863513 2864508 "SOLVERAD" 2866373 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1160 2858278 2858977 2859706 "SOLVEFOR" 2861920 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1159 2851882 2857626 2857723 "SNTSCAT" 2857728 NIL SNTSCAT (NIL T T T T) -9 NIL 2857798 NIL) (-1158 2845433 2850205 2850596 "SMTS" 2851572 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1157 2839155 2845321 2845398 "SMP" 2845403 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1156 2837284 2837615 2838013 "SMITH" 2838852 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1155 2828809 2833863 2833966 "SMATCAT" 2835317 NIL SMATCAT (NIL NIL T T T) -9 NIL 2835867 NIL) (-1154 2825581 2826572 2827750 "SMATCAT-" 2827755 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1153 2823050 2824789 2824832 "SKAGG" 2825093 NIL SKAGG (NIL T) -9 NIL 2825228 NIL) (-1152 2818570 2822533 2822710 "SINT" 2822862 T SINT (NIL) -8 NIL NIL 2823017) (-1151 2818336 2818380 2818446 "SIMPAN" 2818526 T SIMPAN (NIL) -7 NIL NIL NIL) (-1150 2817156 2817395 2817670 "SIGNRF" 2818095 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1149 2815971 2816140 2816424 "SIGNEF" 2816985 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1148 2815211 2815554 2815678 "SIGAST" 2815869 T SIGAST (NIL) -8 NIL NIL NIL) (-1147 2814436 2814746 2814886 "SIG" 2815093 T SIG (NIL) -8 NIL NIL NIL) (-1146 2812088 2812580 2813086 "SHP" 2813977 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1145 2805412 2811989 2812065 "SHDP" 2812070 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1144 2804923 2805163 2805193 "SGROUP" 2805286 T SGROUP (NIL) -9 NIL 2805348 NIL) (-1143 2804775 2804807 2804880 "SGROUP-" 2804885 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1142 2801494 2802264 2802987 "SGCF" 2804074 T SGCF (NIL) -7 NIL NIL NIL) (-1141 2795196 2800940 2801037 "SFRTCAT" 2801042 NIL SFRTCAT (NIL T T T T) -9 NIL 2801081 NIL) (-1140 2788515 2789635 2790771 "SFRGCD" 2794179 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1139 2781533 2782714 2783900 "SFQCMPK" 2787448 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781135 2781242 2781353 "SFORT" 2781474 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1137 2780061 2780975 2781096 "SEXOF" 2781101 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1136 2775650 2776557 2776652 "SEXCAT" 2779274 NIL SEXCAT (NIL T T T T T) -9 NIL 2779834 NIL) (-1135 2774565 2775531 2775599 "SEX" 2775604 T SEX (NIL) -8 NIL NIL NIL) (-1134 2772687 2773278 2773583 "SETMN" 2774306 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1133 2772217 2772405 2772435 "SETCAT" 2772552 T SETCAT (NIL) -9 NIL 2772637 NIL) (-1132 2771985 2772049 2772148 "SETCAT-" 2772153 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1131 2768088 2770446 2770489 "SETAGG" 2771359 NIL SETAGG (NIL T) -9 NIL 2771699 NIL) (-1130 2767510 2767662 2767899 "SETAGG-" 2767904 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1129 2764319 2767444 2767492 "SET" 2767497 NIL SET (NIL T) -8 NIL NIL NIL) (-1128 2763702 2764015 2764116 "SEQAST" 2764240 T SEQAST (NIL) -8 NIL NIL NIL) (-1127 2762829 2763195 2763256 "SEGXCAT" 2763542 NIL SEGXCAT (NIL T T) -9 NIL 2763662 NIL) (-1126 2761754 2762022 2762065 "SEGCAT" 2762587 NIL SEGCAT (NIL T) -9 NIL 2762808 NIL) (-1125 2761369 2761434 2761547 "SEGBIND2" 2761689 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1124 2760259 2760732 2760940 "SEGBIND" 2761196 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1123 2759778 2760060 2760137 "SEGAST" 2760204 T SEGAST (NIL) -8 NIL NIL NIL) (-1122 2758987 2759123 2759327 "SEG2" 2759622 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1121 2757903 2758653 2758835 "SEG" 2758840 NIL SEG (NIL T) -8 NIL NIL NIL) (-1120 2757136 2757838 2757885 "SDVAR" 2757890 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1119 2748494 2756906 2757036 "SDPOL" 2757041 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1118 2747063 2747353 2747672 "SCPKG" 2748209 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1117 2746185 2746399 2746591 "SCOPE" 2746893 T SCOPE (NIL) -8 NIL NIL NIL) (-1116 2745381 2745539 2745718 "SCACHE" 2746040 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1115 2744965 2745199 2745229 "SASTCAT" 2745234 T SASTCAT (NIL) -9 NIL 2745247 NIL) (-1114 2744368 2744800 2744876 "SAOS" 2744911 T SAOS (NIL) -8 NIL NIL NIL) (-1113 2743927 2743968 2744141 "SAERFFC" 2744327 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1112 2743514 2743555 2743714 "SAEFACT" 2743886 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1111 2736562 2743411 2743491 "SAE" 2743496 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2734865 2735197 2735598 "RURPK" 2736228 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1109 2733442 2733808 2734113 "RULESET" 2734699 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1108 2733012 2733236 2733319 "RULECOLD" 2733394 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1107 2730127 2730765 2731223 "RULE" 2732693 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2729911 2729945 2730016 "RTVALUE" 2730078 T RTVALUE (NIL) -8 NIL NIL NIL) (-1105 2729322 2729628 2729722 "RSTRCAST" 2729839 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1104 2724092 2724965 2725885 "RSETGCD" 2728521 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1103 2712656 2718400 2718497 "RSETCAT" 2722616 NIL RSETCAT (NIL T T T T) -9 NIL 2723713 NIL) (-1102 2710475 2711122 2711946 "RSETCAT-" 2711951 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1101 2702783 2704237 2705757 "RSDCMPK" 2709074 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2700652 2701215 2701289 "RRCC" 2702375 NIL RRCC (NIL T T) -9 NIL 2702719 NIL) (-1099 2699973 2700177 2700456 "RRCC-" 2700461 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1098 2699356 2699669 2699770 "RPTAST" 2699894 T RPTAST (NIL) -8 NIL NIL NIL) (-1097 2671742 2682468 2682535 "RPOLCAT" 2693201 NIL RPOLCAT (NIL T T T) -9 NIL 2696361 NIL) (-1096 2662712 2665580 2668702 "RPOLCAT-" 2668707 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1095 2653165 2660923 2661405 "ROUTINE" 2662252 T ROUTINE (NIL) -8 NIL NIL NIL) (-1094 2649228 2652791 2652931 "ROMAN" 2653047 T ROMAN (NIL) -8 NIL NIL NIL) (-1093 2647340 2648088 2648348 "ROIRC" 2649033 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1092 2643113 2645882 2645912 "RNS" 2646181 T RNS (NIL) -9 NIL 2646437 NIL) (-1091 2641520 2642005 2642539 "RNS-" 2642614 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1090 2640481 2640885 2641087 "RNGBIND" 2641371 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1089 2639774 2640278 2640308 "RNG" 2640313 T RNG (NIL) -9 NIL 2640334 NIL) (-1088 2639069 2639547 2639590 "RMODULE" 2639595 NIL RMODULE (NIL T) -9 NIL 2639622 NIL) (-1087 2637893 2637999 2638335 "RMCAT2" 2638970 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1086 2634395 2637239 2637536 "RMATRIX" 2637655 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1085 2626894 2629482 2629597 "RMATCAT" 2632956 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2633938 NIL) (-1084 2626233 2626416 2626723 "RMATCAT-" 2626728 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1083 2625806 2626020 2626063 "RLINSET" 2626125 NIL RLINSET (NIL T) -9 NIL 2626169 NIL) (-1082 2625367 2625448 2625576 "RINTERP" 2625725 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1081 2624291 2624965 2624995 "RING" 2625051 T RING (NIL) -9 NIL 2625143 NIL) (-1080 2624071 2624127 2624224 "RING-" 2624229 NIL RING- (NIL T) -8 NIL NIL NIL) (-1079 2622882 2623149 2623407 "RIDIST" 2623835 T RIDIST (NIL) -7 NIL NIL NIL) (-1078 2613507 2622350 2622556 "RGCHAIN" 2622730 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1077 2612765 2613249 2613290 "RGBCSPC" 2613348 NIL RGBCSPC (NIL T) -9 NIL 2613400 NIL) (-1076 2611831 2612290 2612331 "RGBCMDL" 2612563 NIL RGBCMDL (NIL T) -9 NIL 2612677 NIL) (-1075 2611471 2611540 2611643 "RFFACTOR" 2611762 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1074 2611190 2611231 2611328 "RFFACT" 2611430 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1073 2609241 2609671 2610053 "RFDIST" 2610830 T RFDIST (NIL) -7 NIL NIL NIL) (-1072 2606181 2606849 2607519 "RF" 2608605 NIL RF (NIL T) -7 NIL NIL NIL) (-1071 2605628 2605726 2605889 "RETSOL" 2606083 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1070 2605246 2605344 2605387 "RETRACT" 2605520 NIL RETRACT (NIL T) -9 NIL 2605607 NIL) (-1069 2605089 2605120 2605207 "RETRACT-" 2605212 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1068 2604637 2604911 2604981 "RETAST" 2605041 T RETAST (NIL) -8 NIL NIL NIL) (-1067 2596987 2604290 2604417 "RESULT" 2604532 T RESULT (NIL) -8 NIL NIL NIL) (-1066 2595422 2596256 2596455 "RESRING" 2596890 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1065 2595046 2595107 2595205 "RESLATC" 2595359 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1064 2594745 2594786 2594893 "REPSQ" 2595005 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1063 2594436 2594477 2594588 "REPDB" 2594704 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1062 2588268 2589725 2590948 "REP2" 2593248 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1061 2584571 2585326 2586134 "REP1" 2587495 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1060 2581951 2582573 2583175 "REP" 2583991 T REP (NIL) -7 NIL NIL NIL) (-1059 2573959 2580092 2580548 "REGSET" 2581581 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2572668 2573107 2573357 "REF" 2573744 NIL REF (NIL T) -8 NIL NIL NIL) (-1057 2572033 2572148 2572315 "REDORDER" 2572552 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1056 2567404 2571246 2571473 "RECLOS" 2571861 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1055 2566438 2566637 2566852 "REALSOLV" 2567211 T REALSOLV (NIL) -7 NIL NIL NIL) (-1054 2562885 2563723 2564607 "REAL0Q" 2565603 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1053 2558438 2559474 2560535 "REAL0" 2561866 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1052 2558272 2558325 2558355 "REAL" 2558360 T REAL (NIL) -9 NIL 2558395 NIL) (-1051 2557683 2557989 2558083 "RDUCEAST" 2558200 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1050 2557082 2557160 2557367 "RDIV" 2557605 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1049 2556132 2556324 2556537 "RDIST" 2556904 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1048 2554717 2555016 2555388 "RDETRS" 2555840 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1047 2552511 2552983 2553521 "RDETR" 2554259 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1046 2551130 2551414 2551811 "RDEEFS" 2552227 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1045 2549633 2549945 2550370 "RDEEF" 2550818 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1044 2543112 2546587 2546617 "RCFIELD" 2547912 T RCFIELD (NIL) -9 NIL 2548643 NIL) (-1043 2541068 2541680 2542376 "RCFIELD-" 2542451 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1042 2537120 2539141 2539184 "RCAGG" 2540268 NIL RCAGG (NIL T) -9 NIL 2540733 NIL) (-1041 2536730 2536842 2537005 "RCAGG-" 2537010 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1040 2536047 2536177 2536342 "RATRET" 2536614 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1039 2535588 2535667 2535788 "RATFACT" 2535975 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1038 2534866 2535016 2535168 "RANDSRC" 2535458 T RANDSRC (NIL) -7 NIL NIL NIL) (-1037 2534594 2534644 2534717 "RADUTIL" 2534815 T RADUTIL (NIL) -7 NIL NIL NIL) (-1036 2526739 2533425 2533736 "RADIX" 2534317 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1035 2516354 2526581 2526711 "RADFF" 2526716 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1034 2515983 2516076 2516106 "RADCAT" 2516266 T RADCAT (NIL) -9 NIL NIL NIL) (-1033 2515753 2515813 2515913 "RADCAT-" 2515918 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1032 2513664 2515523 2515615 "QUEUE" 2515696 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1031 2513289 2513338 2513469 "QUATCT2" 2513615 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1030 2505667 2509712 2509754 "QUATCAT" 2510545 NIL QUATCAT (NIL T) -9 NIL 2511311 NIL) (-1029 2501548 2502843 2504233 "QUATCAT-" 2504329 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1028 2497394 2501481 2501529 "QUAT" 2501534 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1027 2494650 2496442 2496485 "QUAGG" 2496866 NIL QUAGG (NIL T) -9 NIL 2497041 NIL) (-1026 2494198 2494472 2494542 "QQUTAST" 2494602 T QQUTAST (NIL) -8 NIL NIL NIL) (-1025 2493109 2493711 2493876 "QFORM" 2494079 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1024 2492734 2492783 2492914 "QFCAT2" 2493060 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1023 2482431 2488581 2488623 "QFCAT" 2489291 NIL QFCAT (NIL T) -9 NIL 2490292 NIL) (-1022 2477765 2479213 2480800 "QFCAT-" 2480896 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2477196 2477330 2477462 "QEQUAT" 2477655 T QEQUAT (NIL) -8 NIL NIL NIL) (-1020 2470214 2471395 2472581 "QCMPACK" 2476129 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2469443 2469625 2469861 "QALGSET2" 2470032 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1018 2466893 2467429 2467859 "QALGSET" 2469098 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2465560 2465802 2466121 "PWFFINTB" 2466666 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1016 2463705 2463903 2464259 "PUSHVAR" 2465374 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1015 2459432 2460648 2460691 "PTRANFN" 2462602 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1014 2457769 2458114 2458438 "PTPACK" 2459143 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1013 2457392 2457455 2457566 "PTFUNC2" 2457706 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1012 2451308 2456181 2456224 "PTCAT" 2456524 NIL PTCAT (NIL T) -9 NIL 2456677 NIL) (-1011 2450957 2450998 2451124 "PSQFR" 2451267 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1010 2449529 2449845 2450181 "PSEUDLIN" 2450655 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1009 2436049 2438624 2440950 "PSETPK" 2447289 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1008 2428757 2431785 2431883 "PSETCAT" 2434924 NIL PSETCAT (NIL T T T T) -9 NIL 2435738 NIL) (-1007 2426482 2427224 2428048 "PSETCAT-" 2428053 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1006 2425795 2425990 2426020 "PSCURVE" 2426292 T PSCURVE (NIL) -9 NIL 2426459 NIL) (-1005 2421518 2423285 2423352 "PSCAT" 2424204 NIL PSCAT (NIL T T T) -9 NIL 2424444 NIL) (-1004 2420512 2420794 2421197 "PSCAT-" 2421202 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1003 2418680 2419571 2419836 "PRTITION" 2420269 T PRTITION (NIL) -8 NIL NIL NIL) (-1002 2418091 2418397 2418491 "PRTDAST" 2418608 T PRTDAST (NIL) -8 NIL NIL NIL) (-1001 2406935 2409357 2411547 "PRS" 2415953 NIL PRS (NIL T T) -7 NIL NIL NIL) (-1000 2404550 2406252 2406294 "PRQAGG" 2406480 NIL PRQAGG (NIL T) -9 NIL 2406582 NIL) (-999 2403729 2404178 2404206 "PROPLOG" 2404345 T PROPLOG (NIL) -9 NIL 2404460 NIL) (-998 2403327 2403390 2403513 "PROPFUN2" 2403652 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-997 2402624 2402763 2402935 "PROPFUN1" 2403188 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-996 2400605 2401371 2401668 "PROPFRML" 2402360 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-995 2400050 2400181 2400309 "PROPERTY" 2400497 T PROPERTY (NIL) -8 NIL NIL NIL) (-994 2393863 2398216 2399036 "PRODUCT" 2399276 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-993 2393653 2393691 2393750 "PRINT" 2393824 T PRINT (NIL) -7 NIL NIL NIL) (-992 2392969 2393110 2393262 "PRIMES" 2393533 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-991 2391016 2391435 2391901 "PRIMELT" 2392548 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-990 2390733 2390794 2390822 "PRIMCAT" 2390946 T PRIMCAT (NIL) -9 NIL NIL NIL) (-989 2389722 2389918 2390146 "PRIMARR2" 2390551 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-988 2385444 2389660 2389705 "PRIMARR" 2389710 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-987 2385081 2385143 2385254 "PREASSOC" 2385382 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-986 2382046 2384539 2384773 "PR" 2384892 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2381497 2381654 2381682 "PPCURVE" 2381887 T PPCURVE (NIL) -9 NIL 2382023 NIL) (-984 2381044 2381292 2381375 "PORTNUM" 2381434 T PORTNUM (NIL) -8 NIL NIL NIL) (-983 2378381 2378802 2379394 "POLYROOT" 2380625 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-982 2377758 2377822 2378056 "POLYLIFT" 2378317 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-981 2373979 2374482 2375111 "POLYCATQ" 2377303 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-980 2359627 2365726 2365791 "POLYCAT" 2369305 NIL POLYCAT (NIL T T T) -9 NIL 2371183 NIL) (-979 2352767 2354952 2357329 "POLYCAT-" 2357334 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-978 2352348 2352422 2352542 "POLY2UP" 2352693 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-977 2351974 2352037 2352146 "POLY2" 2352285 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-976 2345189 2351578 2351738 "POLY" 2351847 NIL POLY (NIL T) -8 NIL NIL NIL) (-975 2343850 2344113 2344389 "POLUTIL" 2344963 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-974 2342169 2342482 2342813 "POLTOPOL" 2343572 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-973 2337165 2342103 2342150 "POINT" 2342155 NIL POINT (NIL T) -8 NIL NIL NIL) (-972 2335298 2335709 2336084 "PNTHEORY" 2336810 T PNTHEORY (NIL) -7 NIL NIL NIL) (-971 2333744 2334053 2334452 "PMTOOLS" 2334996 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-970 2333331 2333415 2333532 "PMSYM" 2333660 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-969 2332833 2332908 2333083 "PMQFCAT" 2333256 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-968 2332214 2332312 2332474 "PMPREDFS" 2332734 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-967 2331557 2331679 2331835 "PMPRED" 2332091 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2330211 2330429 2330807 "PMPLCAT" 2331319 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-965 2329737 2329822 2329974 "PMLSAGG" 2330126 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-964 2329204 2329286 2329468 "PMKERNEL" 2329655 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-963 2328815 2328896 2329009 "PMINS" 2329123 NIL PMINS (NIL T) -7 NIL NIL NIL) (-962 2328251 2328326 2328535 "PMFS" 2328740 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-961 2327467 2327597 2327802 "PMDOWN" 2328128 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-960 2326716 2326850 2327013 "PMASSFS" 2327354 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-959 2325859 2326041 2326222 "PMASS" 2326555 T PMASS (NIL) -7 NIL NIL NIL) (-958 2325508 2325582 2325676 "PLOTTOOL" 2325785 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-957 2321160 2322354 2323276 "PLOT3D" 2324606 T PLOT3D (NIL) -8 NIL NIL NIL) (-956 2320048 2320249 2320484 "PLOT1" 2320964 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-955 2314469 2315859 2317007 "PLOT" 2318920 T PLOT (NIL) -8 NIL NIL NIL) (-954 2289644 2294535 2299386 "PLEQN" 2309735 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-953 2289331 2289384 2289487 "PINTERPA" 2289591 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-952 2288637 2288771 2288951 "PINTERP" 2289196 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2286721 2287887 2287915 "PID" 2288112 T PID (NIL) -9 NIL 2288239 NIL) (-950 2286466 2286509 2286584 "PICOERCE" 2286678 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-949 2285562 2286230 2286317 "PI" 2286357 T PI (NIL) -8 NIL NIL 2286424) (-948 2284870 2285021 2285197 "PGROEB" 2285418 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-947 2280309 2281268 2282174 "PGE" 2283984 T PGE (NIL) -7 NIL NIL NIL) (-946 2278390 2278679 2279045 "PGCD" 2280026 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-945 2277716 2277831 2277992 "PFRPAC" 2278274 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-944 2273974 2276264 2276617 "PFR" 2277395 NIL PFR (NIL T) -8 NIL NIL NIL) (-943 2272327 2272607 2272932 "PFOTOOLS" 2273721 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-942 2270842 2271099 2271450 "PFOQ" 2272084 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-941 2269325 2269555 2269911 "PFO" 2270626 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-940 2266409 2267915 2267943 "PFECAT" 2268536 T PFECAT (NIL) -9 NIL 2268913 NIL) (-939 2265857 2266022 2266229 "PFECAT-" 2266234 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-938 2264430 2264712 2265013 "PFBRU" 2265606 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-937 2262259 2262648 2263080 "PFBR" 2264081 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-936 2258205 2262148 2262217 "PF" 2262222 NIL PF (NIL NIL) -8 NIL NIL NIL) (-935 2253259 2254412 2255282 "PERMGRP" 2257368 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-934 2251171 2252283 2252324 "PERMCAT" 2252724 NIL PERMCAT (NIL T) -9 NIL 2253022 NIL) (-933 2250818 2250865 2250989 "PERMAN" 2251124 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-932 2246620 2248327 2248975 "PERM" 2250203 NIL PERM (NIL T) -8 NIL NIL NIL) (-931 2243861 2246285 2246407 "PENDTREE" 2246531 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-930 2242742 2243005 2243046 "PDSPC" 2243579 NIL PDSPC (NIL T) -9 NIL 2243824 NIL) (-929 2241797 2242063 2242425 "PDSPC-" 2242430 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-928 2240511 2241447 2241488 "PDRING" 2241493 NIL PDRING (NIL T) -9 NIL 2241521 NIL) (-927 2239254 2240016 2240070 "PDMOD" 2240075 NIL PDMOD (NIL T T) -9 NIL 2240179 NIL) (-926 2236421 2237247 2237915 "PDEPROB" 2238606 T PDEPROB (NIL) -8 NIL NIL NIL) (-925 2233930 2234470 2235025 "PDEPACK" 2235886 T PDEPACK (NIL) -7 NIL NIL NIL) (-924 2232818 2233032 2233283 "PDECOMP" 2233729 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-923 2230335 2231226 2231254 "PDECAT" 2232041 T PDECAT (NIL) -9 NIL 2232754 NIL) (-922 2229952 2230019 2230073 "PDDOM" 2230238 NIL PDDOM (NIL T T) -9 NIL 2230318 NIL) (-921 2229765 2229801 2229908 "PDDOM-" 2229913 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-920 2229510 2229549 2229639 "PCOMP" 2229726 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-919 2227550 2228311 2228608 "PBWLB" 2229239 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-918 2227176 2227239 2227348 "PATTERN2" 2227487 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-917 2224885 2225321 2225778 "PATTERN1" 2226765 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-916 2217064 2218958 2220296 "PATTERN" 2223568 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2216622 2216695 2216827 "PATRES2" 2216991 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-914 2213888 2214571 2215052 "PATRES" 2216187 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2211741 2212176 2212583 "PATMATCH" 2213555 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-912 2211195 2211446 2211487 "PATMAB" 2211594 NIL PATMAB (NIL T) -9 NIL 2211677 NIL) (-911 2209641 2210049 2210307 "PATLRES" 2211000 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-910 2209179 2209310 2209351 "PATAB" 2209356 NIL PATAB (NIL T) -9 NIL 2209528 NIL) (-909 2207319 2207756 2208179 "PARTPERM" 2208776 T PARTPERM (NIL) -7 NIL NIL NIL) (-908 2206928 2207003 2207105 "PARSURF" 2207250 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-907 2206554 2206617 2206726 "PARSU2" 2206865 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-906 2206312 2206358 2206425 "PARSER" 2206507 T PARSER (NIL) -7 NIL NIL NIL) (-905 2205921 2205996 2206098 "PARSCURV" 2206243 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-904 2205547 2205610 2205719 "PARSC2" 2205858 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-903 2205174 2205244 2205341 "PARPCURV" 2205483 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-902 2204800 2204863 2204972 "PARPC2" 2205111 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-901 2203789 2204173 2204355 "PARAMAST" 2204638 T PARAMAST (NIL) -8 NIL NIL NIL) (-900 2203297 2203395 2203514 "PAN2EXPR" 2203690 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-899 2201990 2202418 2202646 "PALETTE" 2203089 T PALETTE (NIL) -8 NIL NIL NIL) (-898 2200335 2200995 2201355 "PAIR" 2201676 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-897 2193268 2199592 2199787 "PADICRC" 2200189 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-896 2185525 2192612 2192797 "PADICRAT" 2193115 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-895 2182322 2184185 2184225 "PADICCT" 2184806 NIL PADICCT (NIL NIL) -9 NIL 2185088 NIL) (-894 2180338 2182259 2182304 "PADIC" 2182309 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2179283 2179495 2179763 "PADEPAC" 2180125 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-892 2178483 2178628 2178834 "PADE" 2179145 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-891 2176716 2177691 2177971 "OWP" 2178287 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-890 2176161 2176422 2176519 "OVERSET" 2176639 T OVERSET (NIL) -8 NIL NIL NIL) (-889 2175081 2175766 2175938 "OVAR" 2176029 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-888 2163317 2166190 2168390 "OUTFORM" 2172901 T OUTFORM (NIL) -8 NIL NIL NIL) (-887 2162599 2162914 2163041 "OUTBFILE" 2163210 T OUTBFILE (NIL) -8 NIL NIL NIL) (-886 2161876 2162071 2162099 "OUTBCON" 2162417 T OUTBCON (NIL) -9 NIL 2162583 NIL) (-885 2161459 2161589 2161746 "OUTBCON-" 2161751 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-884 2160699 2160844 2161005 "OUT" 2161318 T OUT (NIL) -7 NIL NIL NIL) (-883 2159995 2160428 2160517 "OSI" 2160630 T OSI (NIL) -8 NIL NIL NIL) (-882 2159414 2159836 2159864 "OSGROUP" 2159869 T OSGROUP (NIL) -9 NIL 2159891 NIL) (-881 2158125 2158386 2158671 "ORTHPOL" 2159161 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-880 2155376 2157960 2158081 "OREUP" 2158086 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-879 2152479 2155067 2155194 "ORESUP" 2155318 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-878 2149979 2150507 2151068 "OREPCTO" 2151968 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-877 2143357 2145852 2145893 "OREPCAT" 2148241 NIL OREPCAT (NIL T) -9 NIL 2149345 NIL) (-876 2140330 2141286 2142344 "OREPCAT-" 2142349 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-875 2139522 2139800 2139828 "ORDTYPE" 2140137 T ORDTYPE (NIL) -9 NIL 2140300 NIL) (-874 2138823 2139039 2139294 "ORDTYPE-" 2139299 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-873 2138179 2138562 2138720 "ORDSTRCT" 2138725 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-872 2137677 2138047 2138075 "ORDSET" 2138080 T ORDSET (NIL) -9 NIL 2138102 NIL) (-871 2136328 2137299 2137327 "ORDRING" 2137332 T ORDRING (NIL) -9 NIL 2137361 NIL) (-870 2135579 2136144 2136172 "ORDMON" 2136177 T ORDMON (NIL) -9 NIL 2136198 NIL) (-869 2134723 2134888 2135083 "ORDFUNS" 2135428 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-868 2133938 2134453 2134481 "ORDFIN" 2134546 T ORDFIN (NIL) -9 NIL 2134620 NIL) (-867 2133192 2133331 2133517 "ORDCOMP2" 2133798 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-866 2129539 2131778 2132187 "ORDCOMP" 2132816 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-865 2126060 2127030 2127844 "OPTPROB" 2128745 T OPTPROB (NIL) -8 NIL NIL NIL) (-864 2122802 2123501 2124205 "OPTPACK" 2125376 T OPTPACK (NIL) -7 NIL NIL NIL) (-863 2120415 2121241 2121269 "OPTCAT" 2122088 T OPTCAT (NIL) -9 NIL 2122738 NIL) (-862 2119733 2120092 2120197 "OPSIG" 2120330 T OPSIG (NIL) -8 NIL NIL NIL) (-861 2119495 2119540 2119606 "OPQUERY" 2119687 T OPQUERY (NIL) -7 NIL NIL NIL) (-860 2118801 2119081 2119122 "OPERCAT" 2119334 NIL OPERCAT (NIL T) -9 NIL 2119431 NIL) (-859 2118544 2118612 2118729 "OPERCAT-" 2118734 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-858 2115460 2116855 2117359 "OP" 2118073 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2114753 2114880 2115054 "ONECOMP2" 2115332 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-856 2111366 2113550 2113919 "ONECOMP" 2114417 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-855 2110767 2110891 2111021 "OMSERVER" 2111256 T OMSERVER (NIL) -7 NIL NIL NIL) (-854 2107279 2110205 2110245 "OMSAGG" 2110306 NIL OMSAGG (NIL T) -9 NIL 2110371 NIL) (-853 2105854 2106165 2106447 "OMPKG" 2107017 T OMPKG (NIL) -7 NIL NIL NIL) (-852 2104201 2105403 2105572 "OMLO" 2105735 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-851 2103137 2103308 2103528 "OMEXPR" 2104027 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-850 2102222 2102558 2102718 "OMERRK" 2102997 T OMERRK (NIL) -8 NIL NIL NIL) (-849 2101459 2101768 2101904 "OMERR" 2102106 T OMERR (NIL) -8 NIL NIL NIL) (-848 2100850 2101136 2101244 "OMENC" 2101371 T OMENC (NIL) -8 NIL NIL NIL) (-847 2094487 2095930 2097101 "OMDEV" 2099699 T OMDEV (NIL) -8 NIL NIL NIL) (-846 2093520 2093727 2093921 "OMCONN" 2094313 T OMCONN (NIL) -8 NIL NIL NIL) (-845 2092926 2093053 2093081 "OM" 2093380 T OM (NIL) -9 NIL NIL NIL) (-844 2091204 2092396 2092424 "OINTDOM" 2092429 T OINTDOM (NIL) -9 NIL 2092450 NIL) (-843 2088279 2089892 2090229 "OFMONOID" 2090899 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-842 2087513 2088216 2088261 "ODVAR" 2088266 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-841 2084657 2087258 2087413 "ODR" 2087418 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-840 2076069 2084433 2084559 "ODPOL" 2084564 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-839 2069363 2075941 2076046 "ODP" 2076051 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-838 2068105 2068344 2068619 "ODETOOLS" 2069137 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-837 2065048 2065730 2066446 "ODESYS" 2067438 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-836 2059878 2060838 2061863 "ODERTRIC" 2064123 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-835 2059298 2059386 2059580 "ODERED" 2059790 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-834 2056150 2056734 2057411 "ODERAT" 2058721 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-833 2053066 2053574 2054171 "ODEPRRIC" 2055679 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-832 2050961 2051605 2052091 "ODEPROB" 2052600 T ODEPROB (NIL) -8 NIL NIL NIL) (-831 2047427 2047966 2048613 "ODEPRIM" 2050440 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-830 2046670 2046778 2047038 "ODEPAL" 2047319 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-829 2042772 2043623 2044487 "ODEPACK" 2045826 T ODEPACK (NIL) -7 NIL NIL NIL) (-828 2041815 2041940 2042162 "ODEINT" 2042661 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-827 2035880 2037341 2038788 "ODEIFTBL" 2040388 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-826 2031230 2032064 2033016 "ODEEF" 2035039 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-825 2030573 2030668 2030891 "ODECONST" 2031135 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-824 2028636 2029345 2029373 "ODECAT" 2029978 T ODECAT (NIL) -9 NIL 2030509 NIL) (-823 2028268 2028317 2028444 "OCTCT2" 2028587 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-822 2024768 2027973 2028095 "OCT" 2028178 NIL OCT (NIL T) -8 NIL NIL NIL) (-821 2023961 2024561 2024589 "OCAMON" 2024594 T OCAMON (NIL) -9 NIL 2024615 NIL) (-820 2018232 2021004 2021044 "OC" 2022141 NIL OC (NIL T) -9 NIL 2022999 NIL) (-819 2015267 2016207 2017197 "OC-" 2017291 NIL OC- (NIL T T) -8 NIL NIL NIL) (-818 2014687 2015112 2015140 "OASGP" 2015145 T OASGP (NIL) -9 NIL 2015165 NIL) (-817 2013783 2014410 2014438 "OAMONS" 2014478 T OAMONS (NIL) -9 NIL 2014521 NIL) (-816 2012959 2013518 2013546 "OAMON" 2013604 T OAMON (NIL) -9 NIL 2013656 NIL) (-815 2012817 2012850 2012918 "OAMON-" 2012923 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-814 2011598 2012351 2012379 "OAGROUP" 2012526 T OAGROUP (NIL) -9 NIL 2012619 NIL) (-813 2011301 2011389 2011507 "OAGROUP-" 2011512 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-812 2010983 2011039 2011128 "NUMTUBE" 2011245 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004502 2006074 2007610 "NUMQUAD" 2009467 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000182 2001216 2002251 "NUMODE" 2003487 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997463 1998403 1998431 "NUMINT" 1999354 T NUMINT (NIL) -9 NIL 2000118 NIL) (-808 1996375 1996608 1996826 "NUMFMT" 1997265 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982558 1985679 1988211 "NUMERIC" 1993882 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976262 1982006 1982101 "NTSCAT" 1982106 NIL NTSCAT (NIL T T T T) -9 NIL 1982145 NIL) (-805 1975442 1975621 1975814 "NTPOLFN" 1976101 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975068 1975131 1975240 "NSUP2" 1975379 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1961850 1971893 1972705 "NSUP" 1974289 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1950693 1961624 1961757 "NSMP" 1961762 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949101 1949426 1949783 "NREP" 1950381 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1947680 1947944 1948302 "NPCOEF" 1948844 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1946728 1946861 1947077 "NORMRETR" 1947561 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1944739 1945059 1945468 "NORMPK" 1946436 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944418 1944452 1944576 "NORMMA" 1944705 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944201 1944236 1944305 "NONE1" 1944382 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1943965 1944158 1944187 "NONE" 1944192 T NONE (NIL) -8 NIL NIL NIL) (-794 1943456 1943524 1943703 "NODE1" 1943897 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941517 1942579 1942834 "NNI" 1943181 T NNI (NIL) -8 NIL NIL 1943416) (-792 1939913 1940250 1940614 "NLINSOL" 1941185 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936094 1937149 1938048 "NIPROB" 1939034 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1934833 1935085 1935387 "NFINTBAS" 1935856 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1933917 1934483 1934524 "NETCLT" 1934696 NIL NETCLT (NIL T) -9 NIL 1934778 NIL) (-788 1932589 1932856 1933137 "NCODIV" 1933685 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932345 1932388 1932463 "NCNTFRAC" 1932546 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930501 1930889 1931309 "NCEP" 1931970 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929164 1930111 1930139 "NASRING" 1930249 T NASRING (NIL) -9 NIL 1930329 NIL) (-784 1928947 1929003 1929097 "NASRING-" 1929102 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1927914 1928565 1928593 "NARNG" 1928710 T NARNG (NIL) -9 NIL 1928801 NIL) (-782 1927588 1927673 1927807 "NARNG-" 1927812 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926425 1926674 1926909 "NAGSP" 1927373 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917469 1919381 1921054 "NAGS" 1924772 T NAGS (NIL) -7 NIL NIL NIL) (-779 1915993 1916325 1916656 "NAGF07" 1917158 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910465 1911822 1913129 "NAGF04" 1914706 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903337 1905047 1906680 "NAGF02" 1908852 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898501 1899661 1900778 "NAGF01" 1902240 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892081 1893695 1895280 "NAGE04" 1896936 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883142 1885371 1887501 "NAGE02" 1889971 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879035 1880042 1881006 "NAGE01" 1882198 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1876812 1877364 1877922 "NAGD03" 1878497 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868508 1870490 1872444 "NAGD02" 1874878 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862247 1863744 1865184 "NAGD01" 1867088 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858384 1859278 1860115 "NAGC06" 1861430 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1856831 1857181 1857537 "NAGC05" 1858048 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856195 1856326 1856470 "NAGC02" 1856707 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1854996 1855723 1855763 "NAALG" 1855842 NIL NAALG (NIL T) -9 NIL 1855903 NIL) (-765 1854825 1854860 1854950 "NAALG-" 1854955 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1848697 1849883 1851070 "MULTSQFR" 1853721 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848004 1848091 1848275 "MULTFACT" 1848609 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840149 1844587 1844640 "MTSCAT" 1845710 NIL MTSCAT (NIL T T) -9 NIL 1846226 NIL) (-761 1839855 1839915 1840007 "MTHING" 1840089 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1839641 1839680 1839740 "MSYSCMD" 1839815 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836386 1839202 1839243 "MSETAGG" 1839248 NIL MSETAGG (NIL T) -9 NIL 1839282 NIL) (-758 1832100 1835141 1835461 "MSET" 1836099 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1827702 1829479 1830224 "MRING" 1831400 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827262 1827335 1827466 "MRF2" 1827629 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1826874 1826915 1827059 "MRATFAC" 1827221 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824444 1824781 1825212 "MPRFF" 1826579 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1817778 1824298 1824395 "MPOLY" 1824400 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817262 1817303 1817511 "MPCPF" 1817737 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1816770 1816819 1817003 "MPC3" 1817213 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1815953 1816046 1816267 "MPC2" 1816685 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814230 1814591 1814981 "MONOTOOL" 1815613 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813375 1813758 1813786 "MONOID" 1814005 T MONOID (NIL) -9 NIL 1814152 NIL) (-747 1812891 1813040 1813221 "MONOID-" 1813226 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1801864 1808711 1808770 "MONOGEN" 1809444 NIL MONOGEN (NIL T T) -9 NIL 1809900 NIL) (-745 1798914 1799817 1800817 "MONOGEN-" 1800936 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797631 1798179 1798207 "MONADWU" 1798599 T MONADWU (NIL) -9 NIL 1798837 NIL) (-743 1796961 1797162 1797410 "MONADWU-" 1797415 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796246 1796550 1796578 "MONAD" 1796785 T MONAD (NIL) -9 NIL 1796897 NIL) (-741 1795913 1796009 1796141 "MONAD-" 1796146 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794052 1794826 1795105 "MOEBIUS" 1795666 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793220 1793720 1793760 "MODULE" 1793765 NIL MODULE (NIL T) -9 NIL 1793804 NIL) (-738 1792758 1792884 1793074 "MODULE-" 1793079 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790288 1791122 1791449 "MODRING" 1792582 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787017 1788393 1788914 "MODOP" 1789817 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785503 1786084 1786361 "MODMONOM" 1786880 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774263 1783794 1784208 "MODMON" 1785140 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771096 1773107 1773383 "MODFIELD" 1774138 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770007 1770377 1770567 "MMLFORM" 1770926 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769527 1769576 1769755 "MMAP" 1769958 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767420 1768359 1768400 "MLO" 1768823 NIL MLO (NIL T) -9 NIL 1769065 NIL) (-729 1764768 1765302 1765904 "MLIFT" 1766901 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764147 1764243 1764397 "MKUCFUNC" 1764679 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1763740 1763816 1763939 "MKRECORD" 1764070 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1762763 1762949 1763177 "MKFUNC" 1763551 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762139 1762255 1762411 "MKFLCFN" 1762646 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761404 1761518 1761703 "MKBCFUNC" 1762032 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757401 1760958 1761094 "MINT" 1761288 T MINT (NIL) -8 NIL NIL NIL) (-722 1756183 1756456 1756733 "MHROWRED" 1757156 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1750934 1754718 1755123 "MFLOAT" 1755798 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750279 1750367 1750538 "MFINFACT" 1750846 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746558 1747442 1748326 "MESH" 1749415 T MESH (NIL) -7 NIL NIL NIL) (-718 1744912 1745260 1745613 "MDDFACT" 1746245 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741448 1744043 1744084 "MDAGG" 1744339 NIL MDAGG (NIL T) -9 NIL 1744482 NIL) (-716 1729171 1740741 1740948 "MCMPLX" 1741261 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728290 1728454 1728655 "MCDEN" 1729020 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726138 1726450 1726830 "MCALCFN" 1728020 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725015 1725303 1725536 "MAYBE" 1725944 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722573 1723150 1723712 "MATSTOR" 1724486 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1717995 1721945 1722193 "MATRIX" 1722358 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713695 1714468 1715204 "MATLIN" 1717352 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712271 1712442 1712775 "MATCAT2" 1713530 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701610 1705328 1705405 "MATCAT" 1710437 NIL MATCAT (NIL T T T) -9 NIL 1711909 NIL) (-707 1697563 1698873 1700286 "MATCAT-" 1700291 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1695639 1695999 1696383 "MAPPKG3" 1697238 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694596 1694793 1695015 "MAPPKG2" 1695463 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693053 1693379 1693706 "MAPPKG1" 1694302 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692054 1692459 1692636 "MAPPAST" 1692896 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691659 1691723 1691846 "MAPHACK3" 1691990 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691239 1691312 1691426 "MAPHACK2" 1691591 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690665 1690780 1690922 "MAPHACK1" 1691130 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688588 1689365 1689669 "MAGMA" 1690393 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688007 1688312 1688403 "MACROAST" 1688517 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684250 1686246 1686707 "M3D" 1687579 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1677722 1682561 1682602 "LZSTAGG" 1683384 NIL LZSTAGG (NIL T) -9 NIL 1683679 NIL) (-695 1673404 1674853 1676310 "LZSTAGG-" 1676315 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670317 1671295 1671782 "LWORD" 1672949 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1669839 1670121 1670196 "LSTAST" 1670262 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1661767 1669610 1669744 "LSQM" 1669749 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1660985 1661130 1661358 "LSPP" 1661622 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1657722 1658438 1659168 "LSMP1" 1660287 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655504 1655835 1656291 "LSMP" 1657411 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1648632 1654594 1654635 "LSAGG" 1654697 NIL LSAGG (NIL T) -9 NIL 1654775 NIL) (-687 1645141 1646251 1647464 "LSAGG-" 1647469 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642436 1644285 1644534 "LPOLY" 1644936 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642012 1642103 1642226 "LPEFRAC" 1642345 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1641695 1641774 1641802 "LOGIC" 1641913 T LOGIC (NIL) -9 NIL 1641995 NIL) (-683 1641551 1641580 1641651 "LOGIC-" 1641656 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1640726 1640884 1641077 "LODOOPS" 1641407 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639250 1639499 1639852 "LODOF" 1640473 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635126 1637885 1637926 "LODOCAT" 1638364 NIL LODOCAT (NIL T) -9 NIL 1638575 NIL) (-679 1634841 1634917 1635044 "LODOCAT-" 1635049 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1631827 1634682 1634800 "LODO2" 1634805 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1628934 1631764 1631809 "LODO1" 1631814 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626029 1628850 1628916 "LODO" 1628921 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1624898 1625075 1625380 "LODEEF" 1625852 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1622884 1623992 1624245 "LO" 1624730 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1617856 1621050 1621091 "LNAGG" 1621953 NIL LNAGG (NIL T) -9 NIL 1622388 NIL) (-672 1616949 1617217 1617559 "LNAGG-" 1617564 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1612929 1613874 1614513 "LMOPS" 1616364 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612228 1612706 1612747 "LMODULE" 1612752 NIL LMODULE (NIL T) -9 NIL 1612778 NIL) (-669 1609183 1611873 1611996 "LMDICT" 1612138 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1608759 1608973 1609014 "LLINSET" 1609075 NIL LLINSET (NIL T) -9 NIL 1609119 NIL) (-667 1608404 1608667 1608727 "LITERAL" 1608732 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1607923 1608003 1608142 "LIST3" 1608324 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606021 1606369 1606768 "LIST2MAP" 1607570 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605010 1605206 1605434 "LIST2" 1605839 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597464 1603944 1604248 "LIST" 1604739 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597047 1597283 1597324 "LINSET" 1597329 NIL LINSET (NIL T) -9 NIL 1597363 NIL) (-661 1595861 1596555 1596722 "LINFORM" 1596932 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594160 1594888 1594929 "LINEXP" 1595419 NIL LINEXP (NIL T) -9 NIL 1595692 NIL) (-659 1592736 1593640 1593821 "LINELT" 1594031 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591293 1591573 1591884 "LINDEP" 1592488 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590429 1591025 1591135 "LINBASIS" 1591223 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587166 1587915 1588692 "LIMITRF" 1589684 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585451 1585765 1586174 "LIMITPS" 1586861 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584279 1584854 1584894 "LIECAT" 1585034 NIL LIECAT (NIL T) -9 NIL 1585185 NIL) (-653 1584114 1584147 1584235 "LIECAT-" 1584240 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578134 1583625 1583853 "LIE" 1583935 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570319 1577674 1577830 "LIB" 1577998 T LIB (NIL) -8 NIL NIL NIL) (-650 1565888 1566837 1567772 "LGROBP" 1569436 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564512 1565420 1565448 "LFCAT" 1565655 T LFCAT (NIL) -9 NIL 1565794 NIL) (-648 1562450 1562784 1563134 "LF" 1564233 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559310 1559982 1560670 "LEXTRIPK" 1561814 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1555898 1556880 1557383 "LEXP" 1558890 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555314 1555619 1555711 "LETAST" 1555826 T LETAST (NIL) -8 NIL NIL NIL) (-644 1553700 1554025 1554426 "LEADCDET" 1554996 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1552878 1552964 1553193 "LAZM3PK" 1553621 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547403 1550955 1551493 "LAUPOL" 1552390 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1546976 1547026 1547187 "LAPLACE" 1547353 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1545824 1546540 1546581 "LALG" 1546643 NIL LALG (NIL T) -9 NIL 1546702 NIL) (-639 1545520 1545597 1545733 "LALG-" 1545738 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543257 1544621 1544872 "LA" 1545353 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543086 1543116 1543157 "KVTFROM" 1543219 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1541843 1542453 1542638 "KTVLOGIC" 1542921 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1541672 1541702 1541743 "KRCFROM" 1541805 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1540564 1540763 1541062 "KOVACIC" 1541472 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540393 1540423 1540464 "KONVERT" 1540526 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540222 1540252 1540293 "KOERCE" 1540355 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1539706 1539799 1539931 "KERNEL2" 1540136 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537393 1538299 1538676 "KERNEL" 1539362 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1530864 1535870 1535924 "KDAGG" 1536301 NIL KDAGG (NIL T T) -9 NIL 1536507 NIL) (-628 1530375 1530517 1530722 "KDAGG-" 1530727 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523075 1530036 1530191 "KAFILE" 1530253 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1522679 1522964 1523027 "JVMOP" 1523032 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521415 1521919 1522168 "JVMMDACC" 1522450 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520351 1520805 1521010 "JVMFDACC" 1521230 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1518932 1519427 1519727 "JVMCSTTG" 1520071 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518068 1518472 1518633 "JVMCFACC" 1518791 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1517746 1517985 1518034 "JVMBCODE" 1518039 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1511765 1517257 1517485 "JORDAN" 1517567 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511078 1511414 1511535 "JOINAST" 1511664 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507113 1509255 1509309 "IXAGG" 1510238 NIL IXAGG (NIL T T) -9 NIL 1510697 NIL) (-617 1505966 1506338 1506757 "IXAGG-" 1506762 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501055 1505888 1505947 "IVECTOR" 1505952 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1499780 1500058 1500324 "ITUPLE" 1500822 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498252 1498459 1498754 "ITRIGMNP" 1499602 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1496979 1497201 1497484 "ITFUN3" 1498028 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1496577 1496640 1496763 "ITFUN2" 1496902 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1495682 1496057 1496231 "ITFORM" 1496423 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493451 1494702 1494980 "ITAYLOR" 1495437 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1481855 1487588 1488751 "ISUPS" 1492321 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1480947 1481099 1481335 "ISUMP" 1481702 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1475797 1480892 1480933 "ISTRING" 1480938 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475213 1475518 1475610 "ISAST" 1475725 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474411 1474504 1474720 "IRURPK" 1475127 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473323 1473548 1473788 "IRSN" 1474191 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471368 1471749 1472178 "IRRF2F" 1472961 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471109 1471153 1471229 "IRREDFFX" 1471324 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1469682 1469983 1470282 "IROOT" 1470842 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1468821 1469175 1469326 "IRFORM" 1469551 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1467903 1468034 1468248 "IR2F" 1468704 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1465492 1466011 1466577 "IR2" 1467381 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1461932 1463176 1463868 "IR" 1464832 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1461717 1461757 1461817 "IPRNTPK" 1461892 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1457691 1461606 1461675 "IPF" 1461680 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1455719 1457616 1457673 "IPADIC" 1457678 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1454977 1455279 1455409 "IP4ADDR" 1455609 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454315 1454606 1454738 "IOMODE" 1454865 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453286 1453912 1454039 "IOBFILE" 1454208 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1452696 1453190 1453218 "IOBCON" 1453223 T IOBCON (NIL) -9 NIL 1453244 NIL) (-589 1452201 1452265 1452448 "INVLAPLA" 1452632 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1441771 1444203 1446589 "INTTR" 1449865 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438064 1438848 1439713 "INTTOOLS" 1440956 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1437644 1437741 1437858 "INTSLPE" 1437967 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435111 1437567 1437626 "INTRVL" 1437631 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1432689 1433225 1433800 "INTRF" 1434596 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432082 1432197 1432339 "INTRET" 1432587 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430055 1430468 1430938 "INTRAT" 1431690 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427300 1427901 1428520 "INTPM" 1429540 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424017 1424644 1425382 "INTPAF" 1426686 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419118 1420158 1421209 "INTPACK" 1422986 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418364 1418522 1418730 "INTHERTR" 1418960 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1417797 1417883 1418071 "INTHERAL" 1418278 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1415565 1416086 1416543 "INTHEORY" 1417360 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1406897 1408592 1410364 "INTG0" 1413917 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387422 1392260 1397070 "INTFTBL" 1402107 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1386647 1386809 1386982 "INTFACT" 1387281 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384044 1384520 1385077 "INTEF" 1386201 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382241 1383136 1383164 "INTDOM" 1383465 T INTDOM (NIL) -9 NIL 1383672 NIL) (-570 1381580 1381784 1382026 "INTDOM-" 1382031 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1377448 1379869 1379923 "INTCAT" 1380722 NIL INTCAT (NIL T) -9 NIL 1381043 NIL) (-568 1376902 1377023 1377151 "INTBIT" 1377340 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1375583 1375755 1376062 "INTALG" 1376747 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375060 1375156 1375313 "INTAF" 1375487 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368027 1374870 1375010 "INTABL" 1375015 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367268 1367830 1367895 "INT8" 1367929 T INT8 (NIL) -8 NIL NIL 1367974) (-563 1366508 1367070 1367135 "INT64" 1367169 T INT64 (NIL) -8 NIL NIL 1367214) (-562 1365748 1366310 1366375 "INT32" 1366409 T INT32 (NIL) -8 NIL NIL 1366454) (-561 1364988 1365550 1365615 "INT16" 1365649 T INT16 (NIL) -8 NIL NIL 1365694) (-560 1361192 1364785 1364894 "INT" 1364899 T INT (NIL) -8 NIL NIL NIL) (-559 1355301 1358740 1358768 "INS" 1359702 T INS (NIL) -9 NIL 1360367 NIL) (-558 1352458 1353378 1354319 "INS-" 1354392 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351215 1351460 1351758 "INPSIGN" 1352211 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350309 1350450 1350647 "INPRODPF" 1351095 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349179 1349320 1349557 "INPRODFF" 1350189 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348167 1348331 1348591 "INNMFACT" 1349015 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347346 1347461 1347649 "INMODGCD" 1348066 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1345830 1346099 1346423 "INFSP" 1347091 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1344990 1345131 1345314 "INFPROD0" 1345710 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1344588 1344660 1344758 "INFORM1" 1344925 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341155 1342653 1343168 "INFORM" 1344081 T INFORM (NIL) -8 NIL NIL NIL) (-548 1340660 1340767 1340881 "INFINITY" 1341061 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1339734 1340380 1340481 "INETCLTS" 1340579 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338332 1338600 1338921 "INEP" 1339482 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337362 1338229 1338294 "INDE" 1338299 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1336914 1336994 1337111 "INCRMAPS" 1337289 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335636 1336183 1336389 "INBFILE" 1336728 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1330816 1331872 1332816 "INBFF" 1334724 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1329670 1329993 1330021 "INBCON" 1330534 T INBCON (NIL) -9 NIL 1330800 NIL) (-540 1328880 1329145 1329421 "INBCON-" 1329426 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328299 1328604 1328695 "INAST" 1328809 T INAST (NIL) -8 NIL NIL NIL) (-538 1327666 1327978 1328084 "IMPTAST" 1328213 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323587 1327510 1327614 "IMATRIX" 1327619 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322279 1322418 1322734 "IMATQF" 1323443 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320459 1320726 1321063 "IMATLIN" 1322035 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314374 1320383 1320441 "ILIST" 1320446 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312040 1314234 1314347 "IIARRAY2" 1314352 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1306861 1311951 1312015 "IFF" 1312020 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306142 1306478 1306594 "IFAST" 1306765 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300654 1305434 1305622 "IFARRAY" 1305999 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1299692 1300558 1300631 "IFAMON" 1300636 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299264 1299341 1299395 "IEVALAB" 1299602 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1298927 1299007 1299167 "IEVALAB-" 1299172 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1297960 1298816 1298891 "IDPOAMS" 1298896 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297062 1297849 1297924 "IDPOAM" 1297929 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296443 1296977 1297039 "IDPO" 1297044 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1294923 1295450 1295502 "IDPC" 1296014 NIL IDPC (NIL T T) -9 NIL 1296295 NIL) (-522 1294255 1294815 1294888 "IDPAM" 1294893 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293470 1294147 1294220 "IDPAG" 1294225 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293014 1293276 1293366 "IDENT" 1293400 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289233 1290117 1291012 "IDECOMP" 1292171 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1281868 1283156 1284203 "IDEAL" 1288269 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281010 1281140 1281340 "ICDEN" 1281752 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1279985 1280490 1280637 "ICARD" 1280883 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278015 1278358 1278763 "IBPTOOLS" 1279662 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273130 1277635 1277748 "IBITS" 1277934 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1269805 1270429 1271124 "IBATOOL" 1272547 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267566 1268046 1268579 "IBACHIN" 1269340 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265156 1267412 1267515 "IARRAY2" 1267520 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1260869 1265082 1265139 "IARRAY1" 1265144 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1253886 1259281 1259762 "IAN" 1260408 T IAN (NIL) -8 NIL NIL NIL) (-508 1253391 1253454 1253627 "IALGFACT" 1253823 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1252883 1253032 1253060 "HYPCAT" 1253267 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252385 1252538 1252724 "HYPCAT-" 1252729 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1251932 1252180 1252263 "HOSTNAME" 1252322 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1251765 1251814 1251855 "HOMOTOP" 1251860 NIL HOMOTOP (NIL T) -9 NIL 1251893 NIL) (-503 1248198 1249697 1249738 "HOAGG" 1250719 NIL HOAGG (NIL T) -9 NIL 1251448 NIL) (-502 1246714 1247191 1247717 "HOAGG-" 1247722 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1239771 1246307 1246457 "HEXADEC" 1246584 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238483 1238741 1239004 "HEUGCD" 1239548 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237415 1238320 1238450 "HELLFDIV" 1238455 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235423 1237190 1237279 "HEAP" 1237358 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234620 1234975 1235109 "HEADAST" 1235309 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1227958 1234535 1234597 "HDP" 1234602 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1220977 1227593 1227745 "HDMP" 1227859 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220283 1220441 1220605 "HB" 1220833 T HB (NIL) -7 NIL NIL NIL) (-493 1213293 1220129 1220233 "HASHTBL" 1220238 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1212709 1213014 1213106 "HASAST" 1213221 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210122 1212331 1212513 "HACKPI" 1212547 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205294 1209975 1210088 "GTSET" 1210093 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198333 1205172 1205270 "GSTBL" 1205275 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190096 1197498 1197754 "GSERIES" 1198133 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189127 1189640 1189668 "GROUP" 1189871 T GROUP (NIL) -9 NIL 1190005 NIL) (-486 1188451 1188652 1188903 "GROUP-" 1188908 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1186800 1187139 1187526 "GROEBSOL" 1188128 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1185628 1185988 1186039 "GRMOD" 1186568 NIL GRMOD (NIL T T) -9 NIL 1186736 NIL) (-483 1185384 1185432 1185560 "GRMOD-" 1185565 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180524 1181738 1182738 "GRIMAGE" 1184404 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1178918 1179251 1179575 "GRDEF" 1180220 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178350 1178478 1178619 "GRAY" 1178797 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177427 1177929 1177980 "GRALG" 1178133 NIL GRALG (NIL T T) -9 NIL 1178226 NIL) (-478 1177064 1177161 1177324 "GRALG-" 1177329 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173545 1176647 1176826 "GPOLSET" 1176970 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1172893 1172956 1173214 "GOSPER" 1173482 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168463 1169331 1169857 "GMODPOL" 1172592 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167450 1167652 1167890 "GHENSEL" 1168275 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161522 1162449 1163469 "GENUPS" 1166534 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161213 1161270 1161359 "GENUFACT" 1161465 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1160613 1160702 1160867 "GENPGCD" 1161131 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160081 1160122 1160335 "GENMFACT" 1160572 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1158618 1158904 1159211 "GENEEZ" 1159824 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1151796 1158229 1158391 "GDMP" 1158541 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140534 1145567 1146673 "GCNAALG" 1150779 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1138661 1139709 1139737 "GCDDOM" 1139992 T GCDDOM (NIL) -9 NIL 1140149 NIL) (-465 1138101 1138258 1138473 "GCDDOM-" 1138478 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1126573 1129047 1131439 "GBINTERN" 1135792 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124374 1124702 1125123 "GBF" 1126248 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123131 1123320 1123587 "GBEUCLID" 1124190 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1121781 1121988 1122292 "GB" 1122910 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121112 1121255 1121404 "GAUSSFAC" 1121652 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119433 1119781 1120095 "GALUTIL" 1120831 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1117693 1118015 1118339 "GALPOLYU" 1119160 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1114992 1115348 1115755 "GALFACTU" 1117390 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106606 1108297 1109905 "GALFACT" 1113424 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1103892 1104652 1104680 "FVFUN" 1105836 T FVFUN (NIL) -9 NIL 1106556 NIL) (-454 1103122 1103340 1103368 "FVC" 1103659 T FVC (NIL) -9 NIL 1103842 NIL) (-453 1102723 1102947 1103015 "FUNDESC" 1103074 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102296 1102520 1102601 "FUNCTION" 1102675 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1100973 1101597 1101800 "FTEM" 1102113 T FTEM (NIL) -8 NIL NIL NIL) (-450 1098603 1099295 1099761 "FT" 1100527 T FT (NIL) -8 NIL NIL NIL) (-449 1096872 1097183 1097580 "FSUPFACT" 1098294 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095191 1095558 1095890 "FST" 1096560 T FST (NIL) -8 NIL NIL NIL) (-447 1094372 1094496 1094684 "FSRED" 1095073 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093061 1093327 1093674 "FSPRMELT" 1094087 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090271 1090805 1091291 "FSPECF" 1092624 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1089793 1089853 1090023 "FSINT" 1090212 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1087929 1088786 1089089 "FSERIES" 1089572 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1086953 1087087 1087311 "FSCINT" 1087809 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1085977 1086138 1086365 "FSAGG2" 1086806 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1081841 1084921 1084962 "FSAGG" 1085332 NIL FSAGG (NIL T) -9 NIL 1085591 NIL) (-439 1079441 1080204 1081000 "FSAGG-" 1081095 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077101 1077399 1077947 "FS2UPS" 1079159 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1075967 1076150 1076452 "FS2EXPXP" 1076926 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1075595 1075644 1075773 "FS2" 1075918 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1055833 1065369 1065410 "FS" 1069294 NIL FS (NIL T) -9 NIL 1071583 NIL) (-434 1043894 1047469 1051526 "FS-" 1051826 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043308 1043435 1043587 "FRUTIL" 1043774 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1037819 1040997 1041037 "FRNAALG" 1042357 NIL FRNAALG (NIL T) -9 NIL 1042955 NIL) (-431 1033300 1034568 1035843 "FRNAALG-" 1036593 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1032932 1032981 1033108 "FRNAAF2" 1033251 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031219 1031781 1032077 "FRMOD" 1032744 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030404 1030497 1030788 "FRIDEAL2" 1031126 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028009 1028779 1029097 "FRIDEAL" 1030195 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027100 1027556 1027597 "FRETRCT" 1027602 NIL FRETRCT (NIL T) -9 NIL 1027778 NIL) (-425 1026158 1026443 1026794 "FRETRCT-" 1026799 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1022979 1024442 1024501 "FRAMALG" 1025383 NIL FRAMALG (NIL T T) -9 NIL 1025675 NIL) (-423 1021017 1021568 1022198 "FRAMALG-" 1022421 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1020647 1020710 1020817 "FRAC2" 1020954 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1013640 1020120 1020397 "FRAC" 1020402 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013270 1013333 1013440 "FR2" 1013577 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004187 1008765 1010123 "FR" 1011944 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998106 1001566 1001594 "FPS" 1002713 T FPS (NIL) -9 NIL 1003270 NIL) (-417 997531 997664 997828 "FPS-" 997974 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994497 996488 996516 "FPC" 996741 T FPC (NIL) -9 NIL 996883 NIL) (-415 994278 994330 994427 "FPC-" 994432 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993036 993766 993807 "FPATMAB" 993812 NIL FPATMAB (NIL T) -9 NIL 993964 NIL) (-413 991179 991778 992125 "FPARFRAC" 992752 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986471 987071 987753 "FORTRAN" 990611 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984045 984709 984737 "FORTFN" 985797 T FORTFN (NIL) -9 NIL 986421 NIL) (-410 983797 983859 983887 "FORTCAT" 983946 T FORTCAT (NIL) -9 NIL 984008 NIL) (-409 981483 982013 982552 "FORT" 983278 T FORT (NIL) -7 NIL NIL NIL) (-408 981265 981301 981370 "FORMULA1" 981447 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979269 979881 980271 "FORMULA" 980895 T FORMULA (NIL) -8 NIL NIL NIL) (-406 978786 978844 979017 "FORDER" 979211 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 977846 978046 978239 "FOP" 978613 T FOP (NIL) -7 NIL NIL NIL) (-404 976259 977126 977300 "FNLA" 977728 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 974878 975389 975417 "FNCAT" 975877 T FNCAT (NIL) -9 NIL 976137 NIL) (-402 974321 974837 974865 "FNAME" 974870 T FNAME (NIL) -8 NIL NIL NIL) (-401 972647 973820 973848 "FMTC" 973853 T FMTC (NIL) -9 NIL 973889 NIL) (-400 971196 972583 972629 "FMONOID" 972634 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 967785 969151 969192 "FMONCAT" 970409 NIL FMONCAT (NIL T) -9 NIL 971014 NIL) (-398 965107 965855 965883 "FMFUN" 967027 T FMFUN (NIL) -9 NIL 967735 NIL) (-397 961980 963032 963086 "FMCAT" 964281 NIL FMCAT (NIL T T) -9 NIL 964776 NIL) (-396 961213 961430 961458 "FMC" 961748 T FMC (NIL) -9 NIL 961930 NIL) (-395 959881 960979 961079 "FM1" 961158 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 958899 959623 959772 "FM" 959777 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 956637 957089 957583 "FLOATRP" 958450 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954039 954575 955153 "FLOATCP" 956104 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 946702 951768 952389 "FLOAT" 953438 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945220 946294 946335 "FLINEXP" 946340 NIL FLINEXP (NIL T) -9 NIL 946433 NIL) (-389 944350 944609 944937 "FLINEXP-" 944942 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943408 943570 943794 "FLASORT" 944202 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940326 941378 941430 "FLALG" 942657 NIL FLALG (NIL T T) -9 NIL 943124 NIL) (-386 939350 939511 939738 "FLAGG2" 940179 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 932605 936759 936800 "FLAGG" 938062 NIL FLAGG (NIL T) -9 NIL 938714 NIL) (-384 931259 931670 932160 "FLAGG-" 932165 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 927897 929104 929163 "FINRALG" 930291 NIL FINRALG (NIL T T) -9 NIL 930799 NIL) (-382 927021 927286 927625 "FINRALG-" 927630 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926327 926626 926654 "FINITE" 926850 T FINITE (NIL) -9 NIL 926957 NIL) (-380 918278 920857 920897 "FINAALG" 924564 NIL FINAALG (NIL T) -9 NIL 926017 NIL) (-379 913394 914660 915804 "FINAALG-" 917183 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 911954 912376 912430 "FILECAT" 913114 NIL FILECAT (NIL T T) -9 NIL 913330 NIL) (-377 911232 911709 911812 "FILE" 911884 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 908635 910462 910490 "FIELD" 910530 T FIELD (NIL) -9 NIL 910610 NIL) (-375 907177 907640 908151 "FIELD-" 908156 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 904860 905812 906159 "FGROUP" 906863 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 903932 904114 904334 "FGLMICPK" 904692 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899187 903857 903914 "FFX" 903919 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 898782 898849 898984 "FFSLPE" 899120 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898280 898322 898531 "FFPOLY2" 898740 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894156 895052 895848 "FFPOLY" 897516 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889425 894075 894138 "FFP" 894143 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 883956 888768 888958 "FFNBX" 889279 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878289 883091 883349 "FFNBP" 883810 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872327 877573 877784 "FFNB" 878122 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871147 871357 871672 "FFINTBAS" 872124 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 866740 869394 869422 "FFIELDC" 870042 T FFIELDC (NIL) -9 NIL 870418 NIL) (-362 865360 865801 866284 "FFIELDC-" 866289 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 864917 864975 865099 "FFHOM" 865302 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862576 863099 863616 "FFF" 864432 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857611 862318 862419 "FFCGX" 862519 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852650 857343 857450 "FFCGP" 857554 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847250 852377 852485 "FFCG" 852586 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846655 846704 846939 "FFCAT2" 847201 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825337 836387 836473 "FFCAT" 841638 NIL FFCAT (NIL T T T) -9 NIL 843089 NIL) (-354 820348 821582 822896 "FFCAT-" 824126 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815169 820259 820323 "FF" 820328 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803822 808141 809361 "FEXPR" 814021 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802750 803219 803260 "FEVALAB" 803344 NIL FEVALAB (NIL T) -9 NIL 803605 NIL) (-350 801867 802119 802457 "FEVALAB-" 802462 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798729 799614 799729 "FDIVCAT" 801297 NIL FDIVCAT (NIL T T T T) -9 NIL 801734 NIL) (-348 798485 798518 798688 "FDIVCAT-" 798693 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797699 797792 798069 "FDIV2" 798392 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796109 797082 797285 "FDIV" 797598 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795017 795404 795606 "FCTRDATA" 795927 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793673 793962 794251 "FCPAK1" 794748 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792676 793173 793314 "FCOMP" 793564 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 775990 779826 783364 "FC" 789158 T FC (NIL) -8 NIL NIL NIL) (-341 767699 772311 772351 "FAXF" 774153 NIL FAXF (NIL T) -9 NIL 774845 NIL) (-340 764840 765647 766465 "FAXF-" 766930 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759409 764216 764392 "FARRAY" 764697 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 753974 756356 756409 "FAMR" 757432 NIL FAMR (NIL T T) -9 NIL 757892 NIL) (-337 752798 753166 753601 "FAMR-" 753606 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751825 752720 752773 "FAMONOID" 752778 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749455 750307 750360 "FAMONC" 751301 NIL FAMONC (NIL T T) -9 NIL 751687 NIL) (-334 747929 749209 749346 "FAGROUP" 749351 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745682 746043 746446 "FACUTIL" 747610 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744769 744966 745188 "FACTFUNC" 745492 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736510 744072 744271 "EXPUPXS" 744625 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 733963 734533 735119 "EXPRTUBE" 735944 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730174 730826 731556 "EXPRODE" 733302 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724608 725315 726121 "EXPR2UPS" 729472 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724234 724297 724406 "EXPR2" 724545 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708542 722883 723312 "EXPR" 723838 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 698880 707693 707984 "EXPEXPAN" 708378 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698300 698604 698695 "EXITAST" 698809 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698064 698257 698286 "EXIT" 698291 T EXIT (NIL) -8 NIL NIL NIL) (-322 697685 697753 697866 "EVALCYC" 697996 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697202 697344 697385 "EVALAB" 697555 NIL EVALAB (NIL T) -9 NIL 697659 NIL) (-320 696659 696805 697026 "EVALAB-" 697031 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693774 695315 695343 "EUCDOM" 695898 T EUCDOM (NIL) -9 NIL 696248 NIL) (-318 692134 692635 693218 "EUCDOM-" 693223 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691760 691823 691932 "ESTOOLS2" 692071 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691505 691553 691633 "ESTOOLS1" 691712 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678822 681803 684553 "ESTOOLS" 688775 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678561 678599 678681 "ESCONT1" 678784 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674869 675696 676476 "ESCONT" 677801 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674538 674594 674694 "ES2" 674813 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674162 674226 674335 "ES1" 674474 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667863 669793 669821 "ES" 672589 T ES (NIL) -9 NIL 673999 NIL) (-309 662540 664097 665914 "ES-" 666078 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661732 661885 662061 "ERROR" 662384 T ERROR (NIL) -7 NIL NIL NIL) (-307 654748 661591 661682 "EQTBL" 661687 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654374 654437 654546 "EQ2" 654685 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646633 649688 651137 "EQ" 652958 NIL -3353 (NIL T) -8 NIL NIL NIL) (-304 641875 642971 644064 "EP" 645572 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640415 640766 641072 "ENV" 641589 T ENV (NIL) -8 NIL NIL NIL) (-302 639375 640049 640077 "ENTIRER" 640082 T ENTIRER (NIL) -9 NIL 640128 NIL) (-301 635794 637557 637918 "EMR" 639183 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 634898 635109 635163 "ELTAGG" 635543 NIL ELTAGG (NIL T T) -9 NIL 635754 NIL) (-299 634605 634679 634820 "ELTAGG-" 634825 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634363 634398 634452 "ELTAB" 634536 NIL ELTAB (NIL T T) -9 NIL 634588 NIL) (-297 633465 633635 633834 "ELFUTS" 634214 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633189 633263 633291 "ELEMFUN" 633396 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633053 633080 633148 "ELEMFUN-" 633153 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627464 631095 631136 "ELAGG" 632076 NIL ELAGG (NIL T) -9 NIL 632539 NIL) (-293 625641 626183 626846 "ELAGG-" 626851 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 624923 625090 625246 "ELABOR" 625505 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623529 623863 624157 "ELABEXPR" 624649 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616041 618166 618995 "EFUPXS" 622804 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609167 611290 612101 "EFULS" 615316 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606604 607010 607482 "EFSTRUC" 608799 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596042 597961 599509 "EF" 605119 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595020 595527 595676 "EAB" 595913 T EAB (NIL) -8 NIL NIL NIL) (-285 594142 594979 595007 "E04UCFA" 595012 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593264 594101 594129 "E04NAFA" 594134 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592386 593223 593251 "E04MBFA" 593256 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591508 592345 592373 "E04JAFA" 592378 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590632 591467 591495 "E04GCFA" 591500 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589756 590591 590619 "E04FDFA" 590624 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588878 589715 589743 "E04DGFA" 589748 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 582955 584403 585767 "E04AGNT" 587534 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581575 582256 582296 "DVARCAT" 582637 NIL DVARCAT (NIL T) -9 NIL 582800 NIL) (-276 580725 580991 581305 "DVARCAT-" 581310 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572693 580524 580653 "DSMP" 580658 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571044 571835 571876 "DSEXT" 572239 NIL DSEXT (NIL T) -9 NIL 572533 NIL) (-273 569233 569757 570423 "DSEXT-" 570428 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 568892 568957 569055 "DROPT1" 569168 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 563911 565133 566270 "DROPT0" 567775 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558494 559856 560924 "DROPT" 562863 T DROPT (NIL) -8 NIL NIL NIL) (-269 556803 557164 557550 "DRAWPT" 558128 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556430 556489 556607 "DRAWHACK" 556744 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555131 555430 555721 "DRAWCX" 556159 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554640 554715 554866 "DRAWCURV" 555057 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 544958 547070 549185 "DRAWCFUN" 552545 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539449 540468 541547 "DRAW" 543932 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 535920 538114 538155 "DQAGG" 538784 NIL DQAGG (NIL T) -9 NIL 539058 NIL) (-262 522503 530131 530214 "DPOLCAT" 532066 NIL DPOLCAT (NIL T T T T) -9 NIL 532611 NIL) (-261 517022 518688 520646 "DPOLCAT-" 520651 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509830 516883 516981 "DPMO" 516986 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502535 509610 509777 "DPMM" 509782 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502057 502319 502408 "DOMTMPLT" 502466 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501406 501859 501939 "DOMCTOR" 501997 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500558 500886 501037 "DOMAIN" 501275 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493577 500193 500345 "DMP" 500459 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491354 492644 492685 "DMEXT" 492690 NIL DMEXT (NIL T) -9 NIL 492866 NIL) (-253 490948 491010 491154 "DLP" 491292 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484071 490275 490465 "DLIST" 490790 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480609 482896 482937 "DLAGG" 483487 NIL DLAGG (NIL T) -9 NIL 483717 NIL) (-250 479121 479935 479963 "DIVRING" 480055 T DIVRING (NIL) -9 NIL 480138 NIL) (-249 478304 478548 478848 "DIVRING-" 478853 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476346 476763 477169 "DISPLAY" 477918 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475176 475397 475662 "DIRPROD2" 476139 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468534 475090 475153 "DIRPROD" 475158 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456697 463245 463298 "DIRPCAT" 463556 NIL DIRPCAT (NIL NIL T) -9 NIL 464431 NIL) (-244 453897 454665 455546 "DIRPCAT-" 455883 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453178 453344 453530 "DIOSP" 453731 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449592 452062 452103 "DIOPS" 452537 NIL DIOPS (NIL T) -9 NIL 452766 NIL) (-241 449111 449255 449446 "DIOPS-" 449451 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448018 448790 448818 "DIFRING" 448823 T DIFRING (NIL) -9 NIL 448845 NIL) (-239 447666 447764 447792 "DIFFSPC" 447911 T DIFFSPC (NIL) -9 NIL 447986 NIL) (-238 447287 447389 447541 "DIFFSPC-" 447546 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446223 446821 446862 "DIFFMOD" 446867 NIL DIFFMOD (NIL T) -9 NIL 446965 NIL) (-236 445919 445976 446017 "DIFFDOM" 446138 NIL DIFFDOM (NIL T) -9 NIL 446206 NIL) (-235 445766 445796 445880 "DIFFDOM-" 445885 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443506 444970 445011 "DIFEXT" 445016 NIL DIFEXT (NIL T) -9 NIL 445169 NIL) (-233 440540 443010 443051 "DIAGG" 443056 NIL DIAGG (NIL T) -9 NIL 443076 NIL) (-232 439888 440081 440333 "DIAGG-" 440338 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434738 438847 439124 "DHMATRIX" 439657 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430206 431259 432269 "DFSFUN" 433748 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424447 429137 429449 "DFLOAT" 429914 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422686 422991 423380 "DFINTTLS" 424155 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419505 420707 421107 "DERHAM" 422352 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417041 419280 419369 "DEQUEUE" 419449 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416283 416428 416611 "DEGRED" 416903 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412689 413458 414304 "DEFINTRF" 415511 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410226 410713 411305 "DEFINTEF" 412208 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409510 409846 409961 "DEFAST" 410131 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402567 409103 409253 "DECIMAL" 409380 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400025 400537 401043 "DDFACT" 402111 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399615 399664 399815 "DBLRESP" 399976 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398816 399385 399476 "DBASIS" 399564 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396600 397046 397407 "DBASE" 398582 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395788 396080 396226 "DATAARY" 396499 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 394846 395747 395775 "D03FAFA" 395780 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 393905 394805 394833 "D03EEFA" 394838 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391831 392321 392810 "D03AGNT" 393436 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391072 391790 391818 "D02EJFA" 391823 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390313 391031 391059 "D02CJFA" 391064 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389554 390272 390300 "D02BHFA" 390305 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388795 389513 389541 "D02BBFA" 389546 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 381926 383581 385187 "D02AGNT" 387209 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379676 380217 380763 "D01WGTS" 381400 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378683 379635 379663 "D01TRNS" 379668 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377691 378642 378670 "D01GBFA" 378675 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376699 377650 377678 "D01FCFA" 377683 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375707 376658 376686 "D01ASFA" 376691 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374715 375666 375694 "D01AQFA" 375699 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373723 374674 374702 "D01APFA" 374707 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372731 373682 373710 "D01ANFA" 373715 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371739 372690 372718 "D01AMFA" 372723 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370747 371698 371726 "D01ALFA" 371731 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369755 370706 370734 "D01AKFA" 370739 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368763 369714 369742 "D01AJFA" 369747 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 361986 363611 365172 "D01AGNT" 367222 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361305 361451 361603 "CYCLOTOM" 361854 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 357960 358753 359480 "CYCLES" 360598 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357260 357406 357577 "CVMP" 357821 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355047 355359 355728 "CTRIGMNP" 356988 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354520 354778 354879 "CTORKIND" 354966 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353725 354113 354141 "CTORCAT" 354323 T CTORCAT (NIL) -9 NIL 354436 NIL) (-188 353299 353434 353593 "CTORCAT-" 353598 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352713 352973 353081 "CTORCALL" 353223 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352071 352507 352580 "CTOR" 352660 T CTOR (NIL) -8 NIL NIL NIL) (-185 351427 351544 351697 "CSTTOOLS" 351968 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347124 347883 348641 "CRFP" 350739 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346539 346845 346937 "CRCEAST" 347052 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345562 345771 345999 "CRAPACK" 346343 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 344942 345047 345251 "CPMATCH" 345438 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344661 344695 344801 "CPIMA" 344908 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 340919 341681 342400 "COORDSYS" 343996 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340307 340452 340594 "CONTOUR" 340797 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335778 338310 338802 "CONTFRAC" 339847 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335652 335679 335707 "CONDUIT" 335744 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334606 335280 335308 "COMRING" 335313 T COMRING (NIL) -9 NIL 335365 NIL) (-174 333588 333964 334148 "COMPPROP" 334442 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333243 333284 333412 "COMPLPAT" 333547 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 332873 332936 333043 "COMPLEX2" 333180 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321277 332682 332791 "COMPLEX" 332796 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320598 320737 320897 "COMPILER" 321137 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320310 320351 320449 "COMPFACT" 320557 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301704 314014 314054 "COMPCAT" 315058 NIL COMPCAT (NIL T) -9 NIL 316406 NIL) (-167 290592 294143 297770 "COMPCAT-" 298126 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290315 290349 290452 "COMMUPC" 290558 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290103 290143 290202 "COMMONOP" 290276 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289625 289907 289982 "COMMAAST" 290048 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289132 289376 289463 "COMM" 289558 T COMM (NIL) -8 NIL NIL NIL) (-162 288327 288575 288603 "COMBOPC" 288941 T COMBOPC (NIL) -9 NIL 289116 NIL) (-161 287181 287433 287675 "COMBINAT" 288117 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283524 284212 284839 "COMBF" 286603 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282186 282640 282875 "COLOR" 283309 T COLOR (NIL) -8 NIL NIL NIL) (-158 281602 281907 281999 "COLONAST" 282114 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281236 281289 281414 "CMPLXRT" 281549 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280624 280936 281035 "CLLCTAST" 281157 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276083 277154 278234 "CLIP" 279564 T CLIP (NIL) -7 NIL NIL NIL) (-154 274256 275184 275424 "CLIF" 275910 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270238 272374 272415 "CLAGG" 273344 NIL CLAGG (NIL T) -9 NIL 273880 NIL) (-152 268582 269117 269700 "CLAGG-" 269705 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268120 268211 268351 "CINTSLPE" 268491 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265585 266092 266640 "CHVAR" 267648 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264625 265299 265327 "CHARZ" 265332 T CHARZ (NIL) -9 NIL 265347 NIL) (-148 264373 264419 264497 "CHARPOL" 264579 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263291 263997 264025 "CHARNZ" 264086 T CHARNZ (NIL) -9 NIL 264135 NIL) (-146 260235 261345 261874 "CHAR" 262782 T CHAR (NIL) -8 NIL NIL NIL) (-145 259943 260022 260050 "CFCAT" 260161 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259166 259295 259478 "CDEN" 259827 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254763 258319 258599 "CCLASS" 258906 T CCLASS (NIL) -8 NIL NIL NIL) (-142 253984 254171 254348 "CATEGORY" 254606 T -10 (NIL) -8 NIL NIL NIL) (-141 253479 253903 253951 "CATCTOR" 253956 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 252870 253182 253280 "CATAST" 253401 T CATAST (NIL) -8 NIL NIL NIL) (-139 252286 252591 252683 "CASEAST" 252798 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251382 251542 251763 "CARTEN2" 252133 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246279 247539 248283 "CARTEN" 250694 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244409 245429 245686 "CARD" 246042 T CARD (NIL) -8 NIL NIL NIL) (-135 243931 244213 244288 "CAPSLAST" 244354 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243373 243629 243657 "CACHSET" 243789 T CACHSET (NIL) -9 NIL 243867 NIL) (-133 242763 243151 243179 "CABMON" 243229 T CABMON (NIL) -9 NIL 243285 NIL) (-132 242200 242467 242577 "BYTEORD" 242673 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237127 241705 241877 "BYTEBUF" 242048 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 235958 236670 236805 "BYTE" 236968 T BYTE (NIL) -8 NIL NIL 237083) (-129 233220 235650 235757 "BTREE" 235884 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230422 232868 232990 "BTOURN" 233130 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227529 229864 229905 "BTCAT" 229973 NIL BTCAT (NIL T) -9 NIL 230050 NIL) (-126 227178 227276 227425 "BTCAT-" 227430 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222067 226424 226452 "BTAGG" 226566 T BTAGG (NIL) -9 NIL 226676 NIL) (-124 221521 221682 221888 "BTAGG-" 221893 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218257 220799 221014 "BSTREE" 221338 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217365 217521 217705 "BRILL" 218113 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213760 216063 216104 "BRAGG" 216753 NIL BRAGG (NIL T) -9 NIL 217011 NIL) (-120 212193 212695 213250 "BRAGG-" 213255 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204450 211537 211722 "BPADICRT" 212040 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202466 204387 204432 "BPADIC" 204437 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202158 202194 202308 "BOUNDZRO" 202430 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 199885 200343 200818 "BOP1" 201716 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194915 196345 197243 "BOP" 199007 T BOP (NIL) -8 NIL NIL NIL) (-114 193580 194503 194645 "BOOLEAN" 194793 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193173 193330 193358 "BOOLE" 193469 T BOOLE (NIL) -9 NIL 193550 NIL) (-112 193041 193068 193134 "BOOLE-" 193139 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192210 192710 192764 "BMODULE" 192769 NIL BMODULE (NIL T T) -9 NIL 192834 NIL) (-110 187531 192008 192081 "BITS" 192157 T BITS (NIL) -8 NIL NIL NIL) (-109 186928 187071 187211 "BINDING" 187411 T BINDING (NIL) -8 NIL NIL NIL) (-108 179988 186523 186672 "BINARY" 186799 T BINARY (NIL) -8 NIL NIL NIL) (-107 177595 179215 179256 "BGAGG" 179516 NIL BGAGG (NIL T) -9 NIL 179653 NIL) (-106 177420 177458 177549 "BGAGG-" 177554 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176443 176804 177009 "BFUNCT" 177235 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175113 175311 175599 "BEZOUT" 176267 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171311 173965 174295 "BBTREE" 174816 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170894 170990 171018 "BASTYPE" 171195 T BASTYPE (NIL) -9 NIL 171294 NIL) (-101 170552 170651 170786 "BASTYPE-" 170791 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 169974 170062 170214 "BALFACT" 170463 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168710 169389 169575 "AUTOMOR" 169819 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168436 168441 168467 "ATTREG" 168472 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166598 167133 167485 "ATTRBUT" 168102 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166152 166426 166492 "ATTRAST" 166550 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165652 165801 165827 "ATRIG" 166028 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165449 165502 165589 "ATRIG-" 165594 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165032 165266 165292 "ASTCAT" 165297 T ASTCAT (NIL) -9 NIL 165327 NIL) (-92 164741 164818 164937 "ASTCAT-" 164942 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162715 164517 164605 "ASTACK" 164684 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161204 161517 161882 "ASSOCEQ" 162397 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160128 160863 160987 "ASP9" 161111 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158888 159733 159875 "ASP80" 160017 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158615 158836 158875 "ASP8" 158880 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157461 158292 158410 "ASP78" 158528 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156322 157141 157258 "ASP77" 157375 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155126 155960 156091 "ASP74" 156222 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153918 154761 154893 "ASP73" 155025 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152708 153553 153685 "ASP7" 153817 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151704 152534 152634 "ASP6" 152639 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150543 151381 151499 "ASP55" 151617 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149384 150217 150336 "ASP50" 150455 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148364 149085 149195 "ASP49" 149305 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147040 147903 148071 "ASP42" 148253 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145709 146573 146743 "ASP41" 146927 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144689 145410 145520 "ASP4" 145630 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143531 144366 144484 "ASP35" 144602 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143260 143479 143518 "ASP34" 143523 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 142979 143064 143140 "ASP33" 143215 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141765 142614 142746 "ASP31" 142878 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141494 141713 141752 "ASP30" 141757 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141211 141298 141374 "ASP29" 141449 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140940 141159 141198 "ASP28" 141203 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140669 140888 140927 "ASP27" 140932 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139645 140367 140478 "ASP24" 140589 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138614 139447 139559 "ASP20" 139564 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137449 138288 138407 "ASP19" 138526 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137168 137253 137329 "ASP12" 137404 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135912 136767 136911 "ASP10" 137055 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134892 135613 135723 "ASP1" 135833 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132504 134736 134827 "ARRAY2" 134832 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131518 131709 131930 "ARRAY12" 132327 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126878 131166 131280 "ARRAY1" 131435 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120923 123080 123155 "ARR2CAT" 125785 NIL ARR2CAT (NIL T T T) -9 NIL 126543 NIL) (-56 118213 119101 120055 "ARR2CAT-" 120060 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117464 117840 117965 "ARITY" 118106 T ARITY (NIL) -8 NIL NIL NIL) (-54 116222 116392 116691 "APPRULE" 117300 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115867 115921 116040 "APPLYORE" 116168 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115121 115268 115425 "ANY1" 115741 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114421 114714 114834 "ANY" 115019 T ANY (NIL) -8 NIL NIL NIL) (-50 111747 112858 113185 "ANTISYM" 114145 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111191 111454 111550 "ANON" 111669 T ANON (NIL) -8 NIL NIL NIL) (-48 104354 109730 110184 "AN" 110755 T AN (NIL) -8 NIL NIL NIL) (-47 100017 101626 101677 "AMR" 102425 NIL AMR (NIL T T) -9 NIL 103025 NIL) (-46 99069 99350 99713 "AMR-" 99718 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82538 98986 99047 "ALIST" 99052 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78835 82132 82301 "ALGSC" 82456 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75285 75945 76552 "ALGPKG" 78275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74550 74663 74847 "ALGMFACT" 75171 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70533 71164 71758 "ALGMANIP" 74134 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59893 70159 70309 "ALGFF" 70466 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59065 59220 59399 "ALGFACT" 59751 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57854 58592 58630 "ALGEBRA" 58635 NIL ALGEBRA (NIL T) -9 NIL 58676 NIL) (-37 57554 57631 57763 "ALGEBRA-" 57768 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38508 55391 55443 "ALAGG" 55579 NIL ALAGG (NIL T T) -9 NIL 55740 NIL) (-35 38008 38157 38183 "AHYP" 38384 T AHYP (NIL) -9 NIL NIL NIL) (-34 36893 37187 37213 "AGG" 37712 T AGG (NIL) -9 NIL 37991 NIL) (-33 36291 36489 36703 "AGG-" 36708 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34051 34520 34925 "AF" 35933 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33471 33776 33866 "ADDAST" 33979 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32703 32998 33154 "ACPLOT" 33333 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20267 29635 29673 "ACFS" 30280 NIL ACFS (NIL T) -9 NIL 30519 NIL) (-28 18174 18784 19546 "ACFS-" 19551 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16207 16233 "ACF" 17112 T ACF (NIL) -9 NIL 17525 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3460156 3460161 3460166 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3460141 3460146 3460151 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3460126 3460131 3460136 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3460111 3460116 3460121 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1329 3459104 3459986 3460063 "ZMOD" 3460068 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1328 3458140 3458322 3458545 "ZLINDEP" 3458936 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1327 3447302 3449208 3451180 "ZDSOLVE" 3456270 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1326 3446536 3446689 3446878 "YSTREAM" 3447148 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1325 3445896 3446205 3446320 "YDIAGRAM" 3446443 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1324 3443344 3445197 3445401 "XRPOLY" 3445739 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1323 3439611 3441215 3441790 "XPR" 3442816 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1322 3436942 3438618 3438673 "XPOLYC" 3438961 NIL XPOLYC (NIL T T) -9 NIL 3439074 NIL) (-1321 3434337 3436273 3436477 "XPOLY" 3436773 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1320 3430283 3432854 3433242 "XPBWPOLY" 3433995 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1319 3425175 3426754 3426809 "XFALG" 3428981 NIL XFALG (NIL T T) -9 NIL 3429770 NIL) (-1318 3420451 3423151 3423193 "XF" 3423814 NIL XF (NIL T) -9 NIL 3424214 NIL) (-1317 3420048 3420160 3420329 "XF-" 3420334 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1316 3419163 3419285 3419490 "XEXPPKG" 3419940 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1315 3416904 3419013 3419109 "XDPOLY" 3419114 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1314 3415559 3416297 3416340 "XALG" 3416345 NIL XALG (NIL T) -9 NIL 3416456 NIL) (-1313 3408583 3413536 3414030 "WUTSET" 3415151 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1312 3406685 3407635 3407958 "WP" 3408394 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1311 3406233 3406507 3406577 "WHILEAST" 3406637 T WHILEAST (NIL) -8 NIL NIL NIL) (-1310 3405645 3405950 3406044 "WHEREAST" 3406161 T WHEREAST (NIL) -8 NIL NIL NIL) (-1309 3404519 3404729 3405024 "WFFINTBS" 3405442 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1308 3402387 3402850 3403312 "WEIER" 3404091 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1307 3401311 3401869 3401911 "VSPACE" 3402047 NIL VSPACE (NIL T) -9 NIL 3402121 NIL) (-1306 3401143 3401176 3401267 "VSPACE-" 3401272 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1305 3400940 3400994 3401062 "VOID" 3401097 T VOID (NIL) -8 NIL NIL NIL) (-1304 3397208 3398003 3398740 "VIEWDEF" 3400225 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1303 3386152 3388756 3390929 "VIEW3D" 3395057 T VIEW3D (NIL) -8 NIL NIL NIL) (-1302 3378169 3380063 3381642 "VIEW2D" 3384595 T VIEW2D (NIL) -8 NIL NIL NIL) (-1301 3376269 3376664 3377070 "VIEW" 3377785 T VIEW (NIL) -7 NIL NIL NIL) (-1300 3374822 3375105 3375423 "VECTOR2" 3375999 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1299 3369842 3374592 3374684 "VECTOR" 3374765 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1298 3362901 3367546 3367589 "VECTCAT" 3368584 NIL VECTCAT (NIL T) -9 NIL 3369171 NIL) (-1297 3361843 3362169 3362559 "VECTCAT-" 3362564 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1296 3361249 3361494 3361614 "VARIABLE" 3361758 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1295 3361182 3361187 3361217 "UTYPE" 3361222 T UTYPE (NIL) -9 NIL NIL NIL) (-1294 3359990 3360166 3360428 "UTSODETL" 3361008 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1293 3357382 3357890 3358414 "UTSODE" 3359531 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1292 3347392 3353315 3353358 "UTSCAT" 3354470 NIL UTSCAT (NIL T) -9 NIL 3355228 NIL) (-1291 3344518 3345462 3346451 "UTSCAT-" 3346456 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1290 3344139 3344188 3344321 "UTS2" 3344469 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1289 3335456 3341900 3342380 "UTS" 3343717 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1288 3329434 3332266 3332309 "URAGG" 3334379 NIL URAGG (NIL T) -9 NIL 3335102 NIL) (-1287 3326466 3327434 3328458 "URAGG-" 3328463 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1286 3321842 3325101 3325566 "UPXSSING" 3326130 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1285 3314271 3321746 3321818 "UPXSCONS" 3321823 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1284 3303029 3310473 3310535 "UPXSCCA" 3311109 NIL UPXSCCA (NIL T T) -9 NIL 3311342 NIL) (-1283 3302649 3302752 3302926 "UPXSCCA-" 3302931 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1282 3291307 3298476 3298519 "UPXSCAT" 3299167 NIL UPXSCAT (NIL T) -9 NIL 3299776 NIL) (-1281 3290731 3290816 3290995 "UPXS2" 3291222 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1280 3282223 3290113 3290377 "UPXS" 3290525 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1279 3280859 3281130 3281481 "UPSQFREE" 3281966 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1278 3273690 3277125 3277180 "UPSCAT" 3278260 NIL UPSCAT (NIL T T) -9 NIL 3279026 NIL) (-1277 3272846 3273101 3273428 "UPSCAT-" 3273433 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1276 3272467 3272516 3272649 "UPOLYC2" 3272797 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1275 3256615 3265594 3265637 "UPOLYC" 3267738 NIL UPOLYC (NIL T) -9 NIL 3268959 NIL) (-1274 3247484 3250383 3253523 "UPOLYC-" 3253528 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1273 3246805 3246930 3247094 "UPMP" 3247373 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1272 3246352 3246439 3246578 "UPDIVP" 3246718 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1271 3244890 3245169 3245485 "UPDECOMP" 3246101 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1270 3244103 3244233 3244419 "UPCDEN" 3244774 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1269 3243616 3243691 3243840 "UP2" 3244028 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1268 3234212 3243299 3243428 "UP" 3243535 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1267 3233417 3233554 3233759 "UNISEG2" 3234055 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1266 3231770 3232621 3232898 "UNISEG" 3233175 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1265 3230812 3231010 3231236 "UNIFACT" 3231586 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1264 3217543 3230716 3230788 "ULSCONS" 3230793 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1263 3197360 3210623 3210685 "ULSCCAT" 3211323 NIL ULSCCAT (NIL T T) -9 NIL 3211612 NIL) (-1262 3196356 3196655 3197043 "ULSCCAT-" 3197048 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3184811 3191902 3191945 "ULSCAT" 3192808 NIL ULSCAT (NIL T) -9 NIL 3193539 NIL) (-1260 3184235 3184320 3184499 "ULS2" 3184726 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1259 3166066 3183547 3183789 "ULS" 3184051 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1258 3164985 3165685 3165799 "UINT8" 3165910 T UINT8 (NIL) -8 NIL NIL 3166002) (-1257 3163903 3164603 3164717 "UINT64" 3164828 T UINT64 (NIL) -8 NIL NIL 3164920) (-1256 3162821 3163521 3163635 "UINT32" 3163746 T UINT32 (NIL) -8 NIL NIL 3163838) (-1255 3161739 3162439 3162553 "UINT16" 3162664 T UINT16 (NIL) -8 NIL NIL 3162756) (-1254 3159818 3160985 3161015 "UFD" 3161227 T UFD (NIL) -9 NIL 3161341 NIL) (-1253 3159600 3159658 3159753 "UFD-" 3159758 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1252 3158658 3158865 3159081 "UDVO" 3159406 T UDVO (NIL) -7 NIL NIL NIL) (-1251 3156424 3156883 3157354 "UDPO" 3158222 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1250 3156136 3156379 3156410 "TYPEAST" 3156415 T TYPEAST (NIL) -8 NIL NIL NIL) (-1249 3156069 3156074 3156104 "TYPE" 3156109 T TYPE (NIL) -9 NIL NIL NIL) (-1248 3155022 3155242 3155482 "TWOFACT" 3155863 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1247 3153997 3154431 3154666 "TUPLE" 3154822 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1246 3151634 3152207 3152746 "TUBETOOL" 3153480 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1245 3150440 3150681 3150923 "TUBE" 3151427 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1244 3138689 3143197 3143294 "TSETCAT" 3148563 NIL TSETCAT (NIL T T T T) -9 NIL 3150095 NIL) (-1243 3133157 3135021 3136912 "TSETCAT-" 3136917 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1242 3127343 3132129 3132412 "TS" 3132909 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3121816 3122829 3123758 "TRMANIP" 3126479 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1240 3121245 3121320 3121483 "TRIMAT" 3121748 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1239 3119057 3119348 3119705 "TRIGMNIP" 3120994 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1238 3118541 3118690 3118720 "TRIGCAT" 3118933 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1237 3118186 3118289 3118430 "TRIGCAT-" 3118435 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1236 3114911 3117044 3117325 "TREE" 3117940 NIL TREE (NIL T) -8 NIL NIL NIL) (-1235 3114017 3114713 3114743 "TRANFUN" 3114778 T TRANFUN (NIL) -9 NIL 3114844 NIL) (-1234 3113236 3113487 3113767 "TRANFUN-" 3113772 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1233 3113034 3113072 3113133 "TOPSP" 3113197 T TOPSP (NIL) -7 NIL NIL NIL) (-1232 3112364 3112497 3112651 "TOOLSIGN" 3112915 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1231 3110878 3111541 3111780 "TEXTFILE" 3112147 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1230 3110653 3110690 3110762 "TEX1" 3110841 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1229 3108457 3109106 3109535 "TEX" 3110246 T TEX (NIL) -8 NIL NIL NIL) (-1228 3108093 3108168 3108258 "TEMUTL" 3108389 T TEMUTL (NIL) -7 NIL NIL NIL) (-1227 3106187 3106527 3106852 "TBCMPPK" 3107816 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1226 3097621 3104273 3104329 "TBAGG" 3104729 NIL TBAGG (NIL T T) -9 NIL 3104940 NIL) (-1225 3092505 3094179 3095933 "TBAGG-" 3095938 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1224 3091871 3091996 3092141 "TANEXP" 3092394 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1223 3091322 3091646 3091736 "TALGOP" 3091816 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1222 3090716 3090833 3090971 "TABLEAU" 3091219 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1221 3083844 3090573 3090666 "TABLE" 3090671 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1220 3078374 3079672 3080920 "TABLBUMP" 3082630 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1219 3077584 3077743 3077924 "SYSTEM" 3078215 T SYSTEM (NIL) -8 NIL NIL NIL) (-1218 3073989 3074742 3075525 "SYSSOLP" 3076835 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1217 3073751 3073944 3073975 "SYSPTR" 3073980 T SYSPTR (NIL) -8 NIL NIL NIL) (-1216 3072590 3073282 3073408 "SYSNNI" 3073594 NIL SYSNNI (NIL NIL) -8 NIL NIL 3073686) (-1215 3071797 3072352 3072431 "SYSINT" 3072491 NIL SYSINT (NIL NIL) -8 NIL NIL 3072536) (-1214 3067895 3069075 3069785 "SYNTAX" 3071109 T SYNTAX (NIL) -8 NIL NIL NIL) (-1213 3064975 3065655 3066287 "SYMTAB" 3067285 T SYMTAB (NIL) -8 NIL NIL NIL) (-1212 3060074 3061126 3062109 "SYMS" 3064014 T SYMS (NIL) -8 NIL NIL NIL) (-1211 3056980 3059525 3059758 "SYMPOLY" 3059876 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1210 3056485 3056572 3056695 "SYMFUNC" 3056892 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1209 3052283 3053797 3054610 "SYMBOL" 3055694 T SYMBOL (NIL) -8 NIL NIL NIL) (-1208 3045756 3047511 3049231 "SWITCH" 3050585 T SWITCH (NIL) -8 NIL NIL NIL) (-1207 3038517 3044712 3045006 "SUTS" 3045520 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1206 3030009 3037899 3038163 "SUPXS" 3038311 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3029156 3029295 3029512 "SUPFRACF" 3029877 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1204 3028771 3028836 3028949 "SUP2" 3029091 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1203 3019315 3028389 3028515 "SUP" 3028680 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3017739 3018037 3018393 "SUMRF" 3019014 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1201 3017062 3017140 3017332 "SUMFS" 3017660 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1200 2998928 3016374 3016616 "SULS" 3016878 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1199 2998476 2998750 2998820 "SUCHTAST" 2998880 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1198 2997717 2998001 2998141 "SUCH" 2998384 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1197 2991356 2992623 2993582 "SUBSPACE" 2996805 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1196 2990776 2990876 2991040 "SUBRESP" 2991244 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1195 2984787 2986069 2987216 "STTFNC" 2989676 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1194 2977981 2979452 2980763 "STTF" 2983523 NIL STTF (NIL T) -7 NIL NIL NIL) (-1193 2969097 2971163 2972957 "STTAYLOR" 2976222 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1192 2961965 2968961 2969044 "STRTBL" 2969049 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1191 2956476 2961674 2961773 "STRING" 2961888 T STRING (NIL) -8 NIL NIL NIL) (-1190 2955980 2956063 2956207 "STREAM3" 2956393 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1189 2954944 2955145 2955380 "STREAM2" 2955793 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1188 2954626 2954684 2954777 "STREAM1" 2954886 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1187 2946740 2952245 2952856 "STREAM" 2954050 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2945732 2945937 2946168 "STINPROD" 2946556 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1185 2944847 2945221 2945369 "STEPAST" 2945606 T STEPAST (NIL) -8 NIL NIL NIL) (-1184 2944343 2944588 2944618 "STEP" 2944712 T STEP (NIL) -9 NIL 2944783 NIL) (-1183 2937513 2944242 2944319 "STBL" 2944324 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1182 2931694 2936307 2936350 "STAGG" 2936782 NIL STAGG (NIL T) -9 NIL 2936961 NIL) (-1181 2929246 2929998 2930870 "STAGG-" 2930875 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1180 2927332 2929016 2929108 "STACK" 2929189 NIL STACK (NIL T) -8 NIL NIL NIL) (-1179 2926649 2927162 2927192 "SRING" 2927197 T SRING (NIL) -9 NIL 2927217 NIL) (-1178 2918771 2924790 2925246 "SREGSET" 2926279 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1177 2911118 2912565 2914078 "SRDCMPK" 2917377 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1176 2903532 2908477 2908507 "SRAGG" 2909810 T SRAGG (NIL) -9 NIL 2910418 NIL) (-1175 2902483 2902804 2903183 "SRAGG-" 2903188 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1174 2896181 2901430 2901851 "SQMATRIX" 2902109 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1173 2889707 2892899 2893626 "SPLTREE" 2895526 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1172 2885532 2886363 2887009 "SPLNODE" 2889133 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1171 2884507 2884812 2884842 "SPFCAT" 2885286 T SPFCAT (NIL) -9 NIL NIL NIL) (-1170 2883202 2883454 2883718 "SPECOUT" 2884265 T SPECOUT (NIL) -7 NIL NIL NIL) (-1169 2873848 2876166 2876196 "SPADXPT" 2880874 T SPADXPT (NIL) -9 NIL 2883040 NIL) (-1168 2873603 2873649 2873718 "SPADPRSR" 2873801 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1167 2871206 2873558 2873589 "SPADAST" 2873594 T SPADAST (NIL) -8 NIL NIL NIL) (-1166 2862807 2864910 2864953 "SPACEC" 2869326 NIL SPACEC (NIL T) -9 NIL 2871142 NIL) (-1165 2860607 2862739 2862788 "SPACE3" 2862793 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1164 2859339 2859530 2859821 "SORTPAK" 2860412 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1163 2857401 2857734 2858146 "SOLVETRA" 2859003 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1162 2856439 2856673 2856934 "SOLVESER" 2857174 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1161 2851671 2852631 2853626 "SOLVERAD" 2855491 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1160 2847396 2848095 2848824 "SOLVEFOR" 2851038 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1159 2841114 2846744 2846841 "SNTSCAT" 2846846 NIL SNTSCAT (NIL T T T T) -9 NIL 2846916 NIL) (-1158 2834665 2839437 2839828 "SMTS" 2840804 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1157 2828387 2834553 2834630 "SMP" 2834635 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1156 2826516 2826847 2827245 "SMITH" 2828084 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1155 2818155 2823095 2823198 "SMATCAT" 2824549 NIL SMATCAT (NIL NIL T T T) -9 NIL 2825099 NIL) (-1154 2814927 2815918 2817096 "SMATCAT-" 2817101 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1153 2812507 2814135 2814178 "SKAGG" 2814439 NIL SKAGG (NIL T) -9 NIL 2814574 NIL) (-1152 2808027 2811990 2812167 "SINT" 2812319 T SINT (NIL) -8 NIL NIL 2812474) (-1151 2807793 2807837 2807903 "SIMPAN" 2807983 T SIMPAN (NIL) -7 NIL NIL NIL) (-1150 2806613 2806852 2807127 "SIGNRF" 2807552 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1149 2805428 2805597 2805881 "SIGNEF" 2806442 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1148 2804668 2805011 2805135 "SIGAST" 2805326 T SIGAST (NIL) -8 NIL NIL NIL) (-1147 2803893 2804203 2804343 "SIG" 2804550 T SIG (NIL) -8 NIL NIL NIL) (-1146 2801545 2802037 2802543 "SHP" 2803434 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1145 2794983 2801446 2801522 "SHDP" 2801527 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1144 2794494 2794734 2794764 "SGROUP" 2794857 T SGROUP (NIL) -9 NIL 2794919 NIL) (-1143 2794346 2794378 2794451 "SGROUP-" 2794456 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1142 2791065 2791835 2792558 "SGCF" 2793645 T SGCF (NIL) -7 NIL NIL NIL) (-1141 2784881 2790511 2790608 "SFRTCAT" 2790613 NIL SFRTCAT (NIL T T T T) -9 NIL 2790652 NIL) (-1140 2778200 2779320 2780456 "SFRGCD" 2783864 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1139 2771218 2772399 2773585 "SFQCMPK" 2777133 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2770820 2770927 2771038 "SFORT" 2771159 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1137 2769746 2770660 2770781 "SEXOF" 2770786 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1136 2765335 2766242 2766337 "SEXCAT" 2768959 NIL SEXCAT (NIL T T T T T) -9 NIL 2769519 NIL) (-1135 2764250 2765216 2765284 "SEX" 2765289 T SEX (NIL) -8 NIL NIL NIL) (-1134 2762372 2762963 2763268 "SETMN" 2763991 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1133 2761902 2762090 2762120 "SETCAT" 2762237 T SETCAT (NIL) -9 NIL 2762322 NIL) (-1132 2761670 2761734 2761833 "SETCAT-" 2761838 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1131 2757884 2760131 2760174 "SETAGG" 2761044 NIL SETAGG (NIL T) -9 NIL 2761384 NIL) (-1130 2757306 2757458 2757695 "SETAGG-" 2757700 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1129 2754229 2757240 2757288 "SET" 2757293 NIL SET (NIL T) -8 NIL NIL NIL) (-1128 2753612 2753925 2754026 "SEQAST" 2754150 T SEQAST (NIL) -8 NIL NIL NIL) (-1127 2752739 2753105 2753166 "SEGXCAT" 2753452 NIL SEGXCAT (NIL T T) -9 NIL 2753572 NIL) (-1126 2751664 2751932 2751975 "SEGCAT" 2752497 NIL SEGCAT (NIL T) -9 NIL 2752718 NIL) (-1125 2751279 2751344 2751457 "SEGBIND2" 2751599 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1124 2750169 2750642 2750850 "SEGBIND" 2751106 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1123 2749688 2749970 2750047 "SEGAST" 2750114 T SEGAST (NIL) -8 NIL NIL NIL) (-1122 2748897 2749033 2749237 "SEG2" 2749532 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1121 2747813 2748563 2748745 "SEG" 2748750 NIL SEG (NIL T) -8 NIL NIL NIL) (-1120 2747046 2747748 2747795 "SDVAR" 2747800 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1119 2738404 2746816 2746946 "SDPOL" 2746951 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1118 2736973 2737263 2737582 "SCPKG" 2738119 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1117 2736095 2736309 2736501 "SCOPE" 2736803 T SCOPE (NIL) -8 NIL NIL NIL) (-1116 2735291 2735449 2735628 "SCACHE" 2735950 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1115 2734875 2735109 2735139 "SASTCAT" 2735144 T SASTCAT (NIL) -9 NIL 2735157 NIL) (-1114 2734278 2734710 2734786 "SAOS" 2734821 T SAOS (NIL) -8 NIL NIL NIL) (-1113 2733837 2733878 2734051 "SAERFFC" 2734237 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1112 2733424 2733465 2733624 "SAEFACT" 2733796 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1111 2726472 2733321 2733401 "SAE" 2733406 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2724775 2725107 2725508 "RURPK" 2726138 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1109 2723352 2723718 2724023 "RULESET" 2724609 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1108 2722922 2723146 2723229 "RULECOLD" 2723304 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1107 2720037 2720675 2721133 "RULE" 2722603 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2719821 2719855 2719926 "RTVALUE" 2719988 T RTVALUE (NIL) -8 NIL NIL NIL) (-1105 2719232 2719538 2719632 "RSTRCAST" 2719749 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1104 2714002 2714875 2715795 "RSETGCD" 2718431 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1103 2702680 2708310 2708407 "RSETCAT" 2712526 NIL RSETCAT (NIL T T T T) -9 NIL 2713623 NIL) (-1102 2700499 2701146 2701970 "RSETCAT-" 2701975 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1101 2692807 2694261 2695781 "RSDCMPK" 2699098 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2690676 2691239 2691313 "RRCC" 2692399 NIL RRCC (NIL T T) -9 NIL 2692743 NIL) (-1099 2689997 2690201 2690480 "RRCC-" 2690485 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1098 2689380 2689693 2689794 "RPTAST" 2689918 T RPTAST (NIL) -8 NIL NIL NIL) (-1097 2661766 2672492 2672559 "RPOLCAT" 2683225 NIL RPOLCAT (NIL T T T) -9 NIL 2686385 NIL) (-1096 2652736 2655604 2658726 "RPOLCAT-" 2658731 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1095 2643303 2650947 2651429 "ROUTINE" 2652276 T ROUTINE (NIL) -8 NIL NIL NIL) (-1094 2639366 2642929 2643069 "ROMAN" 2643185 T ROMAN (NIL) -8 NIL NIL NIL) (-1093 2637478 2638226 2638486 "ROIRC" 2639171 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1092 2633251 2636020 2636050 "RNS" 2636319 T RNS (NIL) -9 NIL 2636575 NIL) (-1091 2631658 2632143 2632677 "RNS-" 2632752 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1090 2630619 2631023 2631225 "RNGBIND" 2631509 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1089 2629912 2630416 2630446 "RNG" 2630451 T RNG (NIL) -9 NIL 2630472 NIL) (-1088 2629207 2629685 2629728 "RMODULE" 2629733 NIL RMODULE (NIL T) -9 NIL 2629760 NIL) (-1087 2628031 2628137 2628473 "RMCAT2" 2629108 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1086 2624647 2627377 2627674 "RMATRIX" 2627793 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1085 2617257 2619734 2619849 "RMATCAT" 2623208 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2624190 NIL) (-1084 2616596 2616779 2617086 "RMATCAT-" 2617091 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1083 2616169 2616383 2616426 "RLINSET" 2616488 NIL RLINSET (NIL T) -9 NIL 2616532 NIL) (-1082 2615730 2615811 2615939 "RINTERP" 2616088 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1081 2614654 2615328 2615358 "RING" 2615414 T RING (NIL) -9 NIL 2615506 NIL) (-1080 2614434 2614490 2614587 "RING-" 2614592 NIL RING- (NIL T) -8 NIL NIL NIL) (-1079 2613245 2613512 2613770 "RIDIST" 2614198 T RIDIST (NIL) -7 NIL NIL NIL) (-1078 2603984 2612713 2612919 "RGCHAIN" 2613093 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1077 2603242 2603726 2603767 "RGBCSPC" 2603825 NIL RGBCSPC (NIL T) -9 NIL 2603877 NIL) (-1076 2602308 2602767 2602808 "RGBCMDL" 2603040 NIL RGBCMDL (NIL T) -9 NIL 2603154 NIL) (-1075 2601948 2602017 2602120 "RFFACTOR" 2602239 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1074 2601667 2601708 2601805 "RFFACT" 2601907 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1073 2599718 2600148 2600530 "RFDIST" 2601307 T RFDIST (NIL) -7 NIL NIL NIL) (-1072 2596658 2597326 2597996 "RF" 2599082 NIL RF (NIL T) -7 NIL NIL NIL) (-1071 2596105 2596203 2596366 "RETSOL" 2596560 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1070 2595723 2595821 2595864 "RETRACT" 2595997 NIL RETRACT (NIL T) -9 NIL 2596084 NIL) (-1069 2595566 2595597 2595684 "RETRACT-" 2595689 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1068 2595114 2595388 2595458 "RETAST" 2595518 T RETAST (NIL) -8 NIL NIL NIL) (-1067 2587578 2594767 2594894 "RESULT" 2595009 T RESULT (NIL) -8 NIL NIL NIL) (-1066 2586013 2586847 2587046 "RESRING" 2587481 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1065 2585637 2585698 2585796 "RESLATC" 2585950 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1064 2585336 2585377 2585484 "REPSQ" 2585596 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1063 2585027 2585068 2585179 "REPDB" 2585295 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1062 2578859 2580316 2581539 "REP2" 2583839 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1061 2575162 2575917 2576725 "REP1" 2578086 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1060 2572542 2573164 2573766 "REP" 2574582 T REP (NIL) -7 NIL NIL NIL) (-1059 2564664 2570683 2571139 "REGSET" 2572172 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2563373 2563812 2564062 "REF" 2564449 NIL REF (NIL T) -8 NIL NIL NIL) (-1057 2562738 2562853 2563020 "REDORDER" 2563257 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1056 2558109 2561951 2562178 "RECLOS" 2562566 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1055 2557143 2557342 2557557 "REALSOLV" 2557916 T REALSOLV (NIL) -7 NIL NIL NIL) (-1054 2553590 2554428 2555312 "REAL0Q" 2556308 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1053 2549143 2550179 2551240 "REAL0" 2552571 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1052 2548977 2549030 2549060 "REAL" 2549065 T REAL (NIL) -9 NIL 2549100 NIL) (-1051 2548388 2548694 2548788 "RDUCEAST" 2548905 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1050 2547787 2547865 2548072 "RDIV" 2548310 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1049 2546837 2547029 2547242 "RDIST" 2547609 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1048 2545422 2545721 2546093 "RDETRS" 2546545 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1047 2543216 2543688 2544226 "RDETR" 2544964 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1046 2541835 2542119 2542516 "RDEEFS" 2542932 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1045 2540338 2540650 2541075 "RDEEF" 2541523 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1044 2533817 2537292 2537322 "RCFIELD" 2538617 T RCFIELD (NIL) -9 NIL 2539348 NIL) (-1043 2531773 2532385 2533081 "RCFIELD-" 2533156 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1042 2527936 2529846 2529889 "RCAGG" 2530973 NIL RCAGG (NIL T) -9 NIL 2531438 NIL) (-1041 2527546 2527658 2527821 "RCAGG-" 2527826 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1040 2526863 2526993 2527158 "RATRET" 2527430 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1039 2526404 2526483 2526604 "RATFACT" 2526791 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1038 2525682 2525832 2525984 "RANDSRC" 2526274 T RANDSRC (NIL) -7 NIL NIL NIL) (-1037 2525410 2525460 2525533 "RADUTIL" 2525631 T RADUTIL (NIL) -7 NIL NIL NIL) (-1036 2517555 2524241 2524552 "RADIX" 2525133 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1035 2507170 2517397 2517527 "RADFF" 2517532 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1034 2506799 2506892 2506922 "RADCAT" 2507082 T RADCAT (NIL) -9 NIL NIL NIL) (-1033 2506569 2506629 2506729 "RADCAT-" 2506734 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1032 2504594 2506339 2506431 "QUEUE" 2506512 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1031 2504219 2504268 2504399 "QUATCT2" 2504545 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1030 2496597 2500642 2500684 "QUATCAT" 2501475 NIL QUATCAT (NIL T) -9 NIL 2502241 NIL) (-1029 2492478 2493773 2495163 "QUATCAT-" 2495259 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1028 2488324 2492411 2492459 "QUAT" 2492464 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1027 2485691 2487372 2487415 "QUAGG" 2487796 NIL QUAGG (NIL T) -9 NIL 2487971 NIL) (-1026 2485239 2485513 2485583 "QQUTAST" 2485643 T QQUTAST (NIL) -8 NIL NIL NIL) (-1025 2484150 2484752 2484917 "QFORM" 2485120 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1024 2483775 2483824 2483955 "QFCAT2" 2484101 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1023 2473472 2479622 2479664 "QFCAT" 2480332 NIL QFCAT (NIL T) -9 NIL 2481333 NIL) (-1022 2468806 2470254 2471841 "QFCAT-" 2471937 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2468237 2468371 2468503 "QEQUAT" 2468696 T QEQUAT (NIL) -8 NIL NIL NIL) (-1020 2461255 2462436 2463622 "QCMPACK" 2467170 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2460484 2460666 2460902 "QALGSET2" 2461073 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1018 2457934 2458470 2458900 "QALGSET" 2460139 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2456601 2456843 2457162 "PWFFINTB" 2457707 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1016 2454746 2454944 2455300 "PUSHVAR" 2456415 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1015 2450473 2451689 2451732 "PTRANFN" 2453643 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1014 2448810 2449155 2449479 "PTPACK" 2450184 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1013 2448433 2448496 2448607 "PTFUNC2" 2448747 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1012 2442463 2447222 2447265 "PTCAT" 2447565 NIL PTCAT (NIL T) -9 NIL 2447718 NIL) (-1011 2442112 2442153 2442279 "PSQFR" 2442422 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1010 2440684 2441000 2441336 "PSEUDLIN" 2441810 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1009 2427204 2429779 2432105 "PSETPK" 2438444 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1008 2420023 2422940 2423038 "PSETCAT" 2426079 NIL PSETCAT (NIL T T T T) -9 NIL 2426893 NIL) (-1007 2417748 2418490 2419314 "PSETCAT-" 2419319 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1006 2417061 2417256 2417286 "PSCURVE" 2417558 T PSCURVE (NIL) -9 NIL 2417725 NIL) (-1005 2412784 2414551 2414618 "PSCAT" 2415470 NIL PSCAT (NIL T T T) -9 NIL 2415710 NIL) (-1004 2411778 2412060 2412463 "PSCAT-" 2412468 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1003 2409946 2410837 2411102 "PRTITION" 2411535 T PRTITION (NIL) -8 NIL NIL NIL) (-1002 2409357 2409663 2409757 "PRTDAST" 2409874 T PRTDAST (NIL) -8 NIL NIL NIL) (-1001 2398201 2400623 2402813 "PRS" 2407219 NIL PRS (NIL T T) -7 NIL NIL NIL) (-1000 2395927 2397518 2397560 "PRQAGG" 2397746 NIL PRQAGG (NIL T) -9 NIL 2397848 NIL) (-999 2395106 2395555 2395583 "PROPLOG" 2395722 T PROPLOG (NIL) -9 NIL 2395837 NIL) (-998 2394704 2394767 2394890 "PROPFUN2" 2395029 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-997 2394001 2394140 2394312 "PROPFUN1" 2394565 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-996 2391982 2392748 2393045 "PROPFRML" 2393737 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-995 2391427 2391558 2391686 "PROPERTY" 2391874 T PROPERTY (NIL) -8 NIL NIL NIL) (-994 2385240 2389593 2390413 "PRODUCT" 2390653 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-993 2385030 2385068 2385127 "PRINT" 2385201 T PRINT (NIL) -7 NIL NIL NIL) (-992 2384346 2384487 2384639 "PRIMES" 2384910 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-991 2382393 2382812 2383278 "PRIMELT" 2383925 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-990 2382110 2382171 2382199 "PRIMCAT" 2382323 T PRIMCAT (NIL) -9 NIL NIL NIL) (-989 2381099 2381295 2381523 "PRIMARR2" 2381928 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-988 2376935 2381037 2381082 "PRIMARR" 2381087 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-987 2376572 2376634 2376745 "PREASSOC" 2376873 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-986 2373537 2376030 2376264 "PR" 2376383 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2372988 2373145 2373173 "PPCURVE" 2373378 T PPCURVE (NIL) -9 NIL 2373514 NIL) (-984 2372535 2372783 2372866 "PORTNUM" 2372925 T PORTNUM (NIL) -8 NIL NIL NIL) (-983 2369872 2370293 2370885 "POLYROOT" 2372116 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-982 2369249 2369313 2369547 "POLYLIFT" 2369808 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-981 2365470 2365973 2366602 "POLYCATQ" 2368794 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-980 2351118 2357217 2357282 "POLYCAT" 2360796 NIL POLYCAT (NIL T T T) -9 NIL 2362674 NIL) (-979 2344258 2346443 2348820 "POLYCAT-" 2348825 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-978 2343839 2343913 2344033 "POLY2UP" 2344184 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-977 2343465 2343528 2343637 "POLY2" 2343776 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-976 2336680 2343069 2343229 "POLY" 2343338 NIL POLY (NIL T) -8 NIL NIL NIL) (-975 2335341 2335604 2335880 "POLUTIL" 2336454 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-974 2333660 2333973 2334304 "POLTOPOL" 2335063 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-973 2328770 2333594 2333641 "POINT" 2333646 NIL POINT (NIL T) -8 NIL NIL NIL) (-972 2326903 2327314 2327689 "PNTHEORY" 2328415 T PNTHEORY (NIL) -7 NIL NIL NIL) (-971 2325349 2325658 2326057 "PMTOOLS" 2326601 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-970 2324936 2325020 2325137 "PMSYM" 2325265 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-969 2324438 2324513 2324688 "PMQFCAT" 2324861 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-968 2323819 2323917 2324079 "PMPREDFS" 2324339 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-967 2323162 2323284 2323440 "PMPRED" 2323696 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2321816 2322034 2322412 "PMPLCAT" 2322924 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-965 2321342 2321427 2321579 "PMLSAGG" 2321731 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-964 2320809 2320891 2321073 "PMKERNEL" 2321260 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-963 2320420 2320501 2320614 "PMINS" 2320728 NIL PMINS (NIL T) -7 NIL NIL NIL) (-962 2319856 2319931 2320140 "PMFS" 2320345 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-961 2319072 2319202 2319407 "PMDOWN" 2319733 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-960 2318321 2318455 2318618 "PMASSFS" 2318959 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-959 2317464 2317646 2317827 "PMASS" 2318160 T PMASS (NIL) -7 NIL NIL NIL) (-958 2317113 2317187 2317281 "PLOTTOOL" 2317390 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-957 2312765 2313959 2314881 "PLOT3D" 2316211 T PLOT3D (NIL) -8 NIL NIL NIL) (-956 2311653 2311854 2312089 "PLOT1" 2312569 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-955 2306074 2307464 2308612 "PLOT" 2310525 T PLOT (NIL) -8 NIL NIL NIL) (-954 2281249 2286140 2290991 "PLEQN" 2301340 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-953 2280936 2280989 2281092 "PINTERPA" 2281196 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-952 2280242 2280376 2280556 "PINTERP" 2280801 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2278326 2279492 2279520 "PID" 2279717 T PID (NIL) -9 NIL 2279844 NIL) (-950 2278071 2278114 2278189 "PICOERCE" 2278283 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-949 2277167 2277835 2277922 "PI" 2277962 T PI (NIL) -8 NIL NIL 2278029) (-948 2276475 2276626 2276802 "PGROEB" 2277023 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-947 2271914 2272873 2273779 "PGE" 2275589 T PGE (NIL) -7 NIL NIL NIL) (-946 2269995 2270284 2270650 "PGCD" 2271631 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-945 2269321 2269436 2269597 "PFRPAC" 2269879 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-944 2265579 2267869 2268222 "PFR" 2269000 NIL PFR (NIL T) -8 NIL NIL NIL) (-943 2263932 2264212 2264537 "PFOTOOLS" 2265326 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-942 2262447 2262704 2263055 "PFOQ" 2263689 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-941 2260930 2261160 2261516 "PFO" 2262231 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-940 2258014 2259520 2259548 "PFECAT" 2260141 T PFECAT (NIL) -9 NIL 2260518 NIL) (-939 2257462 2257627 2257834 "PFECAT-" 2257839 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-938 2256035 2256317 2256618 "PFBRU" 2257211 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-937 2253864 2254253 2254685 "PFBR" 2255686 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-936 2249810 2253753 2253822 "PF" 2253827 NIL PF (NIL NIL) -8 NIL NIL NIL) (-935 2244864 2246017 2246887 "PERMGRP" 2248973 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-934 2242776 2243888 2243929 "PERMCAT" 2244329 NIL PERMCAT (NIL T) -9 NIL 2244627 NIL) (-933 2242423 2242470 2242594 "PERMAN" 2242729 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-932 2238225 2239932 2240580 "PERM" 2241808 NIL PERM (NIL T) -8 NIL NIL NIL) (-931 2235580 2237890 2238012 "PENDTREE" 2238136 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-930 2234461 2234724 2234765 "PDSPC" 2235298 NIL PDSPC (NIL T) -9 NIL 2235543 NIL) (-929 2233516 2233782 2234144 "PDSPC-" 2234149 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-928 2232230 2233166 2233207 "PDRING" 2233212 NIL PDRING (NIL T) -9 NIL 2233240 NIL) (-927 2230973 2231735 2231789 "PDMOD" 2231794 NIL PDMOD (NIL T T) -9 NIL 2231898 NIL) (-926 2228140 2228966 2229634 "PDEPROB" 2230325 T PDEPROB (NIL) -8 NIL NIL NIL) (-925 2225649 2226189 2226744 "PDEPACK" 2227605 T PDEPACK (NIL) -7 NIL NIL NIL) (-924 2224537 2224751 2225002 "PDECOMP" 2225448 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-923 2222054 2222945 2222973 "PDECAT" 2223760 T PDECAT (NIL) -9 NIL 2224473 NIL) (-922 2221671 2221738 2221792 "PDDOM" 2221957 NIL PDDOM (NIL T T) -9 NIL 2222037 NIL) (-921 2221484 2221520 2221627 "PDDOM-" 2221632 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-920 2221229 2221268 2221358 "PCOMP" 2221445 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-919 2219269 2220030 2220327 "PBWLB" 2220958 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-918 2218895 2218958 2219067 "PATTERN2" 2219206 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-917 2216604 2217040 2217497 "PATTERN1" 2218484 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-916 2208783 2210677 2212015 "PATTERN" 2215287 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2208341 2208414 2208546 "PATRES2" 2208710 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-914 2205607 2206290 2206771 "PATRES" 2207906 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2203460 2203895 2204302 "PATMATCH" 2205274 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-912 2202914 2203165 2203206 "PATMAB" 2203313 NIL PATMAB (NIL T) -9 NIL 2203396 NIL) (-911 2201360 2201768 2202026 "PATLRES" 2202719 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-910 2200898 2201029 2201070 "PATAB" 2201075 NIL PATAB (NIL T) -9 NIL 2201247 NIL) (-909 2199038 2199475 2199898 "PARTPERM" 2200495 T PARTPERM (NIL) -7 NIL NIL NIL) (-908 2198647 2198722 2198824 "PARSURF" 2198969 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-907 2198273 2198336 2198445 "PARSU2" 2198584 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-906 2198031 2198077 2198144 "PARSER" 2198226 T PARSER (NIL) -7 NIL NIL NIL) (-905 2197640 2197715 2197817 "PARSCURV" 2197962 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-904 2197266 2197329 2197438 "PARSC2" 2197577 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-903 2196893 2196963 2197060 "PARPCURV" 2197202 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-902 2196519 2196582 2196691 "PARPC2" 2196830 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-901 2195508 2195892 2196074 "PARAMAST" 2196357 T PARAMAST (NIL) -8 NIL NIL NIL) (-900 2195016 2195114 2195233 "PAN2EXPR" 2195409 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-899 2193709 2194137 2194365 "PALETTE" 2194808 T PALETTE (NIL) -8 NIL NIL NIL) (-898 2192054 2192714 2193074 "PAIR" 2193395 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-897 2184987 2191311 2191506 "PADICRC" 2191908 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-896 2177244 2184331 2184516 "PADICRAT" 2184834 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-895 2174041 2175904 2175944 "PADICCT" 2176525 NIL PADICCT (NIL NIL) -9 NIL 2176807 NIL) (-894 2172057 2173978 2174023 "PADIC" 2174028 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2171002 2171214 2171482 "PADEPAC" 2171844 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-892 2170202 2170347 2170553 "PADE" 2170864 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-891 2168435 2169410 2169690 "OWP" 2170006 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-890 2167880 2168141 2168238 "OVERSET" 2168358 T OVERSET (NIL) -8 NIL NIL NIL) (-889 2166800 2167485 2167657 "OVAR" 2167748 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-888 2155036 2157909 2160109 "OUTFORM" 2164620 T OUTFORM (NIL) -8 NIL NIL NIL) (-887 2154318 2154633 2154760 "OUTBFILE" 2154929 T OUTBFILE (NIL) -8 NIL NIL NIL) (-886 2153595 2153790 2153818 "OUTBCON" 2154136 T OUTBCON (NIL) -9 NIL 2154302 NIL) (-885 2153178 2153308 2153465 "OUTBCON-" 2153470 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-884 2152418 2152563 2152724 "OUT" 2153037 T OUT (NIL) -7 NIL NIL NIL) (-883 2151714 2152147 2152236 "OSI" 2152349 T OSI (NIL) -8 NIL NIL NIL) (-882 2151133 2151555 2151583 "OSGROUP" 2151588 T OSGROUP (NIL) -9 NIL 2151610 NIL) (-881 2149844 2150105 2150390 "ORTHPOL" 2150880 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-880 2147095 2149679 2149800 "OREUP" 2149805 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-879 2144198 2146786 2146913 "ORESUP" 2147037 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-878 2141698 2142226 2142787 "OREPCTO" 2143687 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-877 2135076 2137571 2137612 "OREPCAT" 2139960 NIL OREPCAT (NIL T) -9 NIL 2141064 NIL) (-876 2132049 2133005 2134063 "OREPCAT-" 2134068 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-875 2131241 2131519 2131547 "ORDTYPE" 2131856 T ORDTYPE (NIL) -9 NIL 2132019 NIL) (-874 2130542 2130758 2131013 "ORDTYPE-" 2131018 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-873 2129898 2130281 2130439 "ORDSTRCT" 2130444 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-872 2129396 2129766 2129794 "ORDSET" 2129799 T ORDSET (NIL) -9 NIL 2129821 NIL) (-871 2128047 2129018 2129046 "ORDRING" 2129051 T ORDRING (NIL) -9 NIL 2129080 NIL) (-870 2127298 2127863 2127891 "ORDMON" 2127896 T ORDMON (NIL) -9 NIL 2127917 NIL) (-869 2126442 2126607 2126802 "ORDFUNS" 2127147 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-868 2125657 2126172 2126200 "ORDFIN" 2126265 T ORDFIN (NIL) -9 NIL 2126339 NIL) (-867 2124911 2125050 2125236 "ORDCOMP2" 2125517 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-866 2121258 2123497 2123906 "ORDCOMP" 2124535 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-865 2117779 2118749 2119563 "OPTPROB" 2120464 T OPTPROB (NIL) -8 NIL NIL NIL) (-864 2114521 2115220 2115924 "OPTPACK" 2117095 T OPTPACK (NIL) -7 NIL NIL NIL) (-863 2112134 2112960 2112988 "OPTCAT" 2113807 T OPTCAT (NIL) -9 NIL 2114457 NIL) (-862 2111452 2111811 2111916 "OPSIG" 2112049 T OPSIG (NIL) -8 NIL NIL NIL) (-861 2111214 2111259 2111325 "OPQUERY" 2111406 T OPQUERY (NIL) -7 NIL NIL NIL) (-860 2110520 2110800 2110841 "OPERCAT" 2111053 NIL OPERCAT (NIL T) -9 NIL 2111150 NIL) (-859 2110263 2110331 2110448 "OPERCAT-" 2110453 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-858 2107179 2108574 2109078 "OP" 2109792 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2106472 2106599 2106773 "ONECOMP2" 2107051 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-856 2103085 2105269 2105638 "ONECOMP" 2106136 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-855 2102486 2102610 2102740 "OMSERVER" 2102975 T OMSERVER (NIL) -7 NIL NIL NIL) (-854 2099109 2101924 2101964 "OMSAGG" 2102025 NIL OMSAGG (NIL T) -9 NIL 2102090 NIL) (-853 2097684 2097995 2098277 "OMPKG" 2098847 T OMPKG (NIL) -7 NIL NIL NIL) (-852 2096031 2097233 2097402 "OMLO" 2097565 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-851 2094967 2095138 2095358 "OMEXPR" 2095857 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-850 2094052 2094388 2094548 "OMERRK" 2094827 T OMERRK (NIL) -8 NIL NIL NIL) (-849 2093289 2093598 2093734 "OMERR" 2093936 T OMERR (NIL) -8 NIL NIL NIL) (-848 2092680 2092966 2093074 "OMENC" 2093201 T OMENC (NIL) -8 NIL NIL NIL) (-847 2086317 2087760 2088931 "OMDEV" 2091529 T OMDEV (NIL) -8 NIL NIL NIL) (-846 2085350 2085557 2085751 "OMCONN" 2086143 T OMCONN (NIL) -8 NIL NIL NIL) (-845 2084756 2084883 2084911 "OM" 2085210 T OM (NIL) -9 NIL NIL NIL) (-844 2083034 2084226 2084254 "OINTDOM" 2084259 T OINTDOM (NIL) -9 NIL 2084280 NIL) (-843 2080109 2081722 2082059 "OFMONOID" 2082729 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-842 2079343 2080046 2080091 "ODVAR" 2080096 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-841 2076487 2079088 2079243 "ODR" 2079248 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-840 2067899 2076263 2076389 "ODPOL" 2076394 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-839 2061307 2067771 2067876 "ODP" 2067881 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-838 2060049 2060288 2060563 "ODETOOLS" 2061081 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-837 2056992 2057674 2058390 "ODESYS" 2059382 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-836 2051822 2052782 2053807 "ODERTRIC" 2056067 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-835 2051242 2051330 2051524 "ODERED" 2051734 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-834 2048094 2048678 2049355 "ODERAT" 2050665 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-833 2045010 2045518 2046115 "ODEPRRIC" 2047623 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-832 2042905 2043549 2044035 "ODEPROB" 2044544 T ODEPROB (NIL) -8 NIL NIL NIL) (-831 2039371 2039910 2040557 "ODEPRIM" 2042384 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-830 2038614 2038722 2038982 "ODEPAL" 2039263 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-829 2034716 2035567 2036431 "ODEPACK" 2037770 T ODEPACK (NIL) -7 NIL NIL NIL) (-828 2033759 2033884 2034106 "ODEINT" 2034605 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-827 2027824 2029285 2030732 "ODEIFTBL" 2032332 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-826 2023174 2024008 2024960 "ODEEF" 2026983 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-825 2022517 2022612 2022835 "ODECONST" 2023079 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-824 2020580 2021289 2021317 "ODECAT" 2021922 T ODECAT (NIL) -9 NIL 2022453 NIL) (-823 2020212 2020261 2020388 "OCTCT2" 2020531 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-822 2016712 2019917 2020039 "OCT" 2020122 NIL OCT (NIL T) -8 NIL NIL NIL) (-821 2015905 2016505 2016533 "OCAMON" 2016538 T OCAMON (NIL) -9 NIL 2016559 NIL) (-820 2010176 2012948 2012988 "OC" 2014085 NIL OC (NIL T) -9 NIL 2014943 NIL) (-819 2007211 2008151 2009141 "OC-" 2009235 NIL OC- (NIL T T) -8 NIL NIL NIL) (-818 2006631 2007056 2007084 "OASGP" 2007089 T OASGP (NIL) -9 NIL 2007109 NIL) (-817 2005727 2006354 2006382 "OAMONS" 2006422 T OAMONS (NIL) -9 NIL 2006465 NIL) (-816 2004903 2005462 2005490 "OAMON" 2005548 T OAMON (NIL) -9 NIL 2005600 NIL) (-815 2004761 2004794 2004862 "OAMON-" 2004867 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-814 2003542 2004295 2004323 "OAGROUP" 2004470 T OAGROUP (NIL) -9 NIL 2004563 NIL) (-813 2003245 2003333 2003451 "OAGROUP-" 2003456 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-812 2002927 2002983 2003072 "NUMTUBE" 2003189 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 1996446 1998018 1999554 "NUMQUAD" 2001411 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 1992126 1993160 1994195 "NUMODE" 1995431 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1989407 1990347 1990375 "NUMINT" 1991298 T NUMINT (NIL) -9 NIL 1992062 NIL) (-808 1988319 1988552 1988770 "NUMFMT" 1989209 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1974502 1977623 1980155 "NUMERIC" 1985826 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1968320 1973950 1974045 "NTSCAT" 1974050 NIL NTSCAT (NIL T T T T) -9 NIL 1974089 NIL) (-805 1967500 1967679 1967872 "NTPOLFN" 1968159 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1967126 1967189 1967298 "NSUP2" 1967437 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1953908 1963951 1964763 "NSUP" 1966347 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1942751 1953682 1953815 "NSMP" 1953820 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1941159 1941484 1941841 "NREP" 1942439 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1939738 1940002 1940360 "NPCOEF" 1940902 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1938786 1938919 1939135 "NORMRETR" 1939619 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1936797 1937117 1937526 "NORMPK" 1938494 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1936476 1936510 1936634 "NORMMA" 1936763 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1936259 1936294 1936363 "NONE1" 1936440 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1936023 1936216 1936245 "NONE" 1936250 T NONE (NIL) -8 NIL NIL NIL) (-794 1935514 1935582 1935761 "NODE1" 1935955 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1933575 1934637 1934892 "NNI" 1935239 T NNI (NIL) -8 NIL NIL 1935474) (-792 1931971 1932308 1932672 "NLINSOL" 1933243 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1928152 1929207 1930106 "NIPROB" 1931092 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1926891 1927143 1927445 "NFINTBAS" 1927914 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1925975 1926541 1926582 "NETCLT" 1926754 NIL NETCLT (NIL T) -9 NIL 1926836 NIL) (-788 1924647 1924914 1925195 "NCODIV" 1925743 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1924403 1924446 1924521 "NCNTFRAC" 1924604 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1922559 1922947 1923367 "NCEP" 1924028 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1921222 1922169 1922197 "NASRING" 1922307 T NASRING (NIL) -9 NIL 1922387 NIL) (-784 1921005 1921061 1921155 "NASRING-" 1921160 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1919972 1920623 1920651 "NARNG" 1920768 T NARNG (NIL) -9 NIL 1920859 NIL) (-782 1919646 1919731 1919865 "NARNG-" 1919870 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1918483 1918732 1918967 "NAGSP" 1919431 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1909527 1911439 1913112 "NAGS" 1916830 T NAGS (NIL) -7 NIL NIL NIL) (-779 1908051 1908383 1908714 "NAGF07" 1909216 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1902523 1903880 1905187 "NAGF04" 1906764 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1895395 1897105 1898738 "NAGF02" 1900910 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1890559 1891719 1892836 "NAGF01" 1894298 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1884139 1885753 1887338 "NAGE04" 1888994 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1875200 1877429 1879559 "NAGE02" 1882029 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1871093 1872100 1873064 "NAGE01" 1874256 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1868870 1869422 1869980 "NAGD03" 1870555 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1860566 1862548 1864502 "NAGD02" 1866936 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1854305 1855802 1857242 "NAGD01" 1859146 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1850442 1851336 1852173 "NAGC06" 1853488 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1848889 1849239 1849595 "NAGC05" 1850106 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1848253 1848384 1848528 "NAGC02" 1848765 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1847054 1847781 1847821 "NAALG" 1847900 NIL NAALG (NIL T) -9 NIL 1847961 NIL) (-765 1846883 1846918 1847008 "NAALG-" 1847013 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1840755 1841941 1843128 "MULTSQFR" 1845779 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1840062 1840149 1840333 "MULTFACT" 1840667 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1832207 1836645 1836698 "MTSCAT" 1837768 NIL MTSCAT (NIL T T) -9 NIL 1838284 NIL) (-761 1831913 1831973 1832065 "MTHING" 1832147 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1831699 1831738 1831798 "MSYSCMD" 1831873 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1828555 1831260 1831301 "MSETAGG" 1831306 NIL MSETAGG (NIL T) -9 NIL 1831340 NIL) (-758 1824383 1827310 1827630 "MSET" 1828268 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1819985 1821762 1822507 "MRING" 1823683 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1819545 1819618 1819749 "MRF2" 1819912 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1819157 1819198 1819342 "MRATFAC" 1819504 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1816727 1817064 1817495 "MPRFF" 1818862 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1810061 1816581 1816678 "MPOLY" 1816683 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1809545 1809586 1809794 "MPCPF" 1810020 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1809053 1809102 1809286 "MPC3" 1809496 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1808236 1808329 1808550 "MPC2" 1808968 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1806513 1806874 1807264 "MONOTOOL" 1807896 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1805658 1806041 1806069 "MONOID" 1806288 T MONOID (NIL) -9 NIL 1806435 NIL) (-747 1805174 1805323 1805504 "MONOID-" 1805509 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1794147 1800994 1801053 "MONOGEN" 1801727 NIL MONOGEN (NIL T T) -9 NIL 1802183 NIL) (-745 1791197 1792100 1793100 "MONOGEN-" 1793219 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1789914 1790462 1790490 "MONADWU" 1790882 T MONADWU (NIL) -9 NIL 1791120 NIL) (-743 1789244 1789445 1789693 "MONADWU-" 1789698 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1788529 1788833 1788861 "MONAD" 1789068 T MONAD (NIL) -9 NIL 1789180 NIL) (-741 1788196 1788292 1788424 "MONAD-" 1788429 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1786335 1787109 1787388 "MOEBIUS" 1787949 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1785503 1786003 1786043 "MODULE" 1786048 NIL MODULE (NIL T) -9 NIL 1786087 NIL) (-738 1785041 1785167 1785357 "MODULE-" 1785362 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1782571 1783405 1783732 "MODRING" 1784865 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1779300 1780676 1781197 "MODOP" 1782100 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1777786 1778367 1778644 "MODMONOM" 1779163 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1766546 1776077 1776491 "MODMON" 1777423 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1763379 1765390 1765666 "MODFIELD" 1766421 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1762290 1762660 1762850 "MMLFORM" 1763209 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1761810 1761859 1762038 "MMAP" 1762241 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1759703 1760642 1760683 "MLO" 1761106 NIL MLO (NIL T) -9 NIL 1761348 NIL) (-729 1757051 1757585 1758187 "MLIFT" 1759184 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1756430 1756526 1756680 "MKUCFUNC" 1756962 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1756023 1756099 1756222 "MKRECORD" 1756353 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1755046 1755232 1755460 "MKFUNC" 1755834 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1754422 1754538 1754694 "MKFLCFN" 1754929 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1753687 1753801 1753986 "MKBCFUNC" 1754315 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1749684 1753241 1753377 "MINT" 1753571 T MINT (NIL) -8 NIL NIL NIL) (-722 1748466 1748739 1749016 "MHROWRED" 1749439 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1743217 1747001 1747406 "MFLOAT" 1748081 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1742562 1742650 1742821 "MFINFACT" 1743129 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1738841 1739725 1740609 "MESH" 1741698 T MESH (NIL) -7 NIL NIL NIL) (-718 1737195 1737543 1737896 "MDDFACT" 1738528 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1733842 1736326 1736367 "MDAGG" 1736622 NIL MDAGG (NIL T) -9 NIL 1736765 NIL) (-716 1721565 1733135 1733342 "MCMPLX" 1733655 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1720684 1720848 1721049 "MCDEN" 1721414 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1718532 1718844 1719224 "MCALCFN" 1720414 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1717409 1717697 1717930 "MAYBE" 1718338 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1714967 1715544 1716106 "MATSTOR" 1716880 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1710503 1714339 1714587 "MATRIX" 1714752 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1706203 1706976 1707712 "MATLIN" 1709860 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1704779 1704950 1705283 "MATCAT2" 1706038 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1694232 1697836 1697913 "MATCAT" 1702945 NIL MATCAT (NIL T T T) -9 NIL 1704417 NIL) (-707 1690185 1691495 1692908 "MATCAT-" 1692913 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1688261 1688621 1689005 "MAPPKG3" 1689860 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1687218 1687415 1687637 "MAPPKG2" 1688085 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1685675 1686001 1686328 "MAPPKG1" 1686924 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1684676 1685081 1685258 "MAPPAST" 1685518 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1684281 1684345 1684468 "MAPHACK3" 1684612 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1683861 1683934 1684048 "MAPHACK2" 1684213 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1683287 1683402 1683544 "MAPHACK1" 1683752 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1681210 1681987 1682291 "MAGMA" 1683015 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1680629 1680934 1681025 "MACROAST" 1681139 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1676986 1678868 1679329 "M3D" 1680201 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1670458 1675297 1675338 "LZSTAGG" 1676120 NIL LZSTAGG (NIL T) -9 NIL 1676415 NIL) (-695 1666140 1667589 1669046 "LZSTAGG-" 1669051 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1663053 1664031 1664518 "LWORD" 1665685 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1662575 1662857 1662932 "LSTAST" 1662998 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1654617 1662346 1662480 "LSQM" 1662485 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1653835 1653980 1654208 "LSPP" 1654472 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1650572 1651288 1652018 "LSMP1" 1653137 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1648354 1648685 1649141 "LSMP" 1650261 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1641482 1647444 1647485 "LSAGG" 1647547 NIL LSAGG (NIL T) -9 NIL 1647625 NIL) (-687 1637991 1639101 1640314 "LSAGG-" 1640319 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1635286 1637135 1637384 "LPOLY" 1637786 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1634862 1634953 1635076 "LPEFRAC" 1635195 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1634545 1634624 1634652 "LOGIC" 1634763 T LOGIC (NIL) -9 NIL 1634845 NIL) (-683 1634401 1634430 1634501 "LOGIC-" 1634506 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1633576 1633734 1633927 "LODOOPS" 1634257 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1632100 1632349 1632702 "LODOF" 1633323 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1627976 1630735 1630776 "LODOCAT" 1631214 NIL LODOCAT (NIL T) -9 NIL 1631425 NIL) (-679 1627691 1627767 1627894 "LODOCAT-" 1627899 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1624677 1627532 1627650 "LODO2" 1627655 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1621784 1624614 1624659 "LODO1" 1624664 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1618879 1621700 1621766 "LODO" 1621771 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1617748 1617925 1618230 "LODEEF" 1618702 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1615734 1616842 1617095 "LO" 1617580 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1610817 1613900 1613941 "LNAGG" 1614803 NIL LNAGG (NIL T) -9 NIL 1615238 NIL) (-672 1609910 1610178 1610520 "LNAGG-" 1610525 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1605890 1606835 1607474 "LMOPS" 1609325 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1605189 1605667 1605708 "LMODULE" 1605713 NIL LMODULE (NIL T) -9 NIL 1605739 NIL) (-669 1602258 1604834 1604957 "LMDICT" 1605099 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1601834 1602048 1602089 "LLINSET" 1602150 NIL LLINSET (NIL T) -9 NIL 1602194 NIL) (-667 1601479 1601742 1601802 "LITERAL" 1601807 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1600998 1601078 1601217 "LIST3" 1601399 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1599096 1599444 1599843 "LIST2MAP" 1600645 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1598085 1598281 1598509 "LIST2" 1598914 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1590539 1597019 1597323 "LIST" 1597814 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1590122 1590358 1590399 "LINSET" 1590404 NIL LINSET (NIL T) -9 NIL 1590438 NIL) (-661 1588936 1589630 1589797 "LINFORM" 1590007 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1587235 1587963 1588004 "LINEXP" 1588494 NIL LINEXP (NIL T) -9 NIL 1588767 NIL) (-659 1585811 1586715 1586896 "LINELT" 1587106 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1584368 1584648 1584959 "LINDEP" 1585563 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1583504 1584100 1584210 "LINBASIS" 1584298 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1580241 1580990 1581767 "LIMITRF" 1582759 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1578526 1578840 1579249 "LIMITPS" 1579936 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1577354 1577929 1577969 "LIECAT" 1578109 NIL LIECAT (NIL T) -9 NIL 1578260 NIL) (-653 1577189 1577222 1577310 "LIECAT-" 1577315 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1571209 1576700 1576928 "LIE" 1577010 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1563508 1570749 1570905 "LIB" 1571073 T LIB (NIL) -8 NIL NIL NIL) (-650 1559077 1560026 1560961 "LGROBP" 1562625 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1557701 1558609 1558637 "LFCAT" 1558844 T LFCAT (NIL) -9 NIL 1558983 NIL) (-648 1555639 1555973 1556323 "LF" 1557422 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1552499 1553171 1553859 "LEXTRIPK" 1555003 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1549087 1550069 1550572 "LEXP" 1552079 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1548503 1548808 1548900 "LETAST" 1549015 T LETAST (NIL) -8 NIL NIL NIL) (-644 1546889 1547214 1547615 "LEADCDET" 1548185 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1546067 1546153 1546382 "LAZM3PK" 1546810 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1540592 1544144 1544682 "LAUPOL" 1545579 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1540165 1540215 1540376 "LAPLACE" 1540542 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1539013 1539729 1539770 "LALG" 1539832 NIL LALG (NIL T) -9 NIL 1539891 NIL) (-639 1538709 1538786 1538922 "LALG-" 1538927 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1536446 1537810 1538061 "LA" 1538542 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1536275 1536305 1536346 "KVTFROM" 1536408 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1535032 1535642 1535827 "KTVLOGIC" 1536110 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1534861 1534891 1534932 "KRCFROM" 1534994 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1533753 1533952 1534251 "KOVACIC" 1534661 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1533582 1533612 1533653 "KONVERT" 1533715 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1533411 1533441 1533482 "KOERCE" 1533544 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1532895 1532988 1533120 "KERNEL2" 1533325 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1530582 1531488 1531865 "KERNEL" 1532551 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1524164 1529059 1529113 "KDAGG" 1529490 NIL KDAGG (NIL T T) -9 NIL 1529696 NIL) (-628 1523675 1523817 1524022 "KDAGG-" 1524027 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1516489 1523336 1523491 "KAFILE" 1523553 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1516093 1516378 1516441 "JVMOP" 1516446 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1514829 1515333 1515582 "JVMMDACC" 1515864 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1513765 1514219 1514424 "JVMFDACC" 1514644 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1512346 1512841 1513141 "JVMCSTTG" 1513485 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1511482 1511886 1512047 "JVMCFACC" 1512205 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1511160 1511399 1511448 "JVMBCODE" 1511453 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1505179 1510671 1510899 "JORDAN" 1510981 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1504492 1504828 1504949 "JOINAST" 1505078 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1500638 1502669 1502723 "IXAGG" 1503652 NIL IXAGG (NIL T T) -9 NIL 1504111 NIL) (-617 1499491 1499863 1500282 "IXAGG-" 1500287 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1494694 1499413 1499472 "IVECTOR" 1499477 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1493419 1493697 1493963 "ITUPLE" 1494461 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1491891 1492098 1492393 "ITRIGMNP" 1493241 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1490618 1490840 1491123 "ITFUN3" 1491667 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1490216 1490279 1490402 "ITFUN2" 1490541 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1489321 1489696 1489870 "ITFORM" 1490062 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1487090 1488341 1488619 "ITAYLOR" 1489076 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1475494 1481227 1482390 "ISUPS" 1485960 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1474586 1474738 1474974 "ISUMP" 1475341 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1469550 1474531 1474572 "ISTRING" 1474577 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1468966 1469271 1469363 "ISAST" 1469478 T ISAST (NIL) -8 NIL NIL NIL) (-605 1468164 1468257 1468473 "IRURPK" 1468880 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1467076 1467301 1467541 "IRSN" 1467944 T IRSN (NIL) -7 NIL NIL NIL) (-603 1465121 1465502 1465931 "IRRF2F" 1466714 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1464862 1464906 1464982 "IRREDFFX" 1465077 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1463435 1463736 1464035 "IROOT" 1464595 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1462574 1462928 1463079 "IRFORM" 1463304 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1461656 1461787 1462001 "IR2F" 1462457 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1459245 1459764 1460330 "IR2" 1461134 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1455685 1456929 1457621 "IR" 1458585 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1455470 1455510 1455570 "IPRNTPK" 1455645 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1451444 1455359 1455428 "IPF" 1455433 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1449472 1451369 1451426 "IPADIC" 1451431 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1448730 1449032 1449162 "IP4ADDR" 1449362 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1448068 1448359 1448491 "IOMODE" 1448618 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1447039 1447665 1447792 "IOBFILE" 1447961 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1446449 1446943 1446971 "IOBCON" 1446976 T IOBCON (NIL) -9 NIL 1446997 NIL) (-589 1445954 1446018 1446201 "INVLAPLA" 1446385 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1435524 1437956 1440342 "INTTR" 1443618 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1431817 1432601 1433466 "INTTOOLS" 1434709 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1431397 1431494 1431611 "INTSLPE" 1431720 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1428864 1431320 1431379 "INTRVL" 1431384 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1426442 1426978 1427553 "INTRF" 1428349 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1425835 1425950 1426092 "INTRET" 1426340 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1423808 1424221 1424691 "INTRAT" 1425443 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1421053 1421654 1422273 "INTPM" 1423293 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1417770 1418397 1419135 "INTPAF" 1420439 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1412871 1413911 1414962 "INTPACK" 1416739 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1412117 1412275 1412483 "INTHERTR" 1412713 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1411550 1411636 1411824 "INTHERAL" 1412031 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1409318 1409839 1410296 "INTHEORY" 1411113 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1400650 1402345 1404117 "INTG0" 1407670 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1381175 1386013 1390823 "INTFTBL" 1395860 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1380400 1380562 1380735 "INTFACT" 1381034 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1377797 1378273 1378830 "INTEF" 1379954 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1375994 1376889 1376917 "INTDOM" 1377218 T INTDOM (NIL) -9 NIL 1377425 NIL) (-570 1375333 1375537 1375779 "INTDOM-" 1375784 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1371201 1373622 1373676 "INTCAT" 1374475 NIL INTCAT (NIL T) -9 NIL 1374796 NIL) (-568 1370655 1370776 1370904 "INTBIT" 1371093 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1369336 1369508 1369815 "INTALG" 1370500 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1368813 1368909 1369066 "INTAF" 1369240 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1361894 1368623 1368763 "INTABL" 1368768 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1361135 1361697 1361762 "INT8" 1361796 T INT8 (NIL) -8 NIL NIL 1361841) (-563 1360375 1360937 1361002 "INT64" 1361036 T INT64 (NIL) -8 NIL NIL 1361081) (-562 1359615 1360177 1360242 "INT32" 1360276 T INT32 (NIL) -8 NIL NIL 1360321) (-561 1358855 1359417 1359482 "INT16" 1359516 T INT16 (NIL) -8 NIL NIL 1359561) (-560 1355059 1358652 1358761 "INT" 1358766 T INT (NIL) -8 NIL NIL NIL) (-559 1349168 1352607 1352635 "INS" 1353569 T INS (NIL) -9 NIL 1354234 NIL) (-558 1346325 1347245 1348186 "INS-" 1348259 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1345082 1345327 1345625 "INPSIGN" 1346078 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1344176 1344317 1344514 "INPRODPF" 1344962 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1343046 1343187 1343424 "INPRODFF" 1344056 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1342034 1342198 1342458 "INNMFACT" 1342882 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1341213 1341328 1341516 "INMODGCD" 1341933 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1339697 1339966 1340290 "INFSP" 1340958 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1338857 1338998 1339181 "INFPROD0" 1339577 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1338455 1338527 1338625 "INFORM1" 1338792 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1335022 1336520 1337035 "INFORM" 1337948 T INFORM (NIL) -8 NIL NIL NIL) (-548 1334527 1334634 1334748 "INFINITY" 1334928 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1333601 1334247 1334348 "INETCLTS" 1334446 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1332199 1332467 1332788 "INEP" 1333349 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1331229 1332096 1332161 "INDE" 1332166 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1330781 1330861 1330978 "INCRMAPS" 1331156 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1329503 1330050 1330256 "INBFILE" 1330595 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1324683 1325739 1326683 "INBFF" 1328591 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1323537 1323860 1323888 "INBCON" 1324401 T INBCON (NIL) -9 NIL 1324667 NIL) (-540 1322747 1323012 1323288 "INBCON-" 1323293 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1322166 1322471 1322562 "INAST" 1322676 T INAST (NIL) -8 NIL NIL NIL) (-538 1321533 1321845 1321951 "IMPTAST" 1322080 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1317568 1321377 1321481 "IMATRIX" 1321486 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1316260 1316399 1316715 "IMATQF" 1317424 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1314440 1314707 1315044 "IMATLIN" 1316016 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1308355 1314364 1314422 "ILIST" 1314427 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1306135 1308215 1308328 "IIARRAY2" 1308333 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1300956 1306046 1306110 "IFF" 1306115 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1300237 1300573 1300689 "IFAST" 1300860 T IFAST (NIL) -8 NIL NIL NIL) (-530 1294863 1299529 1299717 "IFARRAY" 1300094 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1293901 1294767 1294840 "IFAMON" 1294845 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1293473 1293550 1293604 "IEVALAB" 1293811 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1293136 1293216 1293376 "IEVALAB-" 1293381 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1292169 1293025 1293100 "IDPOAMS" 1293105 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1291271 1292058 1292133 "IDPOAM" 1292138 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1290652 1291186 1291248 "IDPO" 1291253 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1289132 1289659 1289711 "IDPC" 1290223 NIL IDPC (NIL T T) -9 NIL 1290504 NIL) (-522 1288464 1289024 1289097 "IDPAM" 1289102 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1287679 1288356 1288429 "IDPAG" 1288434 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1287223 1287485 1287575 "IDENT" 1287609 T IDENT (NIL) -8 NIL NIL NIL) (-519 1283442 1284326 1285221 "IDECOMP" 1286380 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1276077 1277365 1278412 "IDEAL" 1282478 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1275219 1275349 1275549 "ICDEN" 1275961 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1274194 1274699 1274846 "ICARD" 1275092 T ICARD (NIL) -8 NIL NIL NIL) (-515 1272224 1272567 1272972 "IBPTOOLS" 1273871 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1267453 1271844 1271957 "IBITS" 1272143 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1264128 1264752 1265447 "IBATOOL" 1266870 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1261889 1262369 1262902 "IBACHIN" 1263663 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1259593 1261735 1261838 "IARRAY2" 1261843 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1255420 1259519 1259576 "IARRAY1" 1259581 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1248437 1253832 1254313 "IAN" 1254959 T IAN (NIL) -8 NIL NIL NIL) (-508 1247942 1248005 1248178 "IALGFACT" 1248374 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1247434 1247583 1247611 "HYPCAT" 1247818 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1246936 1247089 1247275 "HYPCAT-" 1247280 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1246483 1246731 1246814 "HOSTNAME" 1246873 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1246316 1246365 1246406 "HOMOTOP" 1246411 NIL HOMOTOP (NIL T) -9 NIL 1246444 NIL) (-503 1242860 1244248 1244289 "HOAGG" 1245270 NIL HOAGG (NIL T) -9 NIL 1245999 NIL) (-502 1241376 1241853 1242379 "HOAGG-" 1242384 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1234433 1240969 1241119 "HEXADEC" 1241246 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1233145 1233403 1233666 "HEUGCD" 1234210 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1232077 1232982 1233112 "HELLFDIV" 1233117 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1230199 1231852 1231941 "HEAP" 1232020 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1229396 1229751 1229885 "HEADAST" 1230085 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1222848 1229311 1229373 "HDP" 1229378 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1215867 1222483 1222635 "HDMP" 1222749 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1215173 1215331 1215495 "HB" 1215723 T HB (NIL) -7 NIL NIL NIL) (-493 1208297 1215019 1215123 "HASHTBL" 1215128 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1207713 1208018 1208110 "HASAST" 1208225 T HASAST (NIL) -8 NIL NIL NIL) (-491 1205126 1207335 1207517 "HACKPI" 1207551 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1200412 1204979 1205092 "GTSET" 1205097 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1193565 1200290 1200388 "GSTBL" 1200393 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1185328 1192730 1192986 "GSERIES" 1193365 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1184359 1184872 1184900 "GROUP" 1185103 T GROUP (NIL) -9 NIL 1185237 NIL) (-486 1183683 1183884 1184135 "GROUP-" 1184140 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1182032 1182371 1182758 "GROEBSOL" 1183360 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1180860 1181220 1181271 "GRMOD" 1181800 NIL GRMOD (NIL T T) -9 NIL 1181968 NIL) (-483 1180616 1180664 1180792 "GRMOD-" 1180797 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1175756 1176970 1177970 "GRIMAGE" 1179636 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1174150 1174483 1174807 "GRDEF" 1175452 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1173582 1173710 1173851 "GRAY" 1174029 T GRAY (NIL) -7 NIL NIL NIL) (-479 1172659 1173161 1173212 "GRALG" 1173365 NIL GRALG (NIL T T) -9 NIL 1173458 NIL) (-478 1172296 1172393 1172556 "GRALG-" 1172561 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1168891 1171879 1172058 "GPOLSET" 1172202 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1168239 1168302 1168560 "GOSPER" 1168828 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1163809 1164677 1165203 "GMODPOL" 1167938 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1162796 1162998 1163236 "GHENSEL" 1163621 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1156868 1157795 1158815 "GENUPS" 1161880 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1156559 1156616 1156705 "GENUFACT" 1156811 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1155959 1156048 1156213 "GENPGCD" 1156477 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1155427 1155468 1155681 "GENMFACT" 1155918 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1153964 1154250 1154557 "GENEEZ" 1155170 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1147142 1153575 1153737 "GDMP" 1153887 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1135880 1140913 1142019 "GCNAALG" 1146125 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1134007 1135055 1135083 "GCDDOM" 1135338 T GCDDOM (NIL) -9 NIL 1135495 NIL) (-465 1133447 1133604 1133819 "GCDDOM-" 1133824 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1121919 1124393 1126785 "GBINTERN" 1131138 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1119720 1120048 1120469 "GBF" 1121594 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1118477 1118666 1118933 "GBEUCLID" 1119536 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1117127 1117334 1117638 "GB" 1118256 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1116458 1116601 1116750 "GAUSSFAC" 1116998 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1114779 1115127 1115441 "GALUTIL" 1116177 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1113039 1113361 1113685 "GALPOLYU" 1114506 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1110338 1110694 1111101 "GALFACTU" 1112736 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1101952 1103643 1105251 "GALFACT" 1108770 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1099238 1099998 1100026 "FVFUN" 1101182 T FVFUN (NIL) -9 NIL 1101902 NIL) (-454 1098468 1098686 1098714 "FVC" 1099005 T FVC (NIL) -9 NIL 1099188 NIL) (-453 1098069 1098293 1098361 "FUNDESC" 1098420 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1097642 1097866 1097947 "FUNCTION" 1098021 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1096319 1096943 1097146 "FTEM" 1097459 T FTEM (NIL) -8 NIL NIL NIL) (-450 1093949 1094641 1095107 "FT" 1095873 T FT (NIL) -8 NIL NIL NIL) (-449 1092218 1092529 1092926 "FSUPFACT" 1093640 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1090537 1090904 1091236 "FST" 1091906 T FST (NIL) -8 NIL NIL NIL) (-447 1089718 1089842 1090030 "FSRED" 1090419 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1088407 1088673 1089020 "FSPRMELT" 1089433 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1085617 1086151 1086637 "FSPECF" 1087970 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1085139 1085199 1085369 "FSINT" 1085558 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1083275 1084132 1084435 "FSERIES" 1084918 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1082299 1082433 1082657 "FSCINT" 1083155 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1081323 1081484 1081711 "FSAGG2" 1082152 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1077298 1080267 1080308 "FSAGG" 1080678 NIL FSAGG (NIL T) -9 NIL 1080937 NIL) (-439 1074898 1075661 1076457 "FSAGG-" 1076552 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1072558 1072856 1073404 "FS2UPS" 1074616 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1071424 1071607 1071909 "FS2EXPXP" 1072383 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1071052 1071101 1071230 "FS2" 1071375 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1051290 1060826 1060867 "FS" 1064751 NIL FS (NIL T) -9 NIL 1067040 NIL) (-434 1039351 1042926 1046983 "FS-" 1047283 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1038765 1038892 1039044 "FRUTIL" 1039231 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1033276 1036454 1036494 "FRNAALG" 1037814 NIL FRNAALG (NIL T) -9 NIL 1038412 NIL) (-431 1028757 1030025 1031300 "FRNAALG-" 1032050 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1028389 1028438 1028565 "FRNAAF2" 1028708 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1026676 1027238 1027534 "FRMOD" 1028201 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1025861 1025954 1026245 "FRIDEAL2" 1026583 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1023466 1024236 1024554 "FRIDEAL" 1025652 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1022557 1023013 1023054 "FRETRCT" 1023059 NIL FRETRCT (NIL T) -9 NIL 1023235 NIL) (-425 1021615 1021900 1022251 "FRETRCT-" 1022256 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1018436 1019899 1019958 "FRAMALG" 1020840 NIL FRAMALG (NIL T T) -9 NIL 1021132 NIL) (-423 1016474 1017025 1017655 "FRAMALG-" 1017878 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1016104 1016167 1016274 "FRAC2" 1016411 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1009097 1015577 1015854 "FRAC" 1015859 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1008727 1008790 1008897 "FR2" 1009034 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 999644 1004222 1005580 "FR" 1007401 NIL FR (NIL T) -8 NIL NIL NIL) (-418 993563 997023 997051 "FPS" 998170 T FPS (NIL) -9 NIL 998727 NIL) (-417 992988 993121 993285 "FPS-" 993431 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 989954 991945 991973 "FPC" 992198 T FPC (NIL) -9 NIL 992340 NIL) (-415 989735 989787 989884 "FPC-" 989889 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 988493 989223 989264 "FPATMAB" 989269 NIL FPATMAB (NIL T) -9 NIL 989421 NIL) (-413 986636 987235 987582 "FPARFRAC" 988209 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 981928 982528 983210 "FORTRAN" 986068 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 979502 980166 980194 "FORTFN" 981254 T FORTFN (NIL) -9 NIL 981878 NIL) (-410 979254 979316 979344 "FORTCAT" 979403 T FORTCAT (NIL) -9 NIL 979465 NIL) (-409 976940 977470 978009 "FORT" 978735 T FORT (NIL) -7 NIL NIL NIL) (-408 976722 976758 976827 "FORMULA1" 976904 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 974726 975338 975728 "FORMULA" 976352 T FORMULA (NIL) -8 NIL NIL NIL) (-406 974243 974301 974474 "FORDER" 974668 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 973303 973503 973696 "FOP" 974070 T FOP (NIL) -7 NIL NIL NIL) (-404 971716 972583 972757 "FNLA" 973185 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 970335 970846 970874 "FNCAT" 971334 T FNCAT (NIL) -9 NIL 971594 NIL) (-402 969778 970294 970322 "FNAME" 970327 T FNAME (NIL) -8 NIL NIL NIL) (-401 968104 969277 969305 "FMTC" 969310 T FMTC (NIL) -9 NIL 969346 NIL) (-400 966653 968040 968086 "FMONOID" 968091 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 963242 964608 964649 "FMONCAT" 965866 NIL FMONCAT (NIL T) -9 NIL 966471 NIL) (-398 960564 961312 961340 "FMFUN" 962484 T FMFUN (NIL) -9 NIL 963192 NIL) (-397 957437 958489 958543 "FMCAT" 959738 NIL FMCAT (NIL T T) -9 NIL 960233 NIL) (-396 956670 956887 956915 "FMC" 957205 T FMC (NIL) -9 NIL 957387 NIL) (-395 955338 956436 956536 "FM1" 956615 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 954356 955080 955229 "FM" 955234 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 952094 952546 953040 "FLOATRP" 953907 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 949496 950032 950610 "FLOATCP" 951561 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 942159 947225 947846 "FLOAT" 948895 T FLOAT (NIL) -8 NIL NIL NIL) (-390 940677 941751 941792 "FLINEXP" 941797 NIL FLINEXP (NIL T) -9 NIL 941890 NIL) (-389 939807 940066 940394 "FLINEXP-" 940399 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 938865 939027 939251 "FLASORT" 939659 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 935783 936835 936887 "FLALG" 938114 NIL FLALG (NIL T T) -9 NIL 938581 NIL) (-386 934807 934968 935195 "FLAGG2" 935636 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 928176 932216 932257 "FLAGG" 933519 NIL FLAGG (NIL T) -9 NIL 934171 NIL) (-384 926830 927241 927731 "FLAGG-" 927736 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 923468 924675 924734 "FINRALG" 925862 NIL FINRALG (NIL T T) -9 NIL 926370 NIL) (-382 922592 922857 923196 "FINRALG-" 923201 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 921898 922197 922225 "FINITE" 922421 T FINITE (NIL) -9 NIL 922528 NIL) (-380 913849 916428 916468 "FINAALG" 920135 NIL FINAALG (NIL T) -9 NIL 921588 NIL) (-379 908965 910231 911375 "FINAALG-" 912754 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 907525 907947 908001 "FILECAT" 908685 NIL FILECAT (NIL T T) -9 NIL 908901 NIL) (-377 906803 907280 907383 "FILE" 907455 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 904206 906033 906061 "FIELD" 906101 T FIELD (NIL) -9 NIL 906181 NIL) (-375 902748 903211 903722 "FIELD-" 903727 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 900431 901383 901730 "FGROUP" 902434 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 899503 899685 899905 "FGLMICPK" 900263 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 894758 899428 899485 "FFX" 899490 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 894353 894420 894555 "FFSLPE" 894691 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 893851 893893 894102 "FFPOLY2" 894311 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 889727 890623 891419 "FFPOLY" 893087 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 884996 889646 889709 "FFP" 889714 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 879527 884339 884529 "FFNBX" 884850 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 873860 878662 878920 "FFNBP" 879381 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 867898 873144 873355 "FFNB" 873693 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 866718 866928 867243 "FFINTBAS" 867695 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 862311 864965 864993 "FFIELDC" 865613 T FFIELDC (NIL) -9 NIL 865989 NIL) (-362 860931 861372 861855 "FFIELDC-" 861860 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 860488 860546 860670 "FFHOM" 860873 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 858147 858670 859187 "FFF" 860003 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 853182 857889 857990 "FFCGX" 858090 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 848221 852914 853021 "FFCGP" 853125 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 842821 847948 848056 "FFCG" 848157 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 842226 842275 842510 "FFCAT2" 842772 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 820908 831958 832044 "FFCAT" 837209 NIL FFCAT (NIL T T T) -9 NIL 838660 NIL) (-354 815919 817153 818467 "FFCAT-" 819697 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 810740 815830 815894 "FF" 815899 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 799393 803712 804932 "FEXPR" 809592 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 798321 798790 798831 "FEVALAB" 798915 NIL FEVALAB (NIL T) -9 NIL 799176 NIL) (-350 797438 797690 798028 "FEVALAB-" 798033 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 794300 795185 795300 "FDIVCAT" 796868 NIL FDIVCAT (NIL T T T T) -9 NIL 797305 NIL) (-348 794056 794089 794259 "FDIVCAT-" 794264 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 793270 793363 793640 "FDIV2" 793963 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 791680 792653 792856 "FDIV" 793169 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 790588 790975 791177 "FCTRDATA" 791498 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 789244 789533 789822 "FCPAK1" 790319 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 788247 788744 788885 "FCOMP" 789135 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 771561 775397 778935 "FC" 784729 T FC (NIL) -8 NIL NIL NIL) (-341 763270 767882 767922 "FAXF" 769724 NIL FAXF (NIL T) -9 NIL 770416 NIL) (-340 760411 761218 762036 "FAXF-" 762501 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 755094 759787 759963 "FARRAY" 760268 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 749659 752041 752094 "FAMR" 753117 NIL FAMR (NIL T T) -9 NIL 753577 NIL) (-337 748483 748851 749286 "FAMR-" 749291 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 747510 748405 748458 "FAMONOID" 748463 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 745140 745992 746045 "FAMONC" 746986 NIL FAMONC (NIL T T) -9 NIL 747372 NIL) (-334 743614 744894 745031 "FAGROUP" 745036 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 741367 741728 742131 "FACUTIL" 743295 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 740454 740651 740873 "FACTFUNC" 741177 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 732195 739757 739956 "EXPUPXS" 740310 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 729648 730218 730804 "EXPRTUBE" 731629 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 725859 726511 727241 "EXPRODE" 728987 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 720293 721000 721806 "EXPR2UPS" 725157 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 719919 719982 720091 "EXPR2" 720230 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 704227 718568 718997 "EXPR" 719523 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 694565 703378 703669 "EXPEXPAN" 704063 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 693985 694289 694380 "EXITAST" 694494 T EXITAST (NIL) -8 NIL NIL NIL) (-323 693749 693942 693971 "EXIT" 693976 T EXIT (NIL) -8 NIL NIL NIL) (-322 693370 693438 693551 "EVALCYC" 693681 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 692887 693029 693070 "EVALAB" 693240 NIL EVALAB (NIL T) -9 NIL 693344 NIL) (-320 692344 692490 692711 "EVALAB-" 692716 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 689459 691000 691028 "EUCDOM" 691583 T EUCDOM (NIL) -9 NIL 691933 NIL) (-318 687819 688320 688903 "EUCDOM-" 688908 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 687445 687508 687617 "ESTOOLS2" 687756 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 687190 687238 687318 "ESTOOLS1" 687397 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 674507 677488 680238 "ESTOOLS" 684460 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 674246 674284 674366 "ESCONT1" 674469 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 670554 671381 672161 "ESCONT" 673486 T ESCONT (NIL) -7 NIL NIL NIL) (-312 670223 670279 670379 "ES2" 670498 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 669847 669911 670020 "ES1" 670159 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 663548 665478 665506 "ES" 668274 T ES (NIL) -9 NIL 669684 NIL) (-309 658225 659782 661599 "ES-" 661763 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 657417 657570 657746 "ERROR" 658069 T ERROR (NIL) -7 NIL NIL NIL) (-307 650547 657276 657367 "EQTBL" 657372 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 650173 650236 650345 "EQ2" 650484 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 642432 645487 646936 "EQ" 648757 NIL -3420 (NIL T) -8 NIL NIL NIL) (-304 637674 638770 639863 "EP" 641371 NIL EP (NIL T) -7 NIL NIL NIL) (-303 636214 636565 636871 "ENV" 637388 T ENV (NIL) -8 NIL NIL NIL) (-302 635174 635848 635876 "ENTIRER" 635881 T ENTIRER (NIL) -9 NIL 635927 NIL) (-301 631593 633356 633717 "EMR" 634982 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 630697 630908 630962 "ELTAGG" 631342 NIL ELTAGG (NIL T T) -9 NIL 631553 NIL) (-299 630404 630478 630619 "ELTAGG-" 630624 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 630162 630197 630251 "ELTAB" 630335 NIL ELTAB (NIL T T) -9 NIL 630387 NIL) (-297 629264 629434 629633 "ELFUTS" 630013 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 628988 629062 629090 "ELEMFUN" 629195 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 628852 628879 628947 "ELEMFUN-" 628952 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 623377 626894 626935 "ELAGG" 627875 NIL ELAGG (NIL T) -9 NIL 628338 NIL) (-293 621554 622096 622759 "ELAGG-" 622764 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 620836 621003 621159 "ELABOR" 621418 T ELABOR (NIL) -8 NIL NIL NIL) (-291 619442 619776 620070 "ELABEXPR" 620562 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 611954 614079 614908 "EFUPXS" 618717 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 605080 607203 608014 "EFULS" 611229 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 602517 602923 603395 "EFSTRUC" 604712 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 591955 593874 595422 "EF" 601032 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 590933 591440 591589 "EAB" 591826 T EAB (NIL) -8 NIL NIL NIL) (-285 590055 590892 590920 "E04UCFA" 590925 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 589177 590014 590042 "E04NAFA" 590047 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 588299 589136 589164 "E04MBFA" 589169 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 587421 588258 588286 "E04JAFA" 588291 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 586545 587380 587408 "E04GCFA" 587413 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 585669 586504 586532 "E04FDFA" 586537 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 584791 585628 585656 "E04DGFA" 585661 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 578868 580316 581680 "E04AGNT" 583447 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 577488 578169 578209 "DVARCAT" 578550 NIL DVARCAT (NIL T) -9 NIL 578713 NIL) (-276 576638 576904 577218 "DVARCAT-" 577223 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 568606 576437 576566 "DSMP" 576571 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 566957 567748 567789 "DSEXT" 568152 NIL DSEXT (NIL T) -9 NIL 568446 NIL) (-273 565146 565670 566336 "DSEXT-" 566341 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 564805 564870 564968 "DROPT1" 565081 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 559824 561046 562183 "DROPT0" 563688 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 554407 555769 556837 "DROPT" 558776 T DROPT (NIL) -8 NIL NIL NIL) (-269 552716 553077 553463 "DRAWPT" 554041 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 552343 552402 552520 "DRAWHACK" 552657 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 551044 551343 551634 "DRAWCX" 552072 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 550553 550628 550779 "DRAWCURV" 550970 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 540871 542983 545098 "DRAWCFUN" 548458 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 535362 536381 537460 "DRAW" 539845 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 531944 534027 534068 "DQAGG" 534697 NIL DQAGG (NIL T) -9 NIL 534971 NIL) (-262 518527 526155 526238 "DPOLCAT" 528090 NIL DPOLCAT (NIL T T T T) -9 NIL 528635 NIL) (-261 513046 514712 516670 "DPOLCAT-" 516675 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 505968 512907 513005 "DPMO" 513010 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 498787 505748 505915 "DPMM" 505920 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 498309 498571 498660 "DOMTMPLT" 498718 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 497658 498111 498191 "DOMCTOR" 498249 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 496810 497138 497289 "DOMAIN" 497527 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 489829 496445 496597 "DMP" 496711 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 487606 488896 488937 "DMEXT" 488942 NIL DMEXT (NIL T) -9 NIL 489118 NIL) (-253 487200 487262 487406 "DLP" 487544 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 480323 486527 486717 "DLIST" 487042 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 476972 479148 479189 "DLAGG" 479739 NIL DLAGG (NIL T) -9 NIL 479969 NIL) (-250 475484 476298 476326 "DIVRING" 476418 T DIVRING (NIL) -9 NIL 476501 NIL) (-249 474667 474911 475211 "DIVRING-" 475216 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 472709 473126 473532 "DISPLAY" 474281 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 471539 471760 472025 "DIRPROD2" 472502 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 465011 471453 471516 "DIRPROD" 471521 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 453288 459722 459775 "DIRPCAT" 460033 NIL DIRPCAT (NIL NIL T) -9 NIL 460908 NIL) (-244 450488 451256 452137 "DIRPCAT-" 452474 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 449769 449935 450121 "DIOSP" 450322 T DIOSP (NIL) -7 NIL NIL NIL) (-242 446294 448653 448694 "DIOPS" 449128 NIL DIOPS (NIL T) -9 NIL 449357 NIL) (-241 445813 445957 446148 "DIOPS-" 446153 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 444720 445492 445520 "DIFRING" 445525 T DIFRING (NIL) -9 NIL 445547 NIL) (-239 444368 444466 444494 "DIFFSPC" 444613 T DIFFSPC (NIL) -9 NIL 444688 NIL) (-238 443989 444091 444243 "DIFFSPC-" 444248 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 442925 443523 443564 "DIFFMOD" 443569 NIL DIFFMOD (NIL T) -9 NIL 443667 NIL) (-236 442621 442678 442719 "DIFFDOM" 442840 NIL DIFFDOM (NIL T) -9 NIL 442908 NIL) (-235 442468 442498 442582 "DIFFDOM-" 442587 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 440208 441672 441713 "DIFEXT" 441718 NIL DIFEXT (NIL T) -9 NIL 441871 NIL) (-233 437353 439712 439753 "DIAGG" 439758 NIL DIAGG (NIL T) -9 NIL 439778 NIL) (-232 436701 436894 437146 "DIAGG-" 437151 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 431665 435660 435937 "DHMATRIX" 436470 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 427133 428186 429196 "DFSFUN" 430675 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 421374 426064 426376 "DFLOAT" 426841 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 419613 419918 420307 "DFINTTLS" 421082 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 416432 417634 418034 "DERHAM" 419279 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 414082 416207 416296 "DEQUEUE" 416376 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 413324 413469 413652 "DEGRED" 413944 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 409730 410499 411345 "DEFINTRF" 412552 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 407267 407754 408346 "DEFINTEF" 409249 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 406551 406887 407002 "DEFAST" 407172 T DEFAST (NIL) -8 NIL NIL NIL) (-221 399608 406144 406294 "DECIMAL" 406421 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 397066 397578 398084 "DDFACT" 399152 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 396656 396705 396856 "DBLRESP" 397017 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 395857 396426 396517 "DBASIS" 396605 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 393641 394087 394448 "DBASE" 395623 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 392829 393121 393267 "DATAARY" 393540 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 391887 392788 392816 "D03FAFA" 392821 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 390946 391846 391874 "D03EEFA" 391879 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 388872 389362 389851 "D03AGNT" 390477 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 388113 388831 388859 "D02EJFA" 388864 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 387354 388072 388100 "D02CJFA" 388105 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 386595 387313 387341 "D02BHFA" 387346 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 385836 386554 386582 "D02BBFA" 386587 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 378967 380622 382228 "D02AGNT" 384250 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 376717 377258 377804 "D01WGTS" 378441 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 375724 376676 376704 "D01TRNS" 376709 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 374732 375683 375711 "D01GBFA" 375716 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 373740 374691 374719 "D01FCFA" 374724 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 372748 373699 373727 "D01ASFA" 373732 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 371756 372707 372735 "D01AQFA" 372740 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 370764 371715 371743 "D01APFA" 371748 T D01APFA (NIL) -8 NIL NIL NIL) (-200 369772 370723 370751 "D01ANFA" 370756 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 368780 369731 369759 "D01AMFA" 369764 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 367788 368739 368767 "D01ALFA" 368772 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 366796 367747 367775 "D01AKFA" 367780 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 365804 366755 366783 "D01AJFA" 366788 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 359027 360652 362213 "D01AGNT" 364263 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 358346 358492 358644 "CYCLOTOM" 358895 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 355001 355794 356521 "CYCLES" 357639 T CYCLES (NIL) -7 NIL NIL NIL) (-192 354301 354447 354618 "CVMP" 354862 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 352088 352400 352769 "CTRIGMNP" 354029 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 351561 351819 351920 "CTORKIND" 352007 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 350766 351154 351182 "CTORCAT" 351364 T CTORCAT (NIL) -9 NIL 351477 NIL) (-188 350340 350475 350634 "CTORCAT-" 350639 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 349754 350014 350122 "CTORCALL" 350264 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 349112 349548 349621 "CTOR" 349701 T CTOR (NIL) -8 NIL NIL NIL) (-185 348468 348585 348738 "CSTTOOLS" 349009 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 344165 344924 345682 "CRFP" 347780 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 343580 343886 343978 "CRCEAST" 344093 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 342603 342812 343040 "CRAPACK" 343384 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 341983 342088 342292 "CPMATCH" 342479 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 341702 341736 341842 "CPIMA" 341949 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 337960 338722 339441 "COORDSYS" 341037 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 337348 337493 337635 "CONTOUR" 337838 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 332819 335351 335843 "CONTFRAC" 336888 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 332693 332720 332748 "CONDUIT" 332785 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 331647 332321 332349 "COMRING" 332354 T COMRING (NIL) -9 NIL 332406 NIL) (-174 330629 331005 331189 "COMPPROP" 331483 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 330284 330325 330453 "COMPLPAT" 330588 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 329914 329977 330084 "COMPLEX2" 330221 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 318318 329723 329832 "COMPLEX" 329837 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 317639 317778 317938 "COMPILER" 318178 T COMPILER (NIL) -8 NIL NIL NIL) (-169 317351 317392 317490 "COMPFACT" 317598 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 298745 311055 311095 "COMPCAT" 312099 NIL COMPCAT (NIL T) -9 NIL 313447 NIL) (-167 287633 291184 294811 "COMPCAT-" 295167 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 287356 287390 287493 "COMMUPC" 287599 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 287144 287184 287243 "COMMONOP" 287317 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 286666 286948 287023 "COMMAAST" 287089 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 286173 286417 286504 "COMM" 286599 T COMM (NIL) -8 NIL NIL NIL) (-162 285368 285616 285644 "COMBOPC" 285982 T COMBOPC (NIL) -9 NIL 286157 NIL) (-161 284222 284474 284716 "COMBINAT" 285158 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 280565 281253 281880 "COMBF" 283644 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 279227 279681 279916 "COLOR" 280350 T COLOR (NIL) -8 NIL NIL NIL) (-158 278643 278948 279040 "COLONAST" 279155 T COLONAST (NIL) -8 NIL NIL NIL) (-157 278277 278330 278455 "CMPLXRT" 278590 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 277665 277977 278076 "CLLCTAST" 278198 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 273125 274195 275275 "CLIP" 276605 T CLIP (NIL) -7 NIL NIL NIL) (-154 271298 272226 272466 "CLIF" 272952 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 267391 269416 269457 "CLAGG" 270386 NIL CLAGG (NIL T) -9 NIL 270922 NIL) (-152 265735 266270 266853 "CLAGG-" 266858 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 265273 265364 265504 "CINTSLPE" 265644 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 262738 263245 263793 "CHVAR" 264801 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 261778 262452 262480 "CHARZ" 262485 T CHARZ (NIL) -9 NIL 262500 NIL) (-148 261526 261572 261650 "CHARPOL" 261732 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 260444 261150 261178 "CHARNZ" 261239 T CHARNZ (NIL) -9 NIL 261288 NIL) (-146 257388 258498 259027 "CHAR" 259935 T CHAR (NIL) -8 NIL NIL NIL) (-145 257096 257175 257203 "CFCAT" 257314 T CFCAT (NIL) -9 NIL NIL NIL) (-144 256319 256448 256631 "CDEN" 256980 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 252030 255472 255752 "CCLASS" 256059 T CCLASS (NIL) -8 NIL NIL NIL) (-142 251251 251438 251615 "CATEGORY" 251873 T -10 (NIL) -8 NIL NIL NIL) (-141 250746 251170 251218 "CATCTOR" 251223 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 250137 250449 250547 "CATAST" 250668 T CATAST (NIL) -8 NIL NIL NIL) (-139 249553 249858 249950 "CASEAST" 250065 T CASEAST (NIL) -8 NIL NIL NIL) (-138 248649 248809 249030 "CARTEN2" 249400 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 243546 244806 245550 "CARTEN" 247961 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 241676 242696 242953 "CARD" 243309 T CARD (NIL) -8 NIL NIL NIL) (-135 241198 241480 241555 "CAPSLAST" 241621 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 240640 240896 240924 "CACHSET" 241056 T CACHSET (NIL) -9 NIL 241134 NIL) (-133 240030 240418 240446 "CABMON" 240496 T CABMON (NIL) -9 NIL 240552 NIL) (-132 239467 239734 239844 "BYTEORD" 239940 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 234508 238972 239144 "BYTEBUF" 239315 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 233339 234051 234186 "BYTE" 234349 T BYTE (NIL) -8 NIL NIL 234464) (-129 230715 233031 233138 "BTREE" 233265 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 228031 230363 230485 "BTOURN" 230625 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 225249 227473 227514 "BTCAT" 227582 NIL BTCAT (NIL T) -9 NIL 227659 NIL) (-126 224898 224996 225145 "BTCAT-" 225150 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 219901 224144 224172 "BTAGG" 224286 T BTAGG (NIL) -9 NIL 224396 NIL) (-124 219355 219516 219722 "BTAGG-" 219727 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 216205 218633 218848 "BSTREE" 219172 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 215313 215469 215653 "BRILL" 216061 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 211819 214011 214052 "BRAGG" 214701 NIL BRAGG (NIL T) -9 NIL 214959 NIL) (-120 210252 210754 211309 "BRAGG-" 211314 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 202509 209596 209781 "BPADICRT" 210099 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 200525 202446 202491 "BPADIC" 202496 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 200217 200253 200367 "BOUNDZRO" 200489 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 197944 198402 198877 "BOP1" 199775 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 192974 194404 195302 "BOP" 197066 T BOP (NIL) -8 NIL NIL NIL) (-114 191639 192562 192704 "BOOLEAN" 192852 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 191232 191389 191417 "BOOLE" 191528 T BOOLE (NIL) -9 NIL 191609 NIL) (-112 191100 191127 191193 "BOOLE-" 191198 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 190269 190769 190823 "BMODULE" 190828 NIL BMODULE (NIL T T) -9 NIL 190893 NIL) (-110 185704 190067 190140 "BITS" 190216 T BITS (NIL) -8 NIL NIL NIL) (-109 185101 185244 185384 "BINDING" 185584 T BINDING (NIL) -8 NIL NIL NIL) (-108 178161 184696 184845 "BINARY" 184972 T BINARY (NIL) -8 NIL NIL NIL) (-107 175879 177388 177429 "BGAGG" 177689 NIL BGAGG (NIL T) -9 NIL 177826 NIL) (-106 175704 175742 175833 "BGAGG-" 175838 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 174727 175088 175293 "BFUNCT" 175519 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 173397 173595 173883 "BEZOUT" 174551 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 169709 172249 172579 "BBTREE" 173100 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 169292 169388 169416 "BASTYPE" 169593 T BASTYPE (NIL) -9 NIL 169692 NIL) (-101 168950 169049 169184 "BASTYPE-" 169189 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 168372 168460 168612 "BALFACT" 168861 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 167108 167787 167973 "AUTOMOR" 168217 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 166834 166839 166865 "ATTREG" 166870 T ATTREG (NIL) -9 NIL NIL NIL) (-97 164996 165531 165883 "ATTRBUT" 166500 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 164550 164824 164890 "ATTRAST" 164948 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 164050 164199 164225 "ATRIG" 164426 T ATRIG (NIL) -9 NIL NIL NIL) (-94 163847 163900 163987 "ATRIG-" 163992 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 163430 163664 163690 "ASTCAT" 163695 T ASTCAT (NIL) -9 NIL 163725 NIL) (-92 163139 163216 163335 "ASTCAT-" 163340 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 161227 162915 163003 "ASTACK" 163082 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 159716 160029 160394 "ASSOCEQ" 160909 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 158640 159375 159499 "ASP9" 159623 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 157400 158245 158387 "ASP80" 158529 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 157127 157348 157387 "ASP8" 157392 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 155973 156804 156922 "ASP78" 157040 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 154834 155653 155770 "ASP77" 155887 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 153638 154472 154603 "ASP74" 154734 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 152430 153273 153405 "ASP73" 153537 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 151220 152065 152197 "ASP7" 152329 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 150216 151046 151146 "ASP6" 151151 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 149055 149893 150011 "ASP55" 150129 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 147896 148729 148848 "ASP50" 148967 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 146876 147597 147707 "ASP49" 147817 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 145552 146415 146583 "ASP42" 146765 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 144221 145085 145255 "ASP41" 145439 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 143201 143922 144032 "ASP4" 144142 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 142043 142878 142996 "ASP35" 143114 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 141772 141991 142030 "ASP34" 142035 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 141491 141576 141652 "ASP33" 141727 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 140277 141126 141258 "ASP31" 141390 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 140006 140225 140264 "ASP30" 140269 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 139723 139810 139886 "ASP29" 139961 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 139452 139671 139710 "ASP28" 139715 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 139181 139400 139439 "ASP27" 139444 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 138157 138879 138990 "ASP24" 139101 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 137126 137959 138071 "ASP20" 138076 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 135961 136800 136919 "ASP19" 137038 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 135680 135765 135841 "ASP12" 135916 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 134424 135279 135423 "ASP10" 135567 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 133404 134125 134235 "ASP1" 134345 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 131130 133248 133339 "ARRAY2" 133344 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 130144 130335 130556 "ARRAY12" 130953 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 125618 129792 129906 "ARRAY1" 130061 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 119774 121820 121895 "ARR2CAT" 124525 NIL ARR2CAT (NIL T T T) -9 NIL 125283 NIL) (-56 117373 118150 119005 "ARR2CAT-" 119010 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 116624 117000 117125 "ARITY" 117266 T ARITY (NIL) -8 NIL NIL NIL) (-54 115382 115552 115851 "APPRULE" 116460 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115027 115081 115200 "APPLYORE" 115328 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 114281 114428 114585 "ANY1" 114901 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 113581 113874 113994 "ANY" 114179 T ANY (NIL) -8 NIL NIL NIL) (-50 110907 112018 112345 "ANTISYM" 113305 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 110351 110614 110710 "ANON" 110829 T ANON (NIL) -8 NIL NIL NIL) (-48 103514 108890 109344 "AN" 109915 T AN (NIL) -8 NIL NIL NIL) (-47 99177 100786 100837 "AMR" 101585 NIL AMR (NIL T T) -9 NIL 102185 NIL) (-46 98229 98510 98873 "AMR-" 98878 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 81698 98146 98207 "ALIST" 98212 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 77995 81292 81461 "ALGSC" 81616 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 74445 75105 75712 "ALGPKG" 77435 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 73710 73823 74007 "ALGMFACT" 74331 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 69693 70324 70918 "ALGMANIP" 73294 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59053 69319 69469 "ALGFF" 69626 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 58225 58380 58559 "ALGFACT" 58911 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57014 57752 57790 "ALGEBRA" 57795 NIL ALGEBRA (NIL T) -9 NIL 57836 NIL) (-37 56714 56791 56923 "ALGEBRA-" 56928 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 37668 54551 54603 "ALAGG" 54739 NIL ALAGG (NIL T T) -9 NIL 54900 NIL) (-35 37168 37317 37343 "AHYP" 37544 T AHYP (NIL) -9 NIL NIL NIL) (-34 36470 36653 36679 "AGG" 36962 T AGG (NIL) -9 NIL 37151 NIL) (-33 36177 36264 36379 "AGG-" 36384 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 33937 34406 34811 "AF" 35819 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33357 33662 33752 "ADDAST" 33865 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32589 32884 33040 "ACPLOT" 33219 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20153 29521 29559 "ACFS" 30166 NIL ACFS (NIL T) -9 NIL 30405 NIL) (-28 18060 18670 19432 "ACFS-" 19437 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13768 16093 16119 "ACF" 16998 T ACF (NIL) -9 NIL 17411 NIL) (-26 12400 12806 13299 "ACF-" 13304 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11910 12153 12179 "ABELSG" 12271 T ABELSG (NIL) -9 NIL 12336 NIL) (-24 11771 11802 11868 "ABELSG-" 11873 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11040 11387 11413 "ABELMON" 11583 T ABELMON (NIL) -9 NIL 11695 NIL) (-22 10680 10788 10926 "ABELMON-" 10931 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9930 10386 10412 "ABELGRP" 10484 T ABELGRP (NIL) -9 NIL 10559 NIL) (-20 9357 9522 9738 "ABELGRP-" 9743 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8619 8658 "A1AGG" 8663 NIL A1AGG (NIL T) -9 NIL 8703 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 1ef2315f..5480399c 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,370 +1,477 @@ -(733382 . 3514591833) -(((*1 *2 *3) - (-12 (-5 *3 (-663 *4)) (-4 *4 (-872)) (-5 *2 (-663 (-686 *4 *5))) - (-5 *1 (-646 *4 *5 *6)) (-4 *5 (-13 (-175) (-739 (-421 (-560))))) - (-14 *6 (-949))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1097 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-817)) - (-4 *4 (-872)) (-4 *2 (-571))))) -(((*1 *2 *3) - (-12 (-5 *2 (-419 (-1203 *1))) (-5 *1 (-326 *4)) (-5 *3 (-1203 *1)) - (-4 *4 (-466)) (-4 *4 (-571)) (-4 *4 (-1133)))) - ((*1 *2 *3) - (-12 (-4 *1 (-940)) (-5 *2 (-419 (-1203 *1))) (-5 *3 (-1203 *1))))) -(((*1 *2 *1) - (-12 (-4 *1 (-708 *3 *4 *5)) (-4 *3 (-1081)) (-4 *4 (-385 *3)) - (-4 *5 (-385 *3)) (-5 *2 (-114)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1085 *3 *4 *5 *6 *7)) (-4 *5 (-1081)) - (-4 *6 (-245 *4 *5)) (-4 *7 (-245 *3 *5)) (-5 *2 (-114))))) +(733460 . 3514823550) +(((*1 *2 *3 *4 *4) + (-12 (-5 *4 (-114)) (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) + (-4 *8 (-1097 *5 *6 *7)) + (-5 *2 + (-2 (|:| |val| (-663 *8)) + (|:| |towers| (-663 (-1059 *5 *6 *7 *8))))) + (-5 *1 (-1059 *5 *6 *7 *8)) (-5 *3 (-663 *8)))) + ((*1 *2 *3 *4 *4) + (-12 (-5 *4 (-114)) (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) + (-4 *8 (-1097 *5 *6 *7)) + (-5 *2 + (-2 (|:| |val| (-663 *8)) + (|:| |towers| (-663 (-1178 *5 *6 *7 *8))))) + (-5 *1 (-1178 *5 *6 *7 *8)) (-5 *3 (-663 *8))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-1 (-114) *4 *4)) (-4 *4 (-1249)) (-5 *1 (-388 *4 *2)) + (-4 *2 (-13 (-385 *4) (-10 -7 (-6 -4511))))))) +(((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-421 (-560))) (-5 *1 (-315))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-663 *6)) (-5 *4 (-1209)) (-4 *6 (-435 *5)) - (-4 *5 (-1133)) (-5 *2 (-663 (-630 *6))) (-5 *1 (-587 *5 *6))))) + (-12 (-4 *5 (-1133)) (-4 *2 (-928 *5)) (-5 *1 (-714 *5 *2 *3 *4)) + (-4 *3 (-385 *2)) (-4 *4 (-13 (-385 *5) (-10 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+(((*1 *1 *2 *3 *1) + (-12 (-5 *2 (-916 *4)) (-4 *4 (-1133)) (-5 *1 (-914 *4 *3)) + (-4 *3 (-1133))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1299 *3)) (-4 *3 (-1081)) (-5 *1 (-734 *3 *4)) + (-4 *4 (-1275 *3))))) +(((*1 *1) (-5 *1 (-342)))) +(((*1 *2 *2) (-12 (-5 *2 (-949)) (-5 *1 (-1304)))) + ((*1 *2) (-12 (-5 *2 (-949)) (-5 *1 (-1304))))) (((*1 *2 *1) - (-12 (-5 *2 (-888)) (-5 *1 (-1187 *3)) (-4 *3 (-1133)) - (-4 *3 (-1249))))) + (-12 (-4 *1 (-1008 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-817)) + (-4 *5 (-872)) (-4 *6 (-1097 *3 *4 *5)) (-4 *3 (-571)) + (-5 *2 (-114))))) (((*1 *1 *1) (-4 *1 (-34))) ((*1 *1 *1) (-5 *1 (-115))) ((*1 *1 *1) (-5 *1 (-174))) ((*1 *1 *1) (-4 *1 (-559))) ((*1 *1 *1) (-12 (-5 *1 (-916 *2)) (-4 *2 (-1133)))) @@ -1332,53 +2353,36 @@ ((*1 *1 *1) (-12 (-5 *1 (-1172 *2 *3)) (-4 *2 (-13 (-1133) (-34))) (-4 *3 (-13 (-1133) (-34)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1070 (-560))) (-4 *1 (-310)) (-5 *2 (-114)))) - ((*1 *2 *1) (-12 (-4 *1 (-559)) (-5 *2 (-114)))) - ((*1 *2 *1) (-12 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(-1213)) (|:| -3317 (-663 (-342))))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-663 (-342))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-1299 (-721))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -2785 (-663 (-342))))) + (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -3317 (-663 (-342))))) (-4 *1 (-455)))) ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-455)))) ((*1 *1 *2) (-12 (-5 *2 (-663 (-342))) (-4 *1 (-455)))) @@ -2195,7 +3346,7 @@ (-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 (-663 (-2 (|:| -2733 *3) (|:| -4163 *4)))) + (-12 (-5 *2 (-663 (-2 (|:| -3002 *3) (|:| -2002 *4)))) (-4 *3 (-1081)) (-4 *4 (-748)) (-5 *1 (-757 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-560)) (-4 *1 (-785)))) ((*1 *1 *2) @@ -2204,25 +3355,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -1813 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -3918 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| |mdnia| (-2 (|:| |fn| (-326 (-229))) - (|:| -1813 (-663 (-1121 (-866 (-229))))) + (|:| -3918 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-326 (-229))) - (|:| -1813 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) + (|:| -3918 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -1813 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -3918 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *2 *3) (-12 (-5 *2 (-795)) (-5 *1 (-796 *3)) (-4 *3 (-1249)))) @@ -2240,23 +3391,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-229))) (|:| -1852 (-663 (-229))) + (-2 (|:| |fn| (-326 (-229))) (|:| -2560 (-663 (-229))) (|:| |lb| (-663 (-866 (-229)))) 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*6 *7)) (-4 *4 (-872)) (-4 *7 (-980 *2 *5 (-889 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-523 *2 *3)) (-4 *3 (-875)) (-4 *2 (-102)))) @@ -7538,37 +4091,62 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1097 *3 *4 *2)) (-4 *3 (-1081)) (-4 *4 (-817)) (-4 *2 (-872))))) -(((*1 *2 *1) (-12 (-4 *1 (-860 *3)) (-4 *3 (-1133)) (-5 *2 (-55))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-571)) - (-5 *2 - (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-1001 *4 *3)) (-4 *3 (-1275 *4))))) +(((*1 *2) + (-12 (-4 *4 (-175)) (-5 *2 (-1203 (-976 *4))) (-5 *1 (-431 *3 *4)) + (-4 *3 (-432 *4)))) + ((*1 *2) + (-12 (-4 *1 (-432 *3)) (-4 *3 (-175)) (-4 *3 (-376)) + (-5 *2 (-1203 (-976 *3))))) + ((*1 *2) + (-12 (-5 *2 (-1203 (-421 (-976 *3)))) (-5 *1 (-467 *3 *4 *5 *6)) + (-4 *3 (-571)) (-4 *3 (-175)) (-14 *4 (-949)) + (-14 *5 (-663 (-1209))) (-14 *6 (-1299 (-711 *3)))))) +(((*1 *2 *2 *3 *4) + (|partial| -12 (-5 *2 (-663 (-1203 *7))) (-5 *3 (-1203 *7)) + (-4 *7 (-980 *5 *6 *4)) (-4 *5 (-940)) (-4 *6 (-817)) + (-4 *4 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(-5 *2 - (-2 (|:| |minor| (-663 (-949))) (|:| -1945 *3) - (|:| |minors| (-663 (-663 (-949)))) (|:| |ops| (-663 *3)))) - (-5 *1 (-90 *5 *3)) (-5 *4 (-949)) (-4 *3 (-680 *5))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-793)) (-4 *4 (-13 (-1081) (-739 (-421 (-560))))) - (-4 *5 (-872)) (-5 *1 (-1316 *4 *5 *2)) (-4 *2 (-1322 *5 *4))))) -(((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) - (|partial| -12 (-5 *5 (-114)) (-4 *6 (-466)) (-4 *7 (-817)) - (-4 *8 (-872)) (-4 *9 (-1097 *6 *7 *8)) - (-5 *2 - (-2 (|:| -1945 (-663 *9)) (|:| -2680 *4) (|:| |ineq| (-663 *9)))) - (-5 *1 (-1020 *6 *7 *8 *9 *4)) (-5 *3 (-663 *9)) - (-4 *4 (-1103 *6 *7 *8 *9)))) - ((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) - (|partial| -12 (-5 *5 (-114)) (-4 *6 (-466)) (-4 *7 (-817)) - (-4 *8 (-872)) (-4 *9 (-1097 *6 *7 *8)) - (-5 *2 - (-2 (|:| -1945 (-663 *9)) (|:| -2680 *4) (|:| |ineq| (-663 *9)))) - (-5 *1 (-1139 *6 *7 *8 *9 *4)) (-5 *3 (-663 *9)) - (-4 *4 (-1103 *6 *7 *8 *9))))) + (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) + (|:| |xpnt| (-560)))) + (-4 *4 (-13 (-1275 *3) (-571) (-10 -8 (-15 -4077 ($ $ $))))) + (-4 *3 (-571)) (-5 *1 (-1279 *3 *4))))) +(((*1 *2 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1303)))) + ((*1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1303))))) +(((*1 *1 *1) (-12 (-4 *1 (-385 *2)) (-4 *2 (-1249)) (-4 *2 (-872)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 (-114) *3 *3)) (-4 *1 (-385 *3)) (-4 *3 (-1249)))) + ((*1 *2 *2) + (-12 (-5 *2 (-663 (-932 *3))) (-5 *1 (-932 *3)) (-4 *3 (-1133)))) + ((*1 *2 *1 *3) + (-12 (-4 *4 (-1081)) (-4 *5 (-817)) (-4 *3 (-872)) + (-4 *6 (-1097 *4 *5 *3)) + (-5 *2 (-2 (|:| |under| *1) (|:| -4173 *1) (|:| |upper| *1))) + (-4 *1 (-1008 *4 *5 *3 *6))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -1852 (-663 (-229))))) + (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2560 (-663 (-229))))) (-5 *2 (-663 (-1209))) (-5 *1 (-278)))) ((*1 *2 *3) (-12 (-5 *3 (-1203 *7)) (-4 *7 (-980 *6 *4 *5)) (-4 *4 (-817)) @@ -8302,7 +4910,7 @@ (-5 *1 (-981 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-376) - (-10 -8 (-15 -4080 ($ *7)) (-15 -2574 (*7 $)) (-15 -2586 (*7 $))))))) + (-10 -8 (-15 -3903 ($ *7)) (-15 -2841 (*7 $)) (-15 -2854 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-1005 *3 *4 *5)) (-4 *3 (-1081)) (-4 *4 (-816)) (-4 *5 (-872)) (-5 *2 (-663 *5)))) @@ -8312,50 +4920,60 @@ ((*1 *2 *3) (-12 (-5 *3 (-421 (-976 *4))) (-4 *4 (-571)) (-5 *2 (-663 (-1209))) (-5 *1 (-1072 *4))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-663 *1)) (-4 *1 (-1097 *4 *5 *6)) (-4 *4 (-1081)) - (-4 *5 (-817)) (-4 *6 (-872)) (-5 *2 (-114)))) - ((*1 *2 *1 *1) - (-12 (-4 *1 (-1097 *3 *4 *5)) (-4 *3 (-1081)) (-4 *4 (-817)) - (-4 *5 (-872)) (-5 *2 (-114)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1244 *3 *4 *5 *6)) (-4 *3 (-571)) (-4 *4 (-817)) - (-4 *5 (-872)) (-4 *6 (-1097 *3 *4 *5)) (-5 *2 (-114)))) - ((*1 *2 *3 *1) - (-12 (-4 *1 (-1244 *4 *5 *6 *3)) (-4 *4 (-571)) (-4 *5 (-817)) - (-4 *6 (-872)) (-4 *3 (-1097 *4 *5 *6)) (-5 *2 (-114))))) -(((*1 *2 *3) - (-12 (-5 *3 (-663 *2)) (-4 *2 (-435 *4)) (-5 *1 (-160 *4 *2)) - (-4 *4 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*1 (-1170)))) + ((*1 *2 *3) + (-12 (-5 *3 (-663 (-888))) (-5 *2 (-1305)) (-5 *1 (-1170))))) (((*1 *2 *3) - (-12 (-5 *2 (-630 *4)) (-5 *1 (-631 *3 *4)) (-4 *3 (-1133)) - (-4 *4 (-1133))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1275 *5)) (-4 *5 (-376)) - (-5 *2 (-2 (|:| |answer| *3) (|:| |polypart| *3))) - (-5 *1 (-588 *5 *3))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-376)) (-5 *1 (-297 *3 *2)) (-4 *2 (-1292 *3))))) + (-12 (-5 *2 (-663 (-1191))) (-5 *1 (-853)) (-5 *3 (-1191))))) +(((*1 *2 *3) + (-12 (-4 *4 (-466)) + (-5 *2 + (-663 + (-2 (|:| |eigval| (-3 (-421 (-976 *4)) (-1198 (-1209) (-976 *4)))) + (|:| |eigmult| (-793)) + (|:| |eigvec| (-663 (-711 (-421 (-976 *4)))))))) + (-5 *1 (-304 *4)) (-5 *3 (-711 (-421 (-976 *4))))))) +(((*1 *2 *1) + (-12 + (-5 *2 + (-663 + (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *3) + (|:| |xpnt| (-560))))) + (-5 *1 (-419 *3)) (-4 *3 (-571)))) + ((*1 *2 *3 *4 *4 *4) + (-12 (-5 *4 (-793)) (-4 *3 (-363)) (-4 *5 (-1275 *3)) + (-5 *2 (-663 (-1203 *3))) (-5 *1 (-512 *3 *5 *6)) + (-4 *6 (-1275 *5))))) +(((*1 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1034)))))) +(((*1 *2) (-12 (-5 *2 (-1305)) (-5 *1 (-827))))) +(((*1 *2 *2 *3 *4) + (|partial| -12 (-5 *3 (-793)) (-4 *4 (-13 (-571) (-149))) + (-5 *1 (-1271 *4 *2)) (-4 *2 (-1275 *4))))) (((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1203 (-421 (-1203 *2)))) (-5 *4 (-630 *2)) (-4 *2 (-13 (-435 *5) (-27) (-1235))) @@ -8372,45 +4990,56 @@ (-4 *6 (-1081)) (-4 *2 (-13 (-376) - (-10 -8 (-15 -4080 ($ *7)) (-15 -2574 (*7 $)) (-15 -2586 (*7 $))))) + (-10 -8 (-15 -3903 ($ *7)) (-15 -2841 (*7 $)) (-15 -2854 (*7 $))))) (-5 *1 (-981 *5 *4 *6 *7 *2)) (-4 *7 (-980 *6 *5 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-421 (-1203 (-421 (-976 *5))))) (-5 *4 (-1209)) (-5 *2 (-421 (-976 *5))) (-5 *1 (-1072 *5)) (-4 *5 (-571))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1299 (-326 (-229)))) - (-5 *2 - (-2 (|:| |additions| (-560)) (|:| |multiplications| (-560)) - (|:| |exponentiations| (-560)) (|:| |functionCalls| (-560)))) - (-5 *1 (-315))))) +(((*1 *2 *3 *4 *4 *5) + (|partial| -12 (-5 *4 (-630 *3)) (-5 *5 (-663 *3)) + (-4 *3 (-13 (-435 *6) (-27) (-1235))) + (-4 *6 (-13 (-466) (-1070 (-560)) (-149) (-660 (-560)))) + (-5 *2 + (-2 (|:| |mainpart| *3) + (|:| |limitedlogs| + (-663 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (-5 *1 (-580 *6 *3 *7)) (-4 *7 (-1133))))) +(((*1 *2 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-560)) (-5 *1 (-248)))) + ((*1 *2 *3) + (-12 (-5 *3 (-663 (-1191))) (-5 *2 (-560)) (-5 *1 (-248))))) +(((*1 *1 *1 *1 *1) (-4 *1 (-783)))) +(((*1 *2) (-12 (-5 *2 (-1305)) (-5 *1 (-405))))) (((*1 *2 *2) - (-12 (-5 *2 (-1187 *3)) (-4 *3 (-1081)) (-5 *1 (-1193 *3)))) + (|partial| -12 (-4 *3 (-376)) (-4 *4 (-385 *3)) (-4 *5 (-385 *3)) + (-5 *1 (-535 *3 *4 *5 *2)) (-4 *2 (-708 *3 *4 *5)))) + ((*1 *2 *3) + (|partial| -12 (-4 *4 (-571)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4)) + (-4 *7 (-1023 *4)) (-4 *2 (-708 *7 *8 *9)) + (-5 *1 (-536 *4 *5 *6 *3 *7 *8 *9 *2)) (-4 *3 (-708 *4 *5 *6)) + (-4 *8 (-385 *7)) (-4 *9 (-385 *7)))) ((*1 *1 *1) - (-12 (-5 *1 (-1289 *2 *3 *4)) (-4 *2 (-1081)) (-14 *3 (-1209)) - (-14 *4 *2)))) -(((*1 *1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-270)))) - ((*1 *2 *3 *2) - (-12 (-5 *2 (-114)) (-5 *3 (-663 (-270))) (-5 *1 (-271)))) - ((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-481)))) + (|partial| -12 (-4 *1 (-708 *2 *3 *4)) (-4 *2 (-1081)) + (-4 *3 (-385 *2)) (-4 *4 (-385 *2)) (-4 *2 (-376)))) + ((*1 *2 *2) + (|partial| -12 (-4 *3 (-376)) (-4 *3 (-175)) (-4 *4 (-385 *3)) + (-4 *5 (-385 *3)) (-5 *1 (-710 *3 *4 *5 *2)) + (-4 *2 (-708 *3 *4 *5)))) + ((*1 *1 *1) + (|partial| -12 (-5 *1 (-711 *2)) (-4 *2 (-376)) (-4 *2 (-1081)))) + ((*1 *1 *1) + (|partial| -12 (-4 *1 (-1155 *2 *3 *4 *5)) (-4 *3 (-1081)) + (-4 *4 (-245 *2 *3)) (-4 *5 (-245 *2 *3)) (-4 *3 (-376)))) + ((*1 *2 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-872)) (-5 *1 (-1220 *3))))) +(((*1 *2 *2 *1) (-12 (-4 *1 (-1027 *2)) (-4 *2 (-1249))))) +(((*1 *2 *1) (-12 (-4 *1 (-1288 *2)) (-4 *2 (-1249))))) +(((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-481)))) ((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-481))))) -(((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-421 (-560))) (-5 *1 (-315))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1299 *4)) (-4 *4 (-1081)) (-4 *2 (-1275 *4)) - (-5 *1 (-458 *4 *2)))) - ((*1 *2 *3 *2 *4) - (-12 (-5 *2 (-421 (-1203 (-326 *5)))) (-5 *3 (-1299 (-326 *5))) - (-5 *4 (-560)) (-4 *5 (-571)) (-5 *1 (-1162 *5))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) -(((*1 *1) (-12 (-5 *1 (-713 *2)) (-4 *2 (-632 (-888)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-949)) (-5 *2 (-1211 (-421 (-560)))) (-5 *1 (-193))))) -(((*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) - (-12 (-4 *1 (-820 *2)) (-4 *2 (-175)))) - ((*1 *1 *2 *2) - (-12 (-5 *2 (-1028 *3)) (-4 *3 (-175)) (-5 *1 (-822 *3))))) -(((*1 *2 *2 *2 *2 *2 *3) - (-12 (-5 *2 (-711 *4)) (-5 *3 (-793)) (-4 *4 (-1081)) - (-5 *1 (-712 *4))))) +(((*1 *1) (-5 *1 (-450)))) +(((*1 *1 *1) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) +(((*1 *2 *3 *4 *4 *5 *3 *3 *3 *3 *3) + (-12 (-5 *3 (-560)) (-5 *5 (-711 (-229))) (-5 *4 (-229)) + (-5 *2 (-1067)) (-5 *1 (-774))))) (((*1 *1 *2 *3) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1081)) (-4 *3 (-816)))) ((*1 *1 *2 *3) @@ -8418,10 +5047,10 @@ (-4 *2 (-376)) (-14 *5 (-1025 *4 *2)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-735 *5 *6 *7)) (-4 *5 (-872)) - (-4 *6 (-245 (-2172 *4) (-793))) + (-4 *6 (-245 (-2236 *4) (-793))) (-14 *7 - (-1 (-114) (-2 (|:| -3624 *5) (|:| -4403 *6)) - (-2 (|:| -3624 *5) (|:| -4403 *6)))) + (-1 (-114) (-2 (|:| -2183 *5) (|:| -4067 *6)) + (-2 (|:| -2183 *5) (|:| -4067 *6)))) (-14 *4 (-663 (-1209))) (-4 *2 (-175)) (-5 *1 (-475 *4 *2 *5 *6 *7 *8)) (-4 *8 (-980 *2 *6 (-889 *4))))) ((*1 *1 *2 *3) @@ -8451,429 +5080,564 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-1005 *4 *3 *2)) (-4 *4 (-1081)) (-4 *3 (-816)) (-4 *2 (-872))))) -(((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-955))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1231))))) +(((*1 *2 *3 *3) + (-12 (-4 *3 (-319)) (-4 *3 (-175)) (-4 *4 (-385 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-12 (-5 *3 (-711 *6)) (-5 *4 (-1209)) @@ -14981,27 +14798,27 @@ (-5 *5 (-1209)) (-4 *7 (-13 (-29 *6) (-1235) (-990))) (-4 *6 (-13 (-319) (-1070 (-560)) (-660 (-560)) (-149))) (-5 *2 - (-2 (|:| |particular| (-1299 *7)) (|:| -3043 (-663 (-1299 *7))))) + (-2 (|:| |particular| (-1299 *7)) (|:| -4235 (-663 (-1299 *7))))) (-5 *1 (-826 *6 *7)))) ((*1 *2 *3 *4 *5) (|partial| -12 (-5 *3 (-663 *7)) (-5 *4 (-663 (-115))) (-5 *5 (-1209)) (-4 *7 (-13 (-29 *6) (-1235) (-990))) (-4 *6 (-13 (-319) (-1070 (-560)) (-660 (-560)) (-149))) (-5 *2 - (-2 (|:| |particular| (-1299 *7)) (|:| -3043 (-663 (-1299 *7))))) + (-2 (|:| |particular| (-1299 *7)) (|:| -4235 (-663 (-1299 *7))))) (-5 *1 (-826 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-305 *7)) (-5 *4 (-115)) (-5 *5 (-1209)) (-4 *7 (-13 (-29 *6) (-1235) (-990))) (-4 *6 (-13 (-319) (-1070 (-560)) (-660 (-560)) (-149))) (-5 *2 - (-3 (-2 (|:| |particular| *7) (|:| -3043 (-663 *7))) *7 "failed")) + (-3 (-2 (|:| |particular| *7) (|:| -4235 (-663 *7))) *7 "failed")) (-5 *1 (-826 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *4 (-115)) (-5 *5 (-1209)) (-4 *6 (-13 (-319) (-1070 (-560)) (-660 (-560)) (-149))) (-5 *2 - (-3 (-2 (|:| |particular| *3) (|:| -3043 (-663 *3))) *3 "failed")) + (-3 (-2 (|:| |particular| *3) (|:| -4235 (-663 *3))) *3 "failed")) (-5 *1 (-826 *6 *3)) (-4 *3 (-13 (-29 *6) (-1235) (-990))))) ((*1 *2 *3 *4 *3 *5) (|partial| -12 (-5 *3 (-305 *2)) (-5 *4 (-115)) (-5 *5 (-663 *2)) @@ -15037,10 +14854,10 @@ (|partial| -12 (-5 *5 (-1 - (-3 (-2 (|:| |particular| *6) (|:| -3043 (-663 *6))) "failed") + (-3 (-2 (|:| |particular| *6) (|:| -4235 (-663 *6))) "failed") *7 *6)) (-4 *6 (-376)) (-4 *7 (-680 *6)) - (-5 *2 (-2 (|:| |particular| (-1299 *6)) (|:| -3043 (-711 *6)))) + (-5 *2 (-2 (|:| |particular| (-1299 *6)) (|:| -4235 (-711 *6)))) (-5 *1 (-837 *6 *7)) (-5 *3 (-711 *6)) (-5 *4 (-1299 *6)))) ((*1 *2 *3) (-12 (-5 *3 (-926)) (-5 *2 (-1067)) (-5 *1 (-925)))) ((*1 *2 *3 *4) @@ -15113,168 +14930,23 @@ ((*1 *2 *3) (-12 (-4 *4 (-571)) (-5 *2 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+16710,14 @@ (-12 (-5 *3 (-1209)) (-5 *2 (-252 (-1191))) (-5 *1 (-217 *4)) (-4 *4 (-13 (-872) - (-10 -8 (-15 -1480 ((-1191) $ *3)) (-15 -1862 ((-1305) $)) - (-15 -2818 ((-1305) $))))))) + (-10 -8 (-15 -1497 ((-1191) $ *3)) (-15 -1857 ((-1305) $)) + (-15 -4387 ((-1305) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1021)) (-5 *1 (-217 *3)) (-4 *3 (-13 (-872) - (-10 -8 (-15 -1480 ((-1191) $ (-1209))) (-15 -1862 ((-1305) $)) - (-15 -2818 ((-1305) $))))))) + (-10 -8 (-15 -1497 ((-1191) $ (-1209))) (-15 -1857 ((-1305) $)) + (-15 -4387 ((-1305) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-793)) (-5 *1 (-252 *4)) (-4 *4 (-872)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-252 *3)) (-4 *3 (-872)))) @@ -16673,552 +16781,305 @@ (-12 (-5 *2 "rest") (-4 *1 (-1288 *3)) (-4 *3 (-1249)))) ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1288 *2)) (-4 *2 (-1249))))) -(((*1 *1 *1 *1) (-5 *1 (-130))) - ((*1 *1 *1 *1) (-12 (-5 *1 (-1216 *2)) (-14 *2 (-949)))) - ((*1 *1 *1 *1) (-5 *1 (-1255))) ((*1 *1 *1 *1) 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(-4468 . 3690) (-4469 . 3495) + (-4470 . 3344) (-4471 . 3291) (-4472 . 3115) (-4473 . 3012) + (-4474 . 2883) (-4475 . 2787) (-4476 . 2586) (-4477 . 2558) + (-4478 . 2481) (-4479 . 2430) (-4480 . 2348) (-4481 . 1869) + (-4482 . 1750) (-4483 . 1494) (-4484 . 1135) (-4485 . 1003) + (-4486 . 904) (-4487 . 751) (-4488 . 677) (-4489 . 540) (-4490 . 30))
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