diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/ChangeLog | 10 | ||||
| -rw-r--r-- | src/interp/c-util.boot | 44 | ||||
| -rw-r--r-- | src/interp/compiler.boot | 34 | ||||
| -rw-r--r-- | src/interp/wi2.boot | 55 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 636 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1398 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1314 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9002 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 27370 |
9 files changed, 19913 insertions, 19950 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 4e605776..43643d8e 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,15 @@ 2010-04-30 Gabriel Dos Reis <gdr@cs.tamu.edu> + * interp/c-util.boot (getSuccessEnvironment): Move to here from + compiler.boot. + (getInverseEnvironment): Likewise. + * interp/wi2.boot (getSuccessEnvironment): Remove. + (getInverseEnvironment): Likewise. + (corrupted?): Likewise. + (unLet): Likewise. + +2010-04-30 Gabriel Dos Reis <gdr@cs.tamu.edu> + * interp/macros.lisp (|check-subtype|): Return coerced value if can. (|check-union|): Likewise. * interp/compiler.boot (coerceSuperset): Tidy. Generate %Retract diff --git a/src/interp/c-util.boot b/src/interp/c-util.boot index 4df0052f..aeb37a22 100644 --- a/src/interp/c-util.boot +++ b/src/interp/c-util.boot @@ -44,6 +44,8 @@ module c_-util where declareUnusedParameters: (%List,%Code) -> %List registerFunctionReplacement: (%Symbol,%Form) -> %Thing getFunctionReplacement: %Symbol -> %Form + getSuccessEnvironment: (%Form,%Env) -> %Env + getInverseEnvironment: (%Form,%Env) -> %Env --% @@ -384,7 +386,47 @@ makeCommonEnvironment(e,e') == nx>ny => fn(rest x,y,nx-1,ny) nx<ny => fn(x,rest y,nx,ny-1) [x,y] - + +++ Return the lexically leftmost location in an assignment for. +lhsOfAssignment x == + x is ["%LET",lhs,:.] => lhsOfAssignment lhs + x + +getSuccessEnvironment(a,e) == + a is ["is",id,m] => + id := lhsOfAssignment id + IDENTP id and isDomainForm(m,$EmptyEnvironment) => + e:=put(id,"specialCase",m,e) + currentProplist:= getProplist(id,e) + [.,.,e] := T := comp(m,$EmptyMode,e) or return nil -- duplicates compIs + newProplist:= consProplistOf(id,currentProplist,"value",[m,:rest removeEnv T]) + addBinding(id,newProplist,e) + e + a is ["case",x,m] and (x := lhsOfAssignment x) and IDENTP x => + put(x,"condition",[a,:get(x,"condition",e)],e) + a is ["and",:args] => + for form in args repeat + e := getSuccessEnvironment(form,e) + e + a is ["not",a'] => getInverseEnvironment(a',e) + e + +getInverseEnvironment(a,e) == + a is ["case",x,m] and (x := lhsOfAssignment x) and IDENTP x => + --the next two lines are necessary to get 3-branched Unions to work + -- old-style unions, that is + (get(x,"condition",e) is [["OR",:oldpred]]) and member(a,oldpred) => + put(x,"condition",LIST MKPF(delete(a,oldpred),"OR"),e) + getUnionMode(x,e) is ["Union",:l] => + l':= delete(m,l) + for u in l' repeat + if u is ['_:,=m,:.] then l':= delete(u,l') + newpred:= MKPF([["case",x,m'] for m' in l'],"OR") + put(x,"condition",[newpred,:get(x,"condition",e)],e) + e + a is ["not",a'] => getSuccessEnvironment(a',e) + e + printEnv E == for x in E for i in 1.. repeat for y in x for j in 1.. repeat diff --git a/src/interp/compiler.boot b/src/interp/compiler.boot index 74847aaa..2e0beda4 100644 --- a/src/interp/compiler.boot +++ b/src/interp/compiler.boot @@ -1258,40 +1258,6 @@ compPredicate(p,E) == [p',m,E] := comp(p,$Boolean,E) or return nil [p',m,getSuccessEnvironment(p,E),getInverseEnvironment(p,E)] -getSuccessEnvironment(a,e) == - a is ["is",id,m] => - IDENTP id and isDomainForm(m,$EmptyEnvironment) => - e:=put(id,"specialCase",m,e) - currentProplist:= getProplist(id,e) - [.,.,e] := T := comp(m,$EmptyMode,e) or return nil -- duplicates compIs - newProplist:= consProplistOf(id,currentProplist,"value",[m,:rest removeEnv T]) - addBinding(id,newProplist,e) - e - a is ["case",x,m] and IDENTP x => - put(x,"condition",[a,:get(x,"condition",e)],e) - a is ["and",:args] => - for form in args repeat - e := getSuccessEnvironment(form,e) - e - a is ["not",a'] => getInverseEnvironment(a',e) - e - -getInverseEnvironment(a,e) == - a is ["case",x,m] and IDENTP x => - --the next two lines are necessary to get 3-branched Unions to work - -- old-style unions, that is - (get(x,"condition",e) is [["OR",:oldpred]]) and member(a,oldpred) => - put(x,"condition",LIST MKPF(delete(a,oldpred),"OR"),e) - getUnionMode(x,e) is ["Union",:l] => - l':= delete(m,l) - for u in l' repeat - if u is ['_:,=m,:.] then l':= delete(u,l') - newpred:= MKPF([["case",x,m'] for m' in l'],"OR") - put(x,"condition",[newpred,:get(x,"condition",e)],e) - e - a is ["not",a'] => getSuccessEnvironment(a',e) - e - getUnionMode(x,e) == m:= atom x => getmode(x,e) diff --git a/src/interp/wi2.boot b/src/interp/wi2.boot index c66763cf..31983811 100644 --- a/src/interp/wi2.boot +++ b/src/interp/wi2.boot @@ -408,61 +408,6 @@ macroExpand(x,e) == --not worked out yet ['MI,a,macroExpand(b,e)] macroExpandList(x,e) -getSuccessEnvironment(a,e) == - -- the next four lines try to ensure that explicit special-case tests - -- prevent implicit ones from being generated - a is ["has",x,m] => - x := unLet x - IDENTP x and isDomainForm(m,$EmptyEnvironment) => put(x,"specialCase",m,e) - e - a is ["is",id,m] => - id := unLet id - IDENTP id and isDomainForm(m,$EmptyEnvironment) => - e:=put(id,"specialCase",m,e) - currentProplist:= getProplist(id,e) - [.,.,e] := T := comp(m,$EmptyMode,e) or return nil -- duplicates compIs - newProplist:= consProplistOf(id,currentProplist,"value",removeEnv T) - addBinding(id,newProplist,e) - e - a is ["case",x,m] and (x := unLet x) and IDENTP x => - put(x,"condition",[a,:get(x,"condition",e)],e) - e - -getInverseEnvironment(a,E) == - atom a => E - [op,:argl]:= a --- the next five lines try to ensure that explicit special-case tests --- prevent implicit ones from being generated - op="has" => - [x,m]:= argl - x := unLet x - IDENTP x and isDomainForm(m,$EmptyEnvironment) => put(x,"specialCase",m,E) - E - a is ["case",x,m] and (x := unLet x) and IDENTP x => - --the next two lines are necessary to get 3-branched Unions to work - -- old-style unions, that is - if corrupted? get(x,"condition",E) then systemError 'condition - (get(x,"condition",E) is [["OR",:oldpred]]) and member(a,oldpred) => - put(x,"condition",LIST MKPF(delete(a,oldpred),"OR"),E) - getUnionMode(x,E) is ["Union",:l] or systemError 'Union - if corrupted? l then systemError 'list - l':= delete(m,l) - for u in l' repeat - if u is ['_:,=m,:.] then l':= delete(u,l') - newpred:= MKPF([["case",x,m'] for m' in l'],"OR") - put(x,"condition",[newpred,:get(x,"condition",E)],E) - E - -unLet x == - x is ["%LET",u,:.] => unLet u - x - -corrupted? u == - u is [op,:r] => - op in '(WI MI PART) => true - or/[corrupted? x for x in r] - false - --====================================================================== -- From apply.boot --====================================================================== diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index bad57efc..6842726e 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2266417 . 3481463044) +(2266417 . 3481665220) (-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 @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1691) +(-32 R -1653) ((|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 -1047) (QUOTE (-570))))) @@ -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 a1,{}...,{}an."))) NIL NIL -(-40 -1691 UP UPUP -1334) +(-40 -1653 UP UPUP -1936) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2905 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2905 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2905 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2905 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) -(-41 R -1691) +((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2854 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2854 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2854 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2854 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) +(-41 R -1653) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -436) (|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."))) ((-4452 . T) (-4453 . T)) -((-2905 (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2361) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2361) (|devaluate| |#2|))))))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2361) (|devaluate| |#2|))))))) +((-2854 (-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|))))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1691) +(-54 |Base| R -1653) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4453 . T) (-4452 . T)) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-61 -3605) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +(-61 -3635) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -3605) +(-62 -3635) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -3605) +(-63 -3635) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -3605) +(-64 -3635) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -3605) +(-65 -3635) ((|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 -3605) +(-66 -3635) ((|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 -3605) +(-67 -3635) ((|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 -3605) +(-68 -3635) ((|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 -3605) +(-69 -3635) ((|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 -3605) +(-70 -3635) ((|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 -3605) +(-71 -3635) ((|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 -3605) +(-72 -3635) ((|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 -3605) +(-73 -3635) ((|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 -3605) +(-74 -3635) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -3605) +(-77 -3635) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -3605) +(-78 -3635) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -3605) +(-79 -3635) ((|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 -3605) +(-80 -3635) ((|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 -3605) +(-81 -3635) ((|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 -3605) +(-82 -3635) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -3605) +(-83 -3635) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3605) +(-84 -3635) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3605) +(-85 -3635) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -3605) +(-86 -3635) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -3605) +(-87 -3635) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -3605) +(-88 -3635) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -3605) +(-89 -3635) ((|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}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) 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 \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -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."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2905 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2854 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -392,7 +392,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-116 -1691 UP) +(-116 -1653 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 @@ -403,7 +403,7 @@ NIL (-118 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-916))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-117 |#1|) (QUOTE (-1031))) (|HasCategory| (-117 |#1|) (QUOTE (-826))) (-2905 (|HasCategory| (-117 |#1|) (QUOTE (-826))) (|HasCategory| (-117 |#1|) (QUOTE (-856)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-1161))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-235))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-311))) (|HasCategory| (-117 |#1|) (QUOTE (-551))) (|HasCategory| (-117 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((|HasCategory| (-117 |#1|) (QUOTE (-916))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-117 |#1|) (QUOTE (-1031))) (|HasCategory| (-117 |#1|) (QUOTE (-826))) (-2854 (|HasCategory| (-117 |#1|) (QUOTE (-826))) (|HasCategory| (-117 |#1|) (QUOTE (-856)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-1161))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-235))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-311))) (|HasCategory| (-117 |#1|) (QUOTE (-551))) (|HasCategory| (-117 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) (-119 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -419,7 +419,7 @@ NIL (-122 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -439,15 +439,15 @@ NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-129) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4453 . T) (-4452 . T)) -((-2905 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-2905 (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-130) (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109)))) (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) +((-2854 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-2854 (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-130) (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109)))) (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -472,11 +472,11 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4454 "*") . T)) NIL -(-136 |minix| -2590 S T$) +(-136 |minix| -2474 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -2590 R) +(-137 |minix| -2474 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -499,7 +499,7 @@ NIL (-142) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4452 . T) (-4442 . T) (-4453 . T)) -((-2905 (-12 (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) +((-2854 (-12 (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-143 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -524,7 +524,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4449 . T)) NIL -(-149 -1691 UP UPUP) +(-149 -1653 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 @@ -564,7 +564,7 @@ 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 -(-159 R -1691) +(-159 R -1653) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -598,7 +598,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-1011))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4448)) (|HasAttribute| |#2| (QUOTE -4451)) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562)))) (-167 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4445 -2905 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3189 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-4445 -2854 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3171 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-168 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -614,8 +614,8 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4445 -2905 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3189 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . 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T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| 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(|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-916))))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-562)))) (-2854 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasAttribute| |#1| (QUOTE -4448)) (|HasAttribute| |#1| (QUOTE -4451)) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-354))))) (-172 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -1691) +(-190 R -1653) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-217 -1691 UP UPUP R) +(-217 -1653 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 -(-218 -1691 FP) +(-218 -1653 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-219) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2905 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2854 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-220) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -1691) +(-221 R -1653) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -827,18 +827,18 @@ NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-225 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4449 . T)) NIL -(-226 R -1691) +(-226 R -1653) ((|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 (-227) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3181 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3161 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-228) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -847,7 +847,7 @@ NIL (-229 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-230 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL @@ -884,22 +884,22 @@ 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 -(-239 S -2590 R) +(-239 S -2474 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854))) (|HasAttribute| |#3| (QUOTE -4449)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-1109)))) -(-240 -2590 R) +(-240 -2474 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) ((-4446 |has| |#2| (-1058)) (-4447 |has| |#2| (-1058)) (-4449 |has| |#2| (-6 -4449)) ((-4454 "*") |has| |#2| (-174)) (-4452 . T)) NIL -(-241 -2590 A B) +(-241 -2474 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-242 -2590 R) +(-242 -2474 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."))) ((-4446 |has| |#2| (-1058)) (-4447 |has| |#2| (-1058)) (-4449 |has| |#2| (-6 -4449)) ((-4454 "*") |has| |#2| (-174)) (-4452 . T)) -((-2905 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -919,7 +919,7 @@ NIL (-247 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) ((-4453 . T) (-4452 . T)) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-248 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -927,7 +927,7 @@ NIL (-249 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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(|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2854 (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-732))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-2854 (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (-2854 (|HasAttribute| |#3| (QUOTE -4449)) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (-255 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -999,7 +999,7 @@ NIL (-267 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2905 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-268 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1044,11 +1044,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-279 R -1691) +(-279 R -1653) ((|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 -(-280 R -1691) +(-280 R -1653) ((|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 @@ -1100,7 +1100,7 @@ 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 -(-293 S R |Mod| -4380 -2549 |exactQuo|) +(-293 S R |Mod| -1313 -2946 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL @@ -1122,21 +1122,21 @@ NIL NIL (-298 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2361) (|devaluate| |#2|)))))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-300) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-301 -1691 S) +(-301 -1653 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 -(-302 E -1691) +(-302 E -1653) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1184,7 +1184,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-314 -1691) +(-314 -1653) ((|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 @@ -1199,7 +1199,7 @@ NIL (-317 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1031))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (-2905 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1161))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-235))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -313) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -290) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-551))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))) (-2905 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))))) +((|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1031))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (-2854 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1161))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-235))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -313) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -290) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-551))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))) (-2854 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))))) (-318 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1210,9 +1210,9 @@ NIL NIL (-320 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4449 -2905 (-1793 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (-12 (|has| |#1| (-562)) (-2905 (-1793 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (|has| |#1| (-1058)) (|has| |#1| (-479)))) (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 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(-1121)))) (-2854 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-2854 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) +(-321 R -1653) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1223,7 +1223,7 @@ NIL (-323 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2905 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3801) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2905 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -1480) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1768) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3894) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-324 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1255,12 +1255,12 @@ NIL (-331 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4453 . T) (-4452 . T)) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) -(-332 S -1691) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +(-332 S -1653) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-373)))) -(-333 -1691) +(-333 -1653) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL @@ -1284,15 +1284,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-339 S -1691 UP UPUP R) +(-339 S -1653 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-340 -1691 UP UPUP R) +(-340 -1653 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-341 -1691 UP UPUP R) +(-341 -1653 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1312,26 +1312,26 @@ NIL ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-346 S -1691 UP UPUP) +(-346 S -1653 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(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 (-373))) (|HasCategory| |#2| (QUOTE (-368)))) -(-347 -1691 UP UPUP) +(-347 -1653 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-348 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2905 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) +((-2854 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-349 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2905 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2854 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-350 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2905 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2854 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-351 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1348,31 +1348,31 @@ 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|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-355 R UP -1691) +(-355 R UP -1653) ((|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 (-356 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2905 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) +((-2854 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-357 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2905 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2854 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-358 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2905 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2854 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-359 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2905 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) +((-2854 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-360 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2905 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) -(-361 -1691 GF) +((-2854 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +(-361 -1653 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL @@ -1380,14 +1380,14 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-363 -1691 FP FPP) +(-363 -1653 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}\\spad{'s} exists."))) NIL NIL (-364 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2905 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2854 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-365 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1466,7 +1466,7 @@ NIL NIL (-384) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4435 . T) (-4443 . T) (-3181 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-4435 . T) (-4443 . T) (-3161 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-385 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1520,7 +1520,7 @@ 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 -(-398 -1691 UP UPUP R) +(-398 -1653 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 @@ -1544,11 +1544,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) NIL NIL -(-404 -3605 |returnType| -1445 |symbols|) +(-404 -3635 |returnType| -4400 |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 -(-405 -1691 UP) +(-405 -1653 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1570,7 +1570,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4435)) (|HasAttribute| |#1| (QUOTE -4443))) (-410) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-3181 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3161 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-411 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1583,7 +1583,7 @@ NIL (-413 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4439 -12 (|has| |#1| (-6 -4450)) (|has| |#1| (-458)) (|has| |#1| (-6 -4439))) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-2905 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2905 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-2905 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-551))) (-12 (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#1| (QUOTE -4439)) (|HasCategory| |#1| (QUOTE (-458)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-2854 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-551))) (-12 (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#1| (QUOTE -4439)) (|HasCategory| |#1| (QUOTE (-458)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-414 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1604,11 +1604,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-419 R -1691 UP A) +(-419 R -1653 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4449 . T)) NIL -(-420 R -1691 UP A |ibasis|) +(-420 R -1653 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 -1047) (|devaluate| |#2|)))) @@ -1627,7 +1627,7 @@ NIL (-424 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -313) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1231))) (-2905 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-1231)))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (-2905 (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-458)))) +((|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -313) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1231))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-1231)))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-458)))) (-425 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL @@ -1656,7 +1656,7 @@ NIL ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4452 . T) (-4442 . T) (-4453 . T)) NIL -(-432 R -1691) +(-432 R -1653) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1664,7 +1664,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4439 -12 (|has| |#1| (-6 -4439)) (|has| |#2| (-6 -4439))) (-4446 . T) (-4447 . T) (-4449 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4439)) (|HasAttribute| |#2| (QUOTE -4439)))) -(-434 R -1691) +(-434 R -1653) ((|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 @@ -1674,17 +1674,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (-436 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4449 -2905 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-562)) (-4444 |has| |#1| (-562))) +((-4449 -2854 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-562)) (-4444 |has| |#1| (-562))) NIL -(-437 R -1691) +(-437 R -1653) ((|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 -(-438 R -1691) +(-438 R -1653) ((|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 a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-439 R -1691) +(-439 R -1653) ((|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 @@ -1692,7 +1692,7 @@ 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 -(-441 R -1691 UP) +(-441 R -1653 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 -1047) (QUOTE (-48))))) @@ -1724,7 +1724,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-449 R UP -1691) +(-449 R UP -1653) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1771,7 +1771,7 @@ NIL (-460 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-2905 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2905 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2905 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2905 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2905 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (-2854 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2854 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-461 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1836,7 +1836,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-477 |lv| -1691 R) +(-477 |lv| -1653 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 @@ -1851,11 +1851,11 @@ NIL (-480 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . 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((-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2361) (|devaluate| |#2|)))))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109)))) (-482 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4453 . T) (-4452 . T)) @@ -1871,7 +1871,7 @@ NIL (-485 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2361) (|devaluate| |#2|)))))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-486) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1879,11 +1879,11 @@ NIL (-487 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . 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(QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2854 (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasAttribute| |#2| (QUOTE -4449)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))))) (-489) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL @@ -1891,8 +1891,8 @@ NIL (-490 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-491 -1691 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +(-491 -1653 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1903,7 +1903,7 @@ NIL (-493) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2905 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2854 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-494 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1928,7 +1928,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-500 -1691 UP |AlExt| |AlPol|) +(-500 -1653 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL @@ -1939,16 +1939,16 @@ NIL (-502 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4453 . T) (-4452 . T)) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-503 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-504 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) NIL NIL -(-505 R UP -1691) +(-505 R UP -1653) ((|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 \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1968,7 +1968,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-510 -1691 |Expon| |VarSet| |DPoly|) +(-510 -1653 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-1186))))) @@ -2019,7 +2019,7 @@ NIL (-522 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4453 . T) (-4452 . T)) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-523) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -2027,15 +2027,15 @@ NIL (-524 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2905 (|HasCategory| (-587 |#1|) (QUOTE (-146))) (|HasCategory| (-587 |#1|) (QUOTE (-373)))) (|HasCategory| (-587 |#1|) (QUOTE (-148))) (|HasCategory| (-587 |#1|) (QUOTE (-373))) (|HasCategory| (-587 |#1|) (QUOTE (-146)))) +((-2854 (|HasCategory| (-587 |#1|) (QUOTE (-146))) (|HasCategory| (-587 |#1|) (QUOTE (-373)))) (|HasCategory| (-587 |#1|) (QUOTE (-148))) (|HasCategory| (-587 |#1|) (QUOTE (-373))) (|HasCategory| (-587 |#1|) (QUOTE (-146)))) (-525 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-526 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4453 . T) (-4452 . T)) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-527 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2047,7 +2047,7 @@ NIL (-529 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-530) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2080,7 +2080,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-538 K -1691 |Par|) +(-538 K -1653 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2104,7 +2104,7 @@ 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 -(-544 K -1691 |Par|) +(-544 K -1653 |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 @@ -2155,12 +2155,12 @@ NIL (-556 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2361) (|devaluate| |#2|)))))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) -(-557 R -1691) +((-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +(-557 R -1653) ((|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 -(-558 R0 -1691 UP UPUP R) +(-558 R0 -1653 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 @@ -2170,7 +2170,7 @@ NIL NIL (-560 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-3181 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3161 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-561 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2180,7 +2180,7 @@ 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."))) ((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-563 R -1691) +(-563 R -1653) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2192,7 +2192,7 @@ 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 -(-566 R -1691 L) +(-566 R -1653 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}\\spad{'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}\\spad{'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 -662) (|devaluate| |#2|)))) @@ -2200,11 +2200,11 @@ 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 -(-568 -1691 UP UPUP R) +(-568 -1653 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 -(-569 -1691 UP) +(-569 -1653 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 @@ -2216,15 +2216,15 @@ 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,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-572 R -1691 L) +(-572 R -1653 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}\\spad{'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 -662) (|devaluate| |#2|)))) -(-573 R -1691) +(-573 R -1653) ((|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 -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1148)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-635))))) -(-574 -1691 UP) +(-574 -1653 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}\\spad{'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 @@ -2232,27 +2232,27 @@ 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 -(-576 -1691) +(-576 -1653) ((|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}\\spad{'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 (-577 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-3181 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3161 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-578) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-579 R -1691) +(-579 R -1653) ((|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 -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-288))) (|HasCategory| |#2| (QUOTE (-635))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-288)))) (|HasCategory| |#1| (QUOTE (-562)))) -(-580 -1691 UP) +(-580 -1653 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 -(-581 R -1691) +(-581 R -1653) ((|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 @@ -2284,11 +2284,11 @@ 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 -(-589 R -1691) +(-589 R -1653) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-590 E -1691) +(-590 E -1653) ((|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 @@ -2296,7 +2296,7 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-592 -1691) +(-592 -1653) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) ((-4447 . T) (-4446 . T)) ((|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186))))) @@ -2327,7 +2327,7 @@ NIL (-599 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4453 . T) (-4452 . T)) -((-2905 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-2905 (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) +((-2854 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-2854 (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-600 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL @@ -2335,7 +2335,7 @@ NIL (-601 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))) (|HasCategory| (-570) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3801) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))) (|HasCategory| (-570) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570)))))) (-602 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) (((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) @@ -2352,7 +2352,7 @@ 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 -(-606 R -1691 FG) +(-606 R -1653 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{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 @@ -2363,7 +2363,7 @@ NIL (-608 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4453 . T) (-4452 . T)) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-609 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2382,12 +2382,12 @@ NIL NIL (-613 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4449 -2905 (-1793 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) -((-2905 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) +((-4449 -2854 (-1754 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) +((-2854 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-614 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2361) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-615 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL @@ -2412,7 +2412,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-621 -1691 UP) +(-621 -1653 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2440,7 +2440,7 @@ NIL ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-854)))) -(-628 R -1691) +(-628 R -1653) ((|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 @@ -2472,18 +2472,18 @@ 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 -(-636 R -1691) +(-636 R -1653) ((|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 -(-637 |lv| -1691) +(-637 |lv| -1653) ((|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 (-638) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|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."))) ((-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2361) (QUOTE (-52))))))) (-2905 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2905 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2905 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2361 (-52))) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2254) (QUOTE (-52))))))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (QUOTE (-1109)))) (-639 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2494,8 +2494,8 @@ NIL NIL (-641 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4449 -2905 (-1793 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) -((-2905 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) +((-4449 -2854 (-1754 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) +((-2854 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-642 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL @@ -2507,7 +2507,7 @@ NIL (-644 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-1780 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) +((-1741 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) (-645 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4449 . T)) @@ -2531,7 +2531,7 @@ NIL (-650 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) ((-4453 . T) (-4452 . T)) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-651 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2543,7 +2543,7 @@ NIL (-653 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-654 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL @@ -2560,7 +2560,7 @@ NIL ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-658 R -1691 L) +(-658 R -1653 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 @@ -2580,11 +2580,11 @@ 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}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-663 -1691 UP) +(-663 -1653 UP) ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a, zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-664 A -2108) +(-664 A -3906) ((|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}}"))) ((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) @@ -2620,11 +2620,11 @@ 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}."))) ((-4453 . T) (-4452 . T)) NIL -(-673 -1691) +(-673 -1653) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-674 -1691 |Row| |Col| M) +(-674 -1653 |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 @@ -2635,7 +2635,7 @@ NIL (-676 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4449 . T) (-4452 . T) (-4446 . T) (-4447 . T)) -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2905 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562))) (-2905 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562))) (-2854 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-677) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2655,7 +2655,7 @@ NIL (-681 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 -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-682) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2711,7 +2711,7 @@ NIL (-695 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) ((-4452 . T) (-4453 . T)) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-696 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2720,7 +2720,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-698 S -1691 FLAF FLAS) +(-698 S -1653 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2730,8 +2730,8 @@ NIL NIL (-700) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4445 . T) (-4450 |has| (-705) (-368)) (-4444 |has| (-705) (-368)) (-3189 . T) (-4451 |has| (-705) (-6 -4451)) (-4448 |has| (-705) (-6 -4448)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-705) (QUOTE (-148))) (|HasCategory| (-705) (QUOTE (-146))) (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-373))) (|HasCategory| (-705) (QUOTE (-368))) (-2905 (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-235))) (-2905 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (LIST (QUOTE -290) (QUOTE (-705)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -313) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2905 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-705) (QUOTE (-1031))) (|HasCategory| (-705) (QUOTE (-1212))) (-12 (|HasCategory| (-705) (QUOTE (-1011))) (|HasCategory| (-705) (QUOTE (-1212)))) (-2905 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-2905 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (|HasCategory| (-705) (QUOTE (-551))) (-12 (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-1212)))) (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916))) (-2905 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-2905 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-562)))) (-12 (|HasCategory| (-705) (QUOTE (-235))) (|HasCategory| (-705) (QUOTE (-368)))) (-12 (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-562))) (|HasAttribute| (-705) (QUOTE -4451)) (|HasAttribute| (-705) (QUOTE -4448)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-354))))) +((-4445 . T) (-4450 |has| (-705) (-368)) (-4444 |has| (-705) (-368)) (-3171 . T) (-4451 |has| (-705) (-6 -4451)) (-4448 |has| (-705) (-6 -4448)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| (-705) (QUOTE (-148))) (|HasCategory| (-705) (QUOTE (-146))) (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-373))) (|HasCategory| (-705) (QUOTE (-368))) (-2854 (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-235))) (-2854 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (LIST (QUOTE -290) (QUOTE (-705)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -313) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2854 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-705) (QUOTE (-1031))) (|HasCategory| (-705) (QUOTE (-1212))) (-12 (|HasCategory| (-705) (QUOTE (-1011))) (|HasCategory| (-705) (QUOTE (-1212)))) (-2854 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-2854 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (|HasCategory| (-705) (QUOTE (-551))) (-12 (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-1212)))) (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916))) (-2854 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-2854 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-562)))) (-12 (|HasCategory| (-705) (QUOTE (-235))) (|HasCategory| (-705) (QUOTE (-368)))) (-12 (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-562))) (|HasAttribute| (-705) (QUOTE -4451)) (|HasAttribute| (-705) (QUOTE -4448)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-354))))) (-701 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) ((-4453 . T)) @@ -2744,13 +2744,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-704 OV E -1691 PG) +(-704 OV E -1653 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL (-705) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-3181 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3161 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-706 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2776,7 +2776,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-712 S -2956 I) +(-712 S -2910 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2796,14 +2796,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-717 R |Mod| -4380 -2549 |exactQuo|) +(-717 R |Mod| -1313 -2946 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-718 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4448 |has| |#1| (-368)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2905 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-719 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2812,7 +2812,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-721 R |Mod| -4380 -2549 |exactQuo|) +(-721 R |Mod| -1313 -2946 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4449 . T)) NIL @@ -2824,7 +2824,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4447 . T) (-4446 . T)) NIL -(-724 -1691) +(-724 -1653) ((|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]]}."))) ((-4449 . T)) NIL @@ -2860,7 +2860,7 @@ 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 -(-733 -1691 UP) +(-733 -1653 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 @@ -2879,7 +2879,7 @@ NIL (-737 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-2905 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2905 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2905 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2905 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2905 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (-2854 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2854 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-738 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -3012,11 +3012,11 @@ 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 -(-771 -1691) +(-771 -1653) ((|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 -(-772 P -1691) +(-772 P -1653) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -3024,7 +3024,7 @@ NIL NIL NIL NIL -(-774 UP -1691) +(-774 UP -1653) ((|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 @@ -3040,7 +3040,7 @@ 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."))) (((-4454 "*") . T)) NIL -(-778 R -1691) +(-778 R -1653) ((|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 @@ -3060,7 +3060,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-783 -1691 |ExtF| |SUEx| |ExtP| |n|) +(-783 -1653 |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 @@ -3075,7 +3075,7 @@ NIL (-786 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . 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(-570))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1741 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570))))) (-1741 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1741 (|HasCategory| |#1| (LIST (QUOTE -1001) (QUOTE (-570))))))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-787 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 @@ -3083,7 +3083,7 @@ NIL (-788 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4448 |has| |#1| (-368)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL @@ -3144,23 +3144,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-804 -2905 R OS S) +(-804 -2854 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-805 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-2905 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2905 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-2854 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2854 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (-806) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-807 R -1691 L) +(-807 R -1653 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}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-808 R -1691) +(-808 R -1653) ((|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 @@ -3168,7 +3168,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-810 R -1691) +(-810 R -1653) ((|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 @@ -3176,11 +3176,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-812 -1691 UP UPUP R) +(-812 -1653 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 -(-813 -1691 UP L LQ) +(-813 -1653 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3188,38 +3188,38 @@ 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 -(-815 -1691 UP L LQ) +(-815 -1653 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}\\spad{'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)}\\spad{'s} such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int 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 \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-816 -1691 UP) +(-816 -1653 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-817 -1691 L UP A LO) +(-817 -1653 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 -(-818 -1691 UP) +(-818 -1653 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int 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)))) -(-819 -1691 LO) +(-819 -1653 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}.") 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2905 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-823 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4454 "*") |has| |#2| (-368)) (-4445 |has| |#2| (-368)) (-4450 |has| |#2| (-368)) (-4444 |has| |#2| (-368)) (-4449 . T) (-4447 . T) (-4446 . T)) @@ -3287,7 +3287,7 @@ NIL (-839 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) ((-4449 |has| |#1| (-854))) -((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2905 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2905 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) +((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2854 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2854 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) (-840 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL @@ -3327,12 +3327,12 @@ NIL (-849 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4449 |has| |#1| (-854))) -((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2905 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2905 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) +((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2854 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2854 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) (-850) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-851 -2590 S) +(-851 -2474 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 @@ -3368,11 +3368,11 @@ 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{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) -(-860 R |sigma| -3256) +(-860 R |sigma| -2783) ((|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."))) ((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) -(-861 |x| R |sigma| -3256) +(-861 |x| R |sigma| -2783) ((|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}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-368)))) @@ -3439,15 +3439,15 @@ NIL (-877 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-876 |#1|) (QUOTE (-916))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-148))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-876 |#1|) (QUOTE (-1031))) (|HasCategory| (-876 |#1|) (QUOTE (-826))) (-2905 (|HasCategory| (-876 |#1|) (QUOTE (-826))) (|HasCategory| (-876 |#1|) (QUOTE (-856)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-1161))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-235))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -876) (|devaluate| |#1|)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (QUOTE (-311))) (|HasCategory| (-876 |#1|) (QUOTE (-551))) (|HasCategory| (-876 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))))) +((|HasCategory| (-876 |#1|) (QUOTE (-916))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-148))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-876 |#1|) (QUOTE (-1031))) (|HasCategory| (-876 |#1|) (QUOTE (-826))) (-2854 (|HasCategory| (-876 |#1|) (QUOTE (-826))) (|HasCategory| (-876 |#1|) (QUOTE (-856)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-1161))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-235))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -876) (|devaluate| |#1|)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (QUOTE (-311))) (|HasCategory| (-876 |#1|) (QUOTE (-551))) (|HasCategory| (-876 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))))) (-878 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-826))) (-2905 (|HasCategory| |#2| (QUOTE (-826))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-826))) (-2854 (|HasCategory| |#2| (QUOTE (-826))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-879 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-880) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3507,7 +3507,7 @@ NIL (-894 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,...,vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,...,en], pat)} matches the pattern pat on the list of expressions \\spad{[e1,...,en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,...,en], pat)} tests if the list of expressions \\spad{[e1,...,en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr, pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-1780 (|HasCategory| |#2| (QUOTE (-1058)))) (-1780 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-1780 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) +((-12 (-1741 (|HasCategory| |#2| (QUOTE (-1058)))) (-1741 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-1741 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-895 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3516,7 +3516,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-897 R -2956) +(-897 R -2910) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3540,7 +3540,7 @@ 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 -(-903 UP -1691) +(-903 UP -1653) ((|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 @@ -3563,7 +3563,7 @@ NIL (-908 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-909 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3579,7 +3579,7 @@ NIL (-912 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4449 . T)) -((-2905 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) +((-2854 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (-913 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3600,7 +3600,7 @@ NIL ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-373)))) -(-918 R0 -1691 UP UPUP R) +(-918 R0 -1653 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 @@ -3628,7 +3628,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(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 -(-925 -1691) +(-925 -1653) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3644,11 +3644,11 @@ NIL ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) (((-4454 "*") . T)) NIL -(-929 -1691 P) +(-929 -1653 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-930 |xx| -1691) +(-930 |xx| -1653) ((|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 @@ -3672,7 +3672,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-936 R -1691) +(-936 R -1653) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3684,7 +3684,7 @@ 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 -(-939 S R -1691) +(-939 S R -1653) ((|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 @@ -3704,11 +3704,11 @@ 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 -893) (|devaluate| |#1|)))) -(-944 R -1691 -2956) +(-944 R -1653 -2910) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-945 -2956) +(-945 -2910) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3731,7 +3731,7 @@ NIL (-950 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4453 . T) (-4452 . T)) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-951 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3756,7 +3756,7 @@ 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 \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL -(-957 E V R P -1691) +(-957 E V R P -1653) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3767,8 +3767,8 @@ NIL (-959 R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2905 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-960 E V R P -1691) +((|HasCategory| |#1| (QUOTE (-916))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-960 E V R P -1653) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-458)))) @@ -3791,12 +3791,12 @@ NIL (-965 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4453 . T) (-4452 . T)) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-966) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-967 -1691) +(-967 -1653) ((|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}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3811,11 +3811,11 @@ NIL (-970 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2905 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4450))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4450))) (-971 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented"))) ((-4449 -12 (|has| |#2| (-479)) (|has| |#1| (-479)))) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-972) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3904,7 +3904,7 @@ 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 -(-994 K R UP -1691) +(-994 K R UP -1653) ((|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 @@ -3963,11 +3963,11 @@ NIL (-1008 R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) ((-4445 |has| |#1| (-294)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368))) (-2905 (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2905 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551)))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551)))) (-1009 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,y,...,z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1010 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3976,14 +3976,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1012 -1691 UP UPUP |radicnd| |n|) +(-1012 -1653 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2905 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2905 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2905 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2905 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) +((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2854 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2854 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2854 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2854 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) (-1013 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,3,4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,1,4,2,8,5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2905 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2854 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-1014) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -4016,19 +4016,19 @@ 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} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4445 . T) (-4450 . T) (-4444 . T) (-4447 . T) (-4446 . T) ((-4454 "*") . T) (-4449 . T)) NIL -(-1022 R -1691) +(-1022 R -1653) ((|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 -(-1023 R -1691) +(-1023 R -1653) ((|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 -(-1024 -1691 UP) +(-1024 -1653 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 -(-1025 -1691 UP) +(-1025 -1653 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 @@ -4063,8 +4063,8 @@ NIL (-1033 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) ((-4445 . T) (-4450 . T) (-4444 . T) (-4447 . T) (-4446 . T) ((-4454 "*") . T) (-4449 . T)) -((-2905 (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570))))) -(-1034 -1691 L) +((-2854 (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570))))) +(-1034 -1653 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 @@ -4100,14 +4100,14 @@ 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 -(-1043 -1691 |Expon| |VarSet| |FPol| |LFPol|) +(-1043 -1653 |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"))) (((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1044) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2361) (QUOTE (-52))))))) (-2905 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2905 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2905 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2254) (QUOTE (-52))))))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1045) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4164,7 +4164,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4449 . T)) NIL -(-1059 |xx| -1691) +(-1059 |xx| -1653) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4183,7 +4183,7 @@ NIL (-1063 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4452 . T) (-4447 . T) (-4446 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-2905 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868))))) +((|HasCategory| |#3| (QUOTE (-174))) (-2854 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868))))) (-1064 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4219,7 +4219,7 @@ NIL (-1072) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2361) (QUOTE (-52))))))) (-2905 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2905 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2905 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2254) (QUOTE (-52))))))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1073 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -4268,11 +4268,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1085 |Base| R -1691) +(-1085 |Base| R -1653) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-1086 |Base| R -1691) +(-1086 |Base| R -1653) ((|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 @@ -4287,7 +4287,7 @@ NIL (-1089 R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) ((-4445 |has| |#1| (-368)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2905 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2905 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368))))) (-1090 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4315,7 +4315,7 @@ NIL (-1096 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2905 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1097 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4375,7 +4375,7 @@ NIL (-1111 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) ((-4452 . T) (-4442 . T) (-4453 . T)) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-1112 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) 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(QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2854 (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (|HasAttribute| |#3| (QUOTE -4449)) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (-1123 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4428,7 +4428,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1125 R -1691) +(-1125 R -1653) ((|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 @@ -4467,16 +4467,16 @@ NIL (-1134 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2905 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1135 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) (-1136 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) ((-4453 . T) (-4452 . T)) NIL -(-1137 UP -1691) +(-1137 UP -1653) ((|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 @@ -4531,11 +4531,11 @@ NIL (-1150 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-2905 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-2854 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) (-1151 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4449 . T) (-4441 |has| |#2| (-6 (-4454 "*"))) (-4452 . T) (-4446 . T) (-4447 . T)) -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2905 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (-2905 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (-2854 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-1152 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4555,7 +4555,7 @@ NIL (-1156 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,y,...,z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1157 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4567,7 +4567,7 @@ NIL (-1159 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2361) (|devaluate| |#2|)))))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109)))) (-1160) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4595,7 +4595,7 @@ NIL (-1166 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1167) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4453 . T) (-4452 . T)) @@ -4603,11 +4603,11 @@ NIL (-1168) NIL ((-4453 . T) (-4452 . 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(|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4638,9 +4638,9 @@ NIL NIL (-1177 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4454 "*") -2905 (-1793 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-174)) (-1793 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-916)))) (-4445 -2905 (-1793 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-562)) (-1793 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . 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-899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1183 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2905 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3801) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2905 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -1480) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1768) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3894) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1184 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3801) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2905 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -1480) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1768) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3894) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1185) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4683,7 +4683,7 @@ NIL (-1188 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4446 . T) (-4447 . T) (-4449 . 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(|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4727,7 +4727,7 @@ NIL (-1199 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2361) (|devaluate| |#2|)))))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2905 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-1200 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL @@ -4783,7 +4783,7 @@ NIL (-1213 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4453 . T) (-4452 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1214 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4792,7 +4792,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1216 R -1691) +(-1216 R -1653) ((|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 @@ -4800,7 +4800,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1218 R -1691) +(-1218 R -1653) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -893) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -893) (|devaluate| |#1|))))) @@ -4815,7 +4815,7 @@ NIL (-1221 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) (-1222 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) 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(|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4828,7 +4828,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-1225 -1691) +(-1225 -1653) ((|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.")) 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(LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2854 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1242 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 @@ -4931,7 +4931,7 @@ NIL (-1250 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4448 |has| |#2| (-368)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2905 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2905 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2905 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2905 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2905 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2905 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2854 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2854 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-1251 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4947,7 +4947,7 @@ NIL (-1254 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3801) (LIST (|devaluate| |#2|) (QUOTE (-1186)))))) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3838) (LIST (|devaluate| |#2|) (QUOTE (-1186)))))) (-1255 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|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."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) @@ -4975,15 +4975,15 @@ NIL (-1261 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2905 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3801) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2905 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -1480) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1768) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) +((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3894) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-1262 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2905 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3801) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2905 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -1480) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1768) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3894) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1263 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) (((-4454 "*") |has| (-1262 |#2| |#3| |#4|) (-174)) (-4445 |has| (-1262 |#2| |#3| |#4|) (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-174))) (-2905 (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-368))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-458))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-562)))) +((|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-174))) (-2854 (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-368))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-458))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-562)))) (-1264 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4999,7 +4999,7 @@ NIL (-1267 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasSignature| |#2| (LIST (QUOTE -1768) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1480) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasSignature| |#2| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3894) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) (-1268 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) @@ -5007,12 +5007,12 @@ NIL (-1269 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2905 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3801) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2905 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -1480) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1768) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3894) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1270 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1271 -1691 UP L UTS) +(-1271 -1653 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-562)))) @@ -5039,7 +5039,7 @@ NIL (-1277 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4453 . T) (-4452 . T)) -((-2905 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2905 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2905 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-1278) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5072,7 +5072,7 @@ 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]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1286 K R UP -1691) +(-1286 K R UP -1653) ((|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 @@ -5108,11 +5108,11 @@ NIL ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4445 |has| |#2| (-6 -4445)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL -(-1295 S -1691) +(-1295 S -1653) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1296 -1691) +(-1296 -1653) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index d7c03d15..1e00e24e 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(189883 . 3481463051) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2361 |#2|))))) -((((-570)) . T) (($) -2905 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2905 (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T)) +(189883 . 3481665227) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) #0#) |has| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (-313 (-2 (|:| -2046 |#1|) (|:| -2254 |#2|))))) +((((-570)) . T) (($) -2854 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2854 (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-570)) . T)) -((($ $) -2905 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2| |#2|) . T) ((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570))))) +((($ $) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2| |#2|) . T) ((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) . T)) -((($) -2905 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570))))) +((($) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570))))) (|has| |#1| (-916)) ((((-868)) . T)) ((((-868)) . T)) @@ -24,19 +24,19 @@ ((((-227)) . T) (((-868)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . T)) -(-2905 (|has| |#1| (-21)) (|has| |#1| (-854))) -((($ $) . T) ((#0=(-413 (-570)) #0#) -2905 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) -(-2905 (|has| |#1| (-826)) (|has| |#1| (-856))) +(-2854 (|has| |#1| (-21)) (|has| |#1| (-854))) +((($ $) . T) ((#0=(-413 (-570)) #0#) -2854 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) +(-2854 (|has| |#1| (-826)) (|has| |#1| (-856))) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) ((((-868)) . T)) ((((-868)) . 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T) (($) -2854 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((($) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2854 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -250,10 +250,10 @@ ((((-171 (-227))) |has| |#1| (-1031)) (((-171 (-384))) |has| |#1| (-1031)) (((-542)) |has| |#1| (-620 (-542))) (((-1182 |#1|)) . T) (((-899 (-570))) |has| |#1| (-620 (-899 (-570)))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384))))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . 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T)) (-12 (|has| |#4| (-235)) (|has| |#4| (-1058))) (-12 (|has| |#3| (-235)) (|has| |#3| (-1058))) -(-2905 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2905 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2854 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2854 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) @@ -271,14 +271,14 @@ (((|#1|) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) (((|#1|) . T) (((-570)) |has| |#1| (-645 (-570)))) -(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -2106 (-1168)) (|:| -2361 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) (|has| |#1| (-562)) -((((-570)) -2905 (|has| |#4| (-174)) (|has| |#4| (-854)) (-12 (|has| |#4| (-1047 (-570))) (|has| |#4| (-1109))) (|has| |#4| (-1058))) ((|#4|) -2905 (|has| |#4| (-174)) (|has| |#4| (-1109))) (((-413 (-570))) -12 (|has| |#4| (-1047 (-413 (-570)))) (|has| |#4| (-1109)))) -((((-570)) -2905 (|has| |#3| (-174)) (|has| |#3| (-854)) (-12 (|has| |#3| (-1047 (-570))) (|has| |#3| (-1109))) (|has| |#3| (-1058))) ((|#3|) -2905 (|has| |#3| (-174)) (|has| |#3| (-1109))) (((-413 (-570))) -12 (|has| |#3| (-1047 (-413 (-570)))) (|has| |#3| (-1109)))) +((((-570)) -2854 (|has| |#4| (-174)) (|has| |#4| (-854)) (-12 (|has| |#4| (-1047 (-570))) (|has| |#4| (-1109))) (|has| |#4| (-1058))) ((|#4|) -2854 (|has| |#4| (-174)) (|has| |#4| (-1109))) (((-413 (-570))) -12 (|has| |#4| (-1047 (-413 (-570)))) (|has| |#4| (-1109)))) +((((-570)) -2854 (|has| |#3| (-174)) (|has| |#3| (-854)) (-12 (|has| |#3| (-1047 (-570))) (|has| |#3| (-1109))) (|has| |#3| (-1058))) ((|#3|) -2854 (|has| |#3| (-174)) (|has| |#3| (-1109))) (((-413 (-570))) -12 (|has| |#3| (-1047 (-413 (-570)))) (|has| |#3| (-1109)))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#1| (-562)) -(-2905 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-2854 (|has| |#1| (-856)) (|has| |#1| (-1109))) (((|#1|) . T)) (|has| |#1| (-562)) (|has| |#1| (-562)) @@ -291,21 +291,21 @@ ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))) ((($) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) -((((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) +((((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) (((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) (($) . 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T)) ((((-542)) |has| |#1| (-620 (-542))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#1| (-620 (-899 (-570))))) -(((|#4|) -2905 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) -(((|#3|) -2905 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) -((((-2 (|:| -2283 |#1|) (|:| -3227 |#2|))) . T)) +(((|#4|) -2854 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) +(((|#3|) -2854 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) +((((-2 (|:| -2190 |#1|) (|:| -3229 |#2|))) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-542)) . T) (((-570)) . T) (((-899 (-570))) . T) (((-384)) . T) (((-227)) . T)) @@ -313,14 +313,14 @@ (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) ((($) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) ((((-413 $) (-413 $)) |has| |#2| (-562)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2361 (-52)))) . T)) +((((-2 (|:| -2046 (-1168)) (|:| -2254 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-916)) ((((-1168) (-52)) . T)) ((((-570)) |has| #0=(-413 |#2|) (-645 (-570))) ((#0#) . T)) ((((-542)) . T) (((-227)) . T) (((-384)) . T) (((-899 (-384))) . T)) ((((-868)) . T)) -(-2905 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-2854 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((|#1|) |has| |#1| (-174))) (((|#1| $) |has| |#1| (-290 |#1| |#1|))) ((((-868)) . T)) @@ -334,15 +334,15 @@ (|has| |#1| (-1109)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) . 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T)) (((|#1| (-980)) . T)) ((((-570)) . T) ((|#2|) . T)) @@ -352,7 +352,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1161)) -((((-2 (|:| -2106 (-1168)) (|:| -2361 |#1|))) . T)) +((((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-146)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-148)) (|has| |#1| (-146)) @@ -364,27 +364,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) -((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-824 (-1186))) . T) (($) -2905 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . T)) +((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-824 (-1186))) . T) (($) -2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . 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T)) +(((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) ((#0=(-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) #0#) |has| (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) (-313 (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))))) ((((-868)) . T)) ((((-570) |#1|) . T)) ((((-542)) -12 (|has| |#1| (-620 (-542))) (|has| |#2| (-620 (-542)))) (((-899 (-384))) -12 (|has| |#1| (-620 (-899 (-384)))) (|has| |#2| (-620 (-899 (-384))))) (((-899 (-570))) -12 (|has| |#1| (-620 (-899 (-570)))) (|has| |#2| (-620 (-899 (-570)))))) ((($) . T)) ((((-868)) . T)) -((($ $) -2905 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) +((($ $) -2854 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) ((((-868)) . T)) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -2905 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2854 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-868)) . T)) ((((-868)) . T)) (|has| (-1262 |#2| |#3| |#4|) (-148)) @@ -395,16 +395,16 @@ ((((-868)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2905 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-2854 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((|#1|) . T)) ((((-570) |#1|) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) |has| |#1| (-174))) (((|#1|) . 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T)) (((#0=(-705) (-1182 #0#)) . T)) ((((-587 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) @@ -452,18 +452,18 @@ ((((-868)) . T) (((-1277 |#3|)) . T)) ((((-587 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) ((($) . T) (((-413 (-570))) . T)) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T) (($) -2905 (|has| |#1| (-174)) (|has| |#1| (-562)))) +((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T) (($) -2854 (|has| |#1| (-174)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) . T)) ((((-868)) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) ((($) . T)) -((($ $) -2905 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((#0=(-413 (-570)) #0#) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((#1=(-1269 |#1| |#2| |#3|) #1#) |has| |#1| (-368)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . 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T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($ $) -2854 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) (|has| (-1103 |#1|) (-1109)) (((|#2| (-825 |#1|)) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) @@ -471,20 +471,20 @@ (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) -((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2905 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2854 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) (((|#2|) . T) ((|#6|) . T)) (|has| |#1| (-368)) ((((-570)) . T) ((|#2|) . T)) -((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . 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T)) -(-2905 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2854 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((((-413 (-570))) . T)) (|has| |#1| (-373)) -(-2905 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((((-570)) . T)) ((((-570)) . T)) (((|#1|) . T) (((-570)) . T)) -(-2905 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((((-868)) . T)) ((((-868)) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) @@ -540,10 +540,10 @@ ((((-570) |#4|) . T)) ((((-570) |#3|) . T)) (((|#1|) . T) (((-570)) |has| |#1| (-645 (-570)))) -(-2905 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2854 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-1263 |#1| |#2| |#3| |#4|)) . 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T)) (|has| (-413 |#2|) (-148)) (|has| (-413 |#2|) (-146)) @@ -856,15 +856,15 @@ (|has| |#1| (-562)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) ((((-868)) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2361 |#1|))) . T)) +((((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) -((((-394) (-2 (|:| -2106 (-1168)) (|:| -2361 |#1|))) . T)) +((((-394) (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#2| (-1161)) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) @@ -882,7 +882,7 @@ ((((-394) (-1168)) . T)) (|has| |#1| (-562)) ((((-1244 (-570)) $) . T) (((-570) |#1|) . 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T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#2| (-854)) (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) -(-2905 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-2854 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-174)) ((|#4|) . T) (((-570)) . T)) (((|#2|) |has| |#2| (-174))) @@ -1010,7 +1010,7 @@ (((|#1|) . T)) ((((-413 (-570))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-413 (-570))) . T)) -((($) . T) (((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) +((($) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) (|has| |#1| (-834)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) (|has| |#1| (-1109)) @@ -1021,13 +1021,13 @@ (((|#4|) |has| |#4| (-1109))) (((|#3|) |has| |#3| (-1109))) (|has| |#3| (-373)) -((($) |has| |#1| (-562)) ((|#1|) . T) (((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) -((((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2905 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +((($) |has| |#1| (-562)) ((|#1|) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) +((((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2854 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) ((((-868)) . T)) ((((-868)) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) -(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2905 (|has| |#1| (-368)) (|has| |#1| (-562)))) +(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2854 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#1| |#1|) |has| |#1| (-174))) (|has| |#2| (-368)) @@ -1035,19 +1035,19 @@ (((|#1|) |has| |#1| (-174))) ((((-413 (-570))) . T) (((-570)) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) -((($ $) -2905 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) +((($ $) -2854 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) ((($) . T) (((-570)) . 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T)) -(-2905 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) +(-2854 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) (((|#1|) |has| |#1| (-174))) (|has| $ (-148)) (|has| $ (-148)) @@ -1057,15 +1057,15 @@ ((((-868)) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2905 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-479)) (|has| |#1| (-562)) (|has| |#1| (-1058)) (|has| |#1| (-1121))) +(-2854 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-479)) (|has| |#1| (-562)) (|has| |#1| (-1058)) (|has| |#1| (-1121))) ((($ $) |has| |#1| (-290 $ $)) ((|#1| $) |has| |#1| (-290 |#1| |#1|))) (((|#1| (-413 (-570))) . T)) (((|#1|) . T)) ((((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((((-1186)) . T)) (|has| |#1| (-562)) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-562)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) @@ -1077,7 +1077,7 @@ (|has| |#1| (-148)) (|has| |#1| (-146)) (|has| |#4| (-854)) -(((|#2| (-242 (-2589 |#1|) (-777)) (-870 |#1|)) . T)) +(((|#2| (-242 (-2473 |#1|) (-777)) (-870 |#1|)) . T)) (|has| |#3| (-854)) (((|#1| (-537 |#3|) |#3|) . T)) (|has| |#1| (-148)) @@ -1091,21 +1091,21 @@ (|has| |#1| (-148)) ((((-413 (-570))) |has| |#2| (-368)) (($) . 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T)) -(-2905 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2854 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (|has| |#1| (-562)) (((|#1|) . T)) (((|#1|) . T)) @@ -1129,11 +1129,11 @@ (((|#1| (-413 (-570))) . T)) (((|#3|) . T) (((-618 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) -((((-570)) -2905 (|has| |#2| (-174)) (|has| |#2| (-854)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-1058))) ((|#2|) -2905 (|has| |#2| (-174)) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-570)) -2854 (|has| |#2| (-174)) (|has| |#2| (-854)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-1058))) ((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1141,8 +1141,8 @@ ((((-868)) . T)) ((((-868)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2361 |#2|))))) -(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2106 (-1168)) (|:| -2361 |#1|))) |has| (-2 (|:| -2106 (-1168)) (|:| -2361 |#1|)) (-313 (-2 (|:| -2106 (-1168)) (|:| -2361 |#1|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) |has| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (-313 (-2 (|:| -2046 |#1|) (|:| -2254 |#2|))))) +(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) |has| (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) (-313 (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))))) ((((-868)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1156,10 +1156,10 @@ ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) ((((-570)) . T) (($) . T) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (|has| (-1103 |#1|) (-1109)) -(((|#2| |#2|) -2905 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($ $) |has| |#2| (-174))) -(((|#2|) -2905 (|has| |#2| (-174)) (|has| |#2| (-368)))) -((((-570) (-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2905 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) +(((|#2| |#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($ $) |has| |#2| (-174))) +(((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)))) +((((-570) (-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) ((((-570)) . T)) ((((-1191)) . T)) ((((-777)) . T)) @@ -1177,39 +1177,39 @@ ((((-117 |#1|)) . T)) (((|#1|) . T)) ((((-413 (-570))) . T) (($) . 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T)) (((|#1|) |has| |#1| (-313 |#1|))) @@ -1261,11 +1261,11 @@ (|has| |#1| (-373)) ((((-1186) $) |has| |#1| (-520 (-1186) $)) (($ $) |has| |#1| (-313 $)) ((|#1| |#1|) |has| |#1| (-313 |#1|)) (((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|))) ((((-1186)) |has| |#1| (-907 (-1186)))) -(-2905 (-12 (|has| |#1| (-235)) (|has| |#1| (-368))) (|has| |#1| (-354))) +(-2854 (-12 (|has| |#1| (-235)) (|has| |#1| (-368))) (|has| |#1| (-354))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-394) |#1|) . T)) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-1109)) (((|#2|) . T) (((-868)) . T)) ((((-868)) . T)) @@ -1273,8 +1273,8 @@ ((((-917 |#1|)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) -((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2905 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2905 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2854 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1283,16 +1283,16 @@ (((|#1|) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) (((|#1| |#1|) . T)) (((#0=(-876 |#1|)) |has| #0# (-313 #0#))) -((((-570)) . 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T)) (|has| |#1| (-1212)) (((#0=(-570) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) @@ -1304,8 +1304,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-413 (-570)) #0#) . T)) (|has| |#1| (-368)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((($ $) . T) ((#0=(-413 (-570)) #0#) -2905 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) -((((-868)) -2905 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((($ $) . T) ((#0=(-413 (-570)) #0#) -2854 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) +((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -1320,29 +1320,29 @@ (((|#1| |#2|) . T)) (|has| |#1| (-854)) (|has| |#1| (-854)) -((($) . T) (((-413 (-570))) -2905 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) -(-2905 (|has| |#1| (-174)) (|has| |#1| (-562))) +((($) . T) (((-413 (-570))) -2854 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . 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T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) ((((-413 (-570))) . T) (((-413 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1182 |#1|)) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1542,8 +1542,8 @@ (((|#1|) . T) (((-570)) . T) (($) . T)) (((|#2|) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2361 |#1|))) . T)) -((((-868)) -2905 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) +((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) |#2|) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . 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T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) |has| |#2| (-174))) -((($) -2905 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((-570)) -2905 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -2905 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) +((($) -2854 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((-570)) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) ((((-570) |#3|) . T)) ((((-570) (-145)) . T)) ((((-145)) . T)) @@ -1601,19 +1601,19 @@ (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1| |#2|) . T)) ((((-1244 (-570)) $) . T) (((-570) (-145)) . 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T)) -(-2905 (|has| |#1| (-148)) (-12 (|has| |#1| (-368)) (|has| |#2| (-148)))) -(-2905 (|has| |#1| (-146)) (-12 (|has| |#1| (-368)) (|has| |#2| (-146)))) +(-2854 (|has| |#1| (-148)) (-12 (|has| |#1| (-368)) (|has| |#2| (-148)))) +(-2854 (|has| |#1| (-146)) (-12 (|has| |#1| (-368)) (|has| |#2| (-146)))) (((|#4|) . T)) (|has| |#1| (-146)) ((((-1168) |#1|) . T)) @@ -1627,24 +1627,24 @@ (((|#3|) . T)) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) -((((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-570)) . T) (($) . T)) +((((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . 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T)) -(((|#4|) -2905 (|has| |#4| (-174)) (|has| |#4| (-368)))) -(((|#3|) -2905 (|has| |#3| (-174)) (|has| |#3| (-368)))) +(((|#4|) -2854 (|has| |#4| (-174)) (|has| |#4| (-368)))) +(((|#3|) -2854 (|has| |#3| (-174)) (|has| |#3| (-368)))) (|has| |#2| (-368)) (((|#1|) |has| |#1| (-174))) -(((|#4|) -2905 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) -(((|#3|) -2905 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) +(((|#4|) -2854 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) +(((|#3|) -2854 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) (((|#2|) |has| |#2| (-1058))) ((((-1168) |#1|) . T)) (((|#3| |#3|) -12 (|has| |#3| (-313 |#3|)) (|has| |#3| (-1109)))) @@ -1653,8 +1653,8 @@ ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) ((((-394) (-1168)) . 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T)) -((((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2905 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2905 (|has| |#1| (-368)) (|has| |#1| (-562)))) +((((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2854 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2854 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) . T) (((-570)) . T) (((-825 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1685,7 +1685,7 @@ ((((-868)) . T)) ((((-868)) . T)) (|has| |#1| (-1109)) -(((|#2| (-488 (-2589 |#1|) (-777)) (-870 |#1|)) . T)) +(((|#2| (-488 (-2473 |#1|) (-777)) (-870 |#1|)) . T)) ((((-413 (-570))) . #0=(|has| |#2| (-368))) (($) . #0#)) (((|#1| (-537 (-1186)) (-1186)) . T)) (((|#1|) . T)) @@ -1706,17 +1706,17 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2106 (-1168)) (|:| -2361 |#1|))) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2106 (-1186)) (|:| -2361 (-52)))) . T)) +((((-2 (|:| -2046 (-1186)) (|:| -2254 (-52)))) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) ((((-1186) (-52)) . T)) ((((-413 (-570)) |#1|) . T) (($ $) . T)) (((|#1| (-570)) . T)) ((((-917 |#1|)) . T)) -(((|#1|) -2905 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2905 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) +(((|#1|) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2854 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) (|has| |#1| (-856)) (|has| |#1| (-856)) @@ -1736,13 +1736,13 @@ (((|#1|) |has| |#1| (-174))) (|has| |#1| (-290 |#1| |#1|)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) -(((|#3|) -2905 (|has| |#3| (-174)) (|has| |#3| (-368)))) -((($) -2905 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -(-2905 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-916))) -((($) -2905 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +(((|#3|) -2854 (|has| |#3| (-174)) (|has| |#3| (-368)))) +((($) -2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +(-2854 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-916))) +((($) -2854 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) ((((-570) |#2|) . T)) -(((|#2|) -2905 (|has| |#2| (-174)) (|has| |#2| (-368)))) +(((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)))) (|has| |#1| (-354)) (((|#3| |#3|) -12 (|has| |#3| (-313 |#3|)) (|has| |#3| (-1109)))) (((|#2|) . T) (((-570)) . T)) @@ -1751,7 +1751,7 @@ (|has| |#1| (-826)) (|has| |#1| (-826)) (((|#1|) . T)) -(-2905 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2854 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-854)) (|has| |#1| (-854)) (|has| |#1| (-854)) @@ -1760,14 +1760,14 @@ ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) ((((-1186)) |has| |#1| (-907 (-1186))) (((-1091)) . T)) (((|#1|) . T)) (|has| |#1| (-854)) -(((#0=(-2 (|:| -2106 (-1168)) (|:| -2361 (-52))) #0#) |has| (-2 (|:| -2106 (-1168)) (|:| -2361 (-52))) (-313 (-2 (|:| -2106 (-1168)) (|:| -2361 (-52)))))) +(((#0=(-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) #0#) |has| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (-313 (-2 (|:| -2046 (-1168)) (|:| -2254 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#1| (-1109)) ((((-868)) . T) (((-1191)) . T)) @@ -1791,11 +1791,11 @@ (((|#1| (-777) (-1091)) . T)) (((|#3|) . T)) ((((-145)) . T)) -((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) -2905 (|has| |#1| (-854)) (|has| |#1| (-1047 (-570)))) ((|#1|) . T)) +((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) -2854 (|has| |#1| (-854)) (|has| |#1| (-1047 (-570)))) ((|#1|) . T)) (((|#1|) . T)) ((((-145)) . 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T)) (|has| |#1| (-916)) (((|#2|) |has| |#2| (-1058))) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2361 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2361 |#2|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) |has| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (-313 (-2 (|:| -2046 |#1|) (|:| -2254 |#2|))))) (|has| |#1| (-368)) (((|#1|) |has| |#1| (-174))) (((|#1| |#1|) . T)) @@ -2150,7 +2150,7 @@ (((|#1|) . T)) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-650 $)) . T) (((-1168)) . T) (((-1186)) . T) (((-570)) . T) (((-227)) . T) (((-868)) . 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T)) +((((-2 (|:| -2046 (-1168)) (|:| -2254 (-52)))) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) @@ -2203,17 +2203,17 @@ ((((-705)) . T) (((-413 (-570))) . T) (((-570)) . T)) (((|#1| |#1|) |has| |#1| (-174))) (((|#2|) . T)) -((($) . T) (((-570)) . T) (((-413 (-570))) -2905 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) . T) (((-570)) . T) (((-413 (-570))) -2854 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) ((((-570) |#1|) . 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T)) ((((-570) |#1|) . T)) ((((-1186)) |has| (-413 |#2|) (-907 (-1186)))) -(((|#1|) . T) (($) -2905 (|has| |#1| (-294)) (|has| |#1| (-368))) (((-413 (-570))) |has| |#1| (-368))) +(((|#1|) . T) (($) -2854 (|has| |#1| (-294)) (|has| |#1| (-368))) (((-413 (-570))) |has| |#1| (-368))) ((((-542)) |has| |#2| (-620 (-542)))) ((((-695 |#2|)) . T) (((-868)) . T)) (((|#1|) . T)) @@ -2363,22 +2363,22 @@ (((|#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) ((((-876 |#1|)) . T)) (((|#1|) |has| |#1| (-174))) -(-2905 (|has| |#4| (-799)) (|has| |#4| (-854))) -(-2905 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-2854 (|has| |#4| (-799)) (|has| |#4| (-854))) +(-2854 (|has| |#3| (-799)) (|has| |#3| (-854))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-868)) . T)) ((((-868)) . T)) (((|#1|) . T)) ((($) . T) (((-570)) . T) ((|#2|) . 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T)) @@ -2489,10 +2489,10 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -(((|#1|) -2905 (|has| |#1| (-174)) (|has| |#1| (-368)))) +(((|#1|) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) @@ -2502,10 +2502,10 @@ (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) |has| |#2| (-368))) -((($) -2905 (|has| |#1| (-368)) (|has| |#1| (-354))) (((-413 (-570))) -2905 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . 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T)) ((((-413 (-570))) |has| |#2| (-1047 (-413 (-570)))) (((-570)) |has| |#2| (-1047 (-570))) ((|#2|) . T) (((-870 |#1|)) . T)) ((($) . T) (((-117 |#1|)) . T) (((-413 (-570))) . T)) ((((-1134 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) @@ -2563,22 +2563,22 @@ (((|#1| |#2|) . T)) ((((-1186) |#1|) . T)) (((|#4|) . T)) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1186) (-52)) . T)) ((((-1262 |#2| |#3| |#4|) (-323 |#2| |#3| |#4|)) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) ((((-868)) . 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T)) (((|#1| $) |has| |#1| (-290 |#1| |#1|))) ((((-1263 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-562)) (($) |has| |#1| (-562))) -((((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2905 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) +((((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) (|has| |#1| (-368)) -((($) |has| |#1| (-854)) (((-570)) -2905 (|has| |#1| (-21)) (|has| |#1| (-854)))) +((($) |has| |#1| (-854)) (((-570)) -2854 (|has| |#1| (-21)) (|has| |#1| (-854)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-148)) @@ -2591,17 +2591,17 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) (((|#2| |#3|) . T)) -(-2905 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2854 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((|#1| (-537 |#2|)) . T)) (((|#1| (-777)) . T)) (((|#1| (-537 (-1097 (-1186)))) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (|has| |#2| (-916)) -(-2905 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-2854 (|has| |#2| (-799)) (|has| |#2| (-854))) ((((-868)) . T)) -(((|#2|) -2905 (|has| |#2| (-174)) (|has| |#2| (-368)))) -(((|#2|) -2905 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) +(((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)))) +(((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) ((($ $) . T) ((#0=(-1262 |#2| |#3| |#4|) #0#) . T) ((#1=(-413 (-570)) #1#) |has| #0# (-38 (-413 (-570))))) ((((-917 |#1|)) . T)) (-12 (|has| |#1| (-368)) (|has| |#2| (-826))) @@ -2609,14 +2609,14 @@ ((((-868)) . T)) ((($) . T)) ((($) . T)) -(-2905 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) +(-2854 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (|has| |#1| (-368)) (|has| |#1| (-368)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1262 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -(-2905 (-12 (|has| |#1| (-311)) (|has| |#1| (-916))) (|has| |#1| (-368)) (|has| |#1| (-354))) -(-2905 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-2854 (-12 (|has| |#1| (-311)) (|has| |#1| (-916))) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2854 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) ((((-570)) |has| |#1| (-645 (-570))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-868)) . T)) @@ -2661,28 +2661,28 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) (((|#2|) . T)) -(((|#2|) -2905 (|has| |#2| (-6 (-4454 "*"))) (|has| |#2| (-174)))) -(-2905 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) -(-2905 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(((|#2|) -2854 (|has| |#2| (-6 (-4454 "*"))) (|has| |#2| (-174)))) +(-2854 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (|has| |#2| (-916)) (|has| |#1| (-916)) (((|#2|) |has| |#2| (-174))) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-868)) . T)) ((((-868)) . T)) ((((-542)) . T) (((-570)) . T) (((-899 (-570))) . T) (((-384)) . T) (((-227)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2361 (-52)))) . T)) +((((-2 (|:| -2046 (-1168)) (|:| -2254 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) ((((-868)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) (((|#1| (-413 (-570))) . T)) (((|#1|) . T)) -(-2905 (|has| |#1| (-294)) (|has| |#1| (-368))) +(-2854 (|has| |#1| (-294)) (|has| |#1| (-368))) ((((-145)) . T)) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) (|has| |#1| (-854)) @@ -2698,7 +2698,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-189)) . T) (((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -2711,7 +2711,7 @@ ((((-868)) . T)) ((((-1168)) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -((((-2 (|:| -2106 (-1168)) (|:| -2361 |#1|))) . T)) +((((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) (|has| |#1| (-856)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) @@ -2723,16 +2723,16 @@ (((|#2|) . T)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T) (((-618 $)) . T)) -(-2905 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2905 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2854 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2854 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-1186) (-52)) . T)) -(-2905 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2905 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -(-2905 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2854 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (|has| |#1| (-916)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) (|has| |#1| (-916)) @@ -2749,12 +2749,12 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (|has| |#1| (-826)) (((#0=(-917 |#1|) #0#) . T) (($ $) . T) ((#1=(-413 (-570)) #1#) . T)) ((((-413 |#2|)) . T)) (|has| |#1| (-854)) -((((-1213 |#1|)) . T) (((-868)) -2905 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-1213 |#1|)) . T) (((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) . T) ((#1=(-570) #1#) . T) (($ $) . T)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) |has| |#2| (-1058)) (((-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058)))) @@ -2770,29 +2770,29 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(-2905 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-2905 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-2905 (|has| |#1| (-146)) (|has| |#1| (-373))) -((((-2 (|:| -2106 (-1186)) (|:| -2361 (-52)))) . T)) +(-2854 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2854 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2854 (|has| |#1| (-146)) (|has| |#1| (-373))) +((((-2 (|:| -2046 (-1186)) (|:| -2254 (-52)))) . T)) ((((-570) |#3|) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2106 (-1186)) (|:| -2361 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2046 (-1186)) (|:| -2254 #0#))) . T)) (|has| |#1| (-354)) ((((-570)) . T)) ((((-868)) . T)) (((|#1|) . T)) (((#0=(-1263 |#1| |#2| |#3| |#4|) $) |has| #0# (-290 #0# #0#))) (|has| |#1| (-368)) -(((|#1|) -2905 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2905 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((-570)) -2905 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) +(((|#1|) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2854 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((-570)) -2854 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) (((#0=(-1091) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) (((#0=(-413 (-570)) #0#) . T) ((#1=(-705) #1#) . T) (($ $) . T)) ((((-320 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) |has| |#1| (-368))) ((((-868)) . T)) (|has| |#1| (-1109)) (((|#1|) . T)) -(((|#1|) -2905 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) -(((|#1|) -2905 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -2854 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -2854 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) (((|#2|) . T)) ((((-413 (-570))) . T) (((-705)) . T) (($) . T)) ((((-585)) . T)) @@ -2817,7 +2817,7 @@ (((|#1|) . T)) ((((-570)) . T)) (((|#2|) . T) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((|#1|) . T) (($) . T) (((-570)) . T)) -(-2905 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2854 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2861,7 +2861,7 @@ (|has| |#2| (-1031)) ((($) . T)) (|has| |#1| (-916)) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2870,10 +2870,10 @@ (|has| |#1| (-368)) ((((-917 |#1|)) . T)) ((($) . T) (((-570)) . T) ((|#1|) . T) (((-413 (-570))) . T)) -((($) -2905 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((($) |has| |#1| (-854)) (((-570)) -2905 (|has| |#1| (-21)) (|has| |#1| (-854)))) +((($) -2854 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) |has| |#1| (-854)) (((-570)) -2854 (|has| |#1| (-21)) (|has| |#1| (-854)))) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) -(-2905 (|has| |#1| (-373)) (|has| |#1| (-856))) +(-2854 (|has| |#1| (-373)) (|has| |#1| (-856))) (((|#1|) . T)) ((((-777)) . T)) ((((-868)) . T)) @@ -2884,17 +2884,17 @@ ((((-570)) . T) (($) . T)) ((((-570)) . T) (($) . T)) ((((-777) |#1|) . T)) -(((|#2| (-242 (-2589 |#1|) (-777))) . T)) +(((|#2| (-242 (-2473 |#1|) (-777))) . T)) (((|#1| (-537 |#3|)) . T)) ((((-413 (-570))) . T)) -(-2905 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((((-1168)) . T) (((-868)) . T)) -(((#0=(-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) #0#) |has| (-2 (|:| -2106 (-1186)) (|:| -2361 (-52))) (-313 (-2 (|:| -2106 (-1186)) (|:| -2361 (-52)))))) +(((#0=(-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) #0#) |has| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (-313 (-2 (|:| -2046 (-1186)) (|:| -2254 (-52)))))) ((((-1168)) . T)) (|has| |#1| (-916)) (|has| |#2| (-368)) (((|#1|) . T) (($) . T) (((-570)) . T)) -(-2905 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2854 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-171 (-384))) . T) (((-227)) . T) (((-384)) . T)) ((((-868)) . T)) (((|#1|) . T)) @@ -2911,11 +2911,11 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2905 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2854 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (-12 (|has| |#1| (-551)) (|has| |#1| (-834))) ((((-868)) . T)) -((((-1186)) -2905 (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))) (-12 (|has| |#1| (-368)) (|has| |#2| (-907 (-1186)))))) +((((-1186)) -2854 (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))) (-12 (|has| |#1| (-368)) (|has| |#2| (-907 (-1186)))))) (|has| |#1| (-368)) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-907 (-1186))))) (|has| |#1| (-368)) @@ -2927,7 +2927,7 @@ (((|#2|) |has| |#1| (-368))) (((|#2|) |has| |#1| (-368))) ((((-570)) . T) (($) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) @@ -2956,11 +2956,11 @@ (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#2|) |has| |#1| (-368))) ((((-384)) -12 (|has| |#1| (-368)) (|has| |#2| (-893 (-384)))) (((-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-893 (-570))))) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) (((|#1|) . T)) ((($) . T) (((-570)) . T) ((|#2|) . T)) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) (((|#3|) . T)) ((((-1168)) . T) (((-512)) . T) (((-227)) . T) (((-570)) . T)) (((|#1|) . T)) @@ -2968,23 +2968,23 @@ (|has| |#1| (-562)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) -(-2905 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2854 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#2|) . T)) (((|#2|) . T)) -(-2905 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2361 |#1|))) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +(-2854 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-413 (-570)))) -(-2905 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2854 (|has| |#1| (-146)) (|has| |#1| (-373))) ((($) . T)) ((((-1168) |#1|) . T)) (|has| |#1| (-148)) -(-2905 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2854 (|has| |#1| (-146)) (|has| |#1| (-373))) (|has| |#1| (-148)) -(-2905 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2854 (|has| |#1| (-146)) (|has| |#1| (-373))) ((($) . T)) (|has| |#1| (-148)) ((((-587 |#1|)) . T)) @@ -2998,7 +2998,7 @@ ((((-413 (-570))) |has| |#2| (-1047 (-570))) (((-570)) |has| |#2| (-1047 (-570))) (((-1186)) |has| |#2| (-1047 (-1186))) ((|#2|) . T)) (((#0=(-413 |#2|) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2905 (|has| |#1| (-146)) (|has| |#1| (-354))) +(-2854 (|has| |#1| (-146)) (|has| |#1| (-354))) (|has| |#1| (-148)) ((((-868)) . T)) ((($) . T)) @@ -3024,7 +3024,7 @@ ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2905 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3046,7 +3046,7 @@ ((((-570)) . T)) ((((-868)) . T)) ((((-570)) . T)) -(-2905 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-2854 (|has| |#2| (-799)) (|has| |#2| (-854))) ((((-171 (-384))) . T) (((-227)) . T) (((-384)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -3058,10 +3058,10 @@ (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (|has| |#1| (-368)) (|has| |#1| (-368)) -((((-868)) -2905 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) -((((-868)) -2905 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) $) . T) (((-650 (-570)) $) . T)) -(-2905 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)) (|has| |#1| (-1121)) (|has| |#1| (-1109))) +(-2854 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)) (|has| |#1| (-1121)) (|has| |#1| (-1109))) (|has| |#1| (-1161)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) @@ -3078,9 +3078,9 @@ (((|#1|) |has| |#1| (-313 |#1|))) ((((-570) |#1|) . T) (((-1244 (-570)) $) . T)) ((((-1186) |#1|) . T)) -(((|#1|) -2905 (|has| |#1| (-174)) (|has| |#1| (-368)))) +(((|#1|) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)))) (((|#1|) . T)) -(((|#1|) -2905 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058)))) +(((|#1|) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058)))) ((((-570)) . T) (((-413 (-570))) . T)) (((|#1|) . T)) (|has| |#1| (-562)) @@ -3089,14 +3089,14 @@ ((((-384)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) (|has| |#1| (-562)) (|has| |#1| (-1109)) ((((-786 |#1| (-870 |#2|))) |has| (-786 |#1| (-870 |#2|)) (-313 (-786 |#1| (-870 |#2|))))) -(-2905 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2854 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3108,13 +3108,13 @@ (|has| |#2| (-368)) ((((-587 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2361 (-52)))) . T)) +((((-2 (|:| -2046 (-1168)) (|:| -2254 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-570)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-868)) . T)) ((((-868)) . T)) -(-2905 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-2854 (|has| |#3| (-799)) (|has| |#3| (-854))) ((((-868)) . T)) ((((-1129)) . T) (((-868)) . T)) ((((-542)) . T) (((-868)) . T)) @@ -3125,12 +3125,12 @@ ((((-570)) . T)) (((|#3|) . T)) ((((-868)) . T)) -(-2905 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) -((((-570)) . T) (((-413 (-570))) -2905 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570))))) ((|#2|) . T) (($) -2905 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-870 |#1|)) . T)) -((((-1134 |#1| |#2|)) . T) ((|#2|) . T) (($) -2905 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) -((((-1182 |#1|)) . T) (((-570)) . 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T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) +((((-1182 |#1|)) . T) (((-570)) . T) (($) -2854 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((-1091)) . T) ((|#1|) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) +(-2854 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) +((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-1097 (-1186))) . T) (($) -2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . T)) (((#0=(-587 |#1|) #0#) . T) (($ $) . T) ((#1=(-413 (-570)) #1#) . T)) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) (((|#1|) |has| |#1| (-174))) @@ -3148,7 +3148,7 @@ (((|#1|) . T)) ((((-868)) . T)) ((((-298 |#3|)) . T)) -(((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570)))) ((|#2| |#2|) . T) (($ $) -2905 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +(((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570)))) ((|#2| |#2|) . T) (($ $) -2854 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) @@ -3156,21 +3156,21 @@ (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) -((($ $) -2905 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) -((($ $) -2905 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . 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T)) (((|#1|) |has| |#1| (-174))) -(-2905 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2854 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#1|) . T)) (((|#1|) . T)) -(-2905 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#1|) . T)) ((((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((((-542)) . T)) @@ -3211,14 +3211,14 @@ ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) ((((-1186)) |has| |#1| (-907 (-1186)))) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) -((($) . T) (((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) -(((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570)))) ((|#1| |#1|) . 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T)) (|has| |#2| (-826)) (|has| |#2| (-826)) -((((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#2|) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2905 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) +((((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#2|) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) ((((-570)) |has| |#1| (-893 (-570))) (((-384)) |has| |#1| (-893 (-384)))) @@ -3255,7 +3255,7 @@ (((|#1|) . 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T)) -((($) -2905 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((($ $) . T) (((-1186) $) . T)) (|has| |#2| (-916)) ((((-1269 |#1| |#2| |#3|)) . T)) @@ -3666,7 +3666,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-174))) ((((-705)) . T)) -((((-868)) -2905 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-1191)) . T)) (((|#1|) |has| |#1| (-174))) ((((-1191)) . T)) @@ -3683,13 +3683,13 @@ ((((-1191)) . T)) ((((-1191)) . T)) ((((-1191)) . T)) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-354))) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1191)) . T)) ((((-1191)) . T)) (|has| |#1| (-368)) (|has| |#1| (-368)) -(-2905 (|has| |#1| (-174)) (|has| |#1| (-562))) +(-2854 (|has| |#1| (-174)) (|has| |#1| (-562))) (((|#1| (-570)) . T)) (((|#1| (-413 (-570))) . T)) (((|#1| (-777)) . T)) @@ -3704,16 +3704,16 @@ ((((-899 (-384))) . T) (((-899 (-570))) . T) (((-1186)) . T) (((-542)) . T)) (((|#1|) . T)) ((((-868)) . T)) -(-2905 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -(-2905 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799)))) +(-2854 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2854 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799)))) ((((-570)) . T)) ((((-570)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2905 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2854 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058)))) -(-2905 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-2854 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-368)) @@ -3744,7 +3744,7 @@ (((|#1| |#2|) . T)) ((((-570)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-570)) . T)) -(-2905 (|has| |#1| (-354)) (|has| |#1| (-373))) +(-2854 (|has| |#1| (-354)) (|has| |#1| (-373))) (((|#1| |#2|) . T)) ((((-227)) . T)) ((((-413 (-570))) . T) (($) . T) (((-570)) . T)) @@ -3756,7 +3756,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2905 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-570) $) . T) (((-650 (-570)) $) . T)) ((($) . T) (((-413 (-570))) . T)) (|has| |#1| (-916)) @@ -3768,14 +3768,14 @@ (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-570)) . T)) ((((-1191)) . T)) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2905 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2854 (|has| |#1| (-21)) (|has| |#1| (-854))) (((|#2|) . T)) -(-2905 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-2854 (|has| |#1| (-21)) (|has| |#1| (-854))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-868)) -2905 (-12 (|has| |#1| (-619 (-868))) (|has| |#2| (-619 (-868)))) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))))) +((((-868)) -2854 (-12 (|has| |#1| (-619 (-868))) (|has| |#2| (-619 (-868)))) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))))) ((((-413 |#2|) |#3|) . T)) ((((-413 (-570))) . T) (($) . T)) (|has| |#1| (-38 (-413 (-570)))) @@ -3789,19 +3789,19 @@ (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((#0=(-570) #0#) . T)) ((($) . T) (((-413 (-570))) . T)) -(-2905 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2905 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2854 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2854 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-868)) . T) (((-1191)) . T)) (|has| |#4| (-799)) -(-2905 (|has| |#4| (-799)) (|has| |#4| (-854))) +(-2854 (|has| |#4| (-799)) (|has| |#4| (-854))) (|has| |#4| (-854)) (|has| |#3| (-799)) ((((-1191)) . T)) -(-2905 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-2854 (|has| |#3| (-799)) (|has| |#3| (-854))) (|has| |#3| (-854)) ((((-570)) . T)) (((|#2|) . T)) -((((-1186)) -2905 (-12 (|has| (-1184 |#1| |#2| |#3|) (-907 (-1186))) (|has| |#1| (-368))) (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))))) +((((-1186)) -2854 (-12 (|has| (-1184 |#1| |#2| |#3|) (-907 (-1186))) (|has| |#1| (-368))) (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))))) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-907 (-1186))))) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-777) |#1|))) (|has| |#1| (-907 (-1186))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3816,11 +3816,11 @@ ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-1149 |#1| |#2|)) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) -((((-2 (|:| -2106 (-1186)) (|:| -2361 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -2046 (-1186)) (|:| -2254 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1031)) -(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) ((((-868)) . T)) ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570)))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-384)) . #0=(|has| |#2| (-1031))) (((-227)) . #0#)) ((((-298 |#3|)) . T)) @@ -3837,15 +3837,15 @@ ((((-1184 |#1| |#2| |#3|)) . T)) ((((-1184 |#1| |#2| |#3|)) . T) (((-1177 |#1| |#2| |#3|)) . T)) ((((-868)) . T)) -((((-868)) -2905 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) |#1|) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-368)) -(((|#3|) . T) ((|#2|) . T) (($) -2905 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) ((|#4|) -2905 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) -(((|#2|) . T) (($) -2905 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -2905 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) +(((|#3|) . T) ((|#2|) . T) (($) -2854 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) ((|#4|) -2854 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) +(((|#2|) . T) (($) -2854 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -2854 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) (((|#1|) . T)) (((|#1|) . T)) ((((-117 |#1|)) . T)) @@ -3859,7 +3859,7 @@ ((((-189)) . T) (((-868)) . T)) ((((-868)) . T)) (((|#1|) . T)) -((((-868)) -2905 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-130)) . T) (((-868)) . T)) ((((-570) |#1|) . T) (((-1244 (-570)) $) . T)) ((((-130)) . T)) @@ -3868,13 +3868,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-368)) (|has| |#2| (-290 |#2| |#2|))) (($ $) . T) (((-570) |#1|) . T)) ((($ $) . T) (((-413 (-570)) |#1|) . T)) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-916))) -(-2905 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-916))) +(-2854 (|has| |#1| (-856)) (|has| |#1| (-1109))) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) (((|#1| (-537 |#2|)) . T)) -((((-2 (|:| -2106 (-1186)) (|:| -2361 (-52)))) . T)) +((((-2 (|:| -2046 (-1186)) (|:| -2254 (-52)))) . T)) ((((-570) (-130)) . T)) (((|#1| (-570)) . T)) (((|#1| (-413 (-570))) . T)) @@ -3889,8 +3889,8 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) -(-2905 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) -(-2905 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2854 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((($) . T)) (((|#2| (-537 (-870 |#1|))) . T)) ((((-1191)) . T)) @@ -3905,13 +3905,13 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) -((((-868)) -2905 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1|) . T)) (((|#2| (-777)) . T)) (((|#1| |#2|) . T)) ((((-1168) |#1|) . T)) ((((-413 |#2|)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2361 |#2|))) . T)) +((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) (|has| |#1| (-562)) (|has| |#1| (-562)) ((($) . T) ((|#2|) . T)) @@ -3922,14 +3922,14 @@ ((((-570)) . T) (($) . T)) (((|#2| $) |has| |#2| (-290 |#2| |#2|))) (((|#1| (-650 |#1|)) |has| |#1| (-854))) -(-2905 (|has| |#1| (-235)) (|has| |#1| (-354))) -(-2905 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2854 (|has| |#1| (-235)) (|has| |#1| (-354))) +(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1273 |#1|)) . T) (((-570)) . T) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-1047 (-413 (-570))))) (|has| |#1| (-1109)) (((|#1|) . T)) -((((-1273 |#1|)) . T) (((-570)) . T) (($) -2905 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-1091)) . T) ((|#2|) . T) (((-413 (-570))) -2905 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570)))))) +((((-1273 |#1|)) . T) (((-570)) . T) (($) -2854 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-1091)) . T) ((|#2|) . T) (((-413 (-570))) -2854 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570)))))) ((((-413 (-570))) . T) (($) . T)) -((((-1008 |#1|)) . T) ((|#1|) . T) (((-570)) -2905 (|has| (-1008 |#1|) (-1047 (-570))) (|has| |#1| (-1047 (-570)))) (((-413 (-570))) -2905 (|has| (-1008 |#1|) (-1047 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) +((((-1008 |#1|)) . T) ((|#1|) . T) (((-570)) -2854 (|has| (-1008 |#1|) (-1047 (-570))) (|has| |#1| (-1047 (-570)))) (((-413 (-570))) -2854 (|has| (-1008 |#1|) (-1047 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) @@ -3945,11 +3945,11 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1149 |#1| |#2|) #0#) |has| (-1149 |#1| |#2|) (-313 (-1149 |#1| |#2|)))) (((|#1|) . 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185915) ((-608 . -290) 185867) ((-611 . -619) 185834) ((-394 . -102) T) ((-1129 . -144) T) ((-127 . -619) 185766) ((-880 . -1109) T) ((-664 . -417) 185750) ((-720 . -619) 185732) ((-251 . -619) 185699) ((-189 . -619) 185681) ((-163 . -619) 185663) ((-158 . -619) 185645) ((-1292 . -732) T) ((-1111 . -34) T) ((-877 . -801) NIL) ((-877 . -798) NIL) ((-864 . -856) T) ((-737 . -893) NIL) ((-1301 . -132) T) ((-386 . -132) T) ((-899 . -622) 185613) ((-911 . -102) T) ((-737 . -1047) 185489) ((-1184 . -1227) T) ((-537 . -132) T) ((-1183 . -1227) T) ((-1096 . -417) 185473) ((-1009 . -495) 185457) ((-118 . -406) 185434) ((-1177 . -1227) T) ((-788 . -417) 185418) ((-786 . -417) 185402) ((-950 . -34) T) ((-700 . -1161) NIL) ((-254 . -654) 185237) ((-253 . -654) 185059) ((-823 . -927) 185038) ((-460 . -417) 185022) ((-608 . -19) 185006) ((-1155 . -1220) 184975) ((-1177 . -893) NIL) ((-1177 . -891) 184927) ((-608 . -610) 184904) ((-1213 . -619) 184836) ((-1185 . -619) 184818) ((-62 . -401) T) ((-1183 . -1047) 184753) ((-1177 . -1047) 184719) ((-700 . -38) 184669) ((-40 . -652) 184599) ((-480 . -290) 184557) ((-1233 . -619) 184539) ((-737 . -382) 184523) ((-844 . -619) 184505) ((-664 . -1067) T) ((-1261 . -1011) 184471) ((-1240 . -1011) 184437) ((-252 . -1227) T) ((-1097 . -622) 184421) ((-1072 . -1203) 184396) ((-1085 . -622) 184373) ((-878 . -620) 184180) ((-878 . -619) 184162) ((-1199 . -495) 184099) ((-424 . -1031) 184077) ((-48 . -313) 184064) ((-1072 . -107) 184010) ((-485 . -495) 183947) ((-526 . -1227) T) ((-1177 . -343) 183899) ((-1150 . -495) 183870) ((-1177 . -382) 183822) ((-1096 . -1067) T) ((-443 . -102) T) ((-185 . -1109) T) ((-254 . -34) T) ((-253 . -34) T) ((-788 . -1067) T) ((-786 . -1067) T) ((-737 . -907) 183799) ((-460 . -1067) T) ((-59 . -495) 183783) ((-1043 . -1065) 183757) ((-525 . -495) 183741) ((-522 . -495) 183725) ((-503 . -495) 183709) ((-502 . -495) 183693) ((-247 . -520) 183626) ((-1043 . -111) 183593) ((-1184 . -907) 183506) ((-1183 . -907) 183412) 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182045) ((-523 . -622) 182026) ((-570 . -834) T) ((-242 . -1227) T) ((-1043 . -622) 181995) ((-842 . -111) 181960) ((-833 . -111) 181939) ((-1261 . -619) 181921) ((-1240 . -619) 181903) ((-1240 . -620) 181574) ((-1182 . -916) 181553) ((-1134 . -916) 181532) ((-48 . -38) 181497) ((-1299 . -1121) T) ((-542 . -290) 181453) ((-608 . -619) 181365) ((-608 . -620) 181326) ((-1297 . -1121) T) ((-366 . -622) 181310) ((-326 . -622) 181294) ((-242 . -1047) 181121) ((-1182 . -654) 181046) ((-1134 . -654) 180971) ((-860 . -654) 180945) ((-724 . -619) 180927) ((-552 . -373) T) ((-1299 . -23) T) ((-1297 . -23) T) ((-497 . -1109) T) ((-384 . -622) 180877) ((-384 . -624) 180859) ((-1043 . -1058) T) ((-871 . -102) T) ((-1199 . -290) 180838) ((-171 . -373) 180789) ((-1013 . -1227) T) ((-842 . -622) 180743) ((-833 . -622) 180698) ((-44 . -23) T) ((-485 . -290) 180677) ((-592 . -1109) T) ((-1155 . -1118) 180646) ((-1113 . -1112) 180598) ((-396 . -21) T) ((-396 . -25) T) ((-153 . -1121) T) ((-1306 . -102) T) ((-1013 . -891) 180580) ((-1013 . -893) 180562) ((-1221 . -723) 180459) ((-629 . -233) 180443) ((-627 . -21) T) ((-293 . -562) T) ((-627 . -25) T) ((-1207 . -1109) T) ((-717 . -723) 180408) ((-242 . -382) 180377) ((-1013 . -1047) 180337) ((-384 . -1058) T) ((-225 . -1067) T) ((-118 . -233) 180314) ((-59 . -290) 180266) ((-153 . -23) T) ((-522 . -290) 180218) ((-331 . -520) 180151) ((-502 . -290) 180103) ((-384 . -245) T) ((-384 . -235) T) ((-842 . -1058) T) ((-833 . -1058) T) ((-718 . -956) 180072) ((-707 . -856) T) ((-480 . -619) 180054) ((-1263 . -1060) 179959) ((-586 . -652) 179931) ((-570 . -652) 179903) ((-501 . -652) 179853) ((-833 . -235) 179832) ((-135 . -856) T) ((-1263 . -646) 179724) ((-664 . -1109) T) ((-1199 . -610) 179703) ((-556 . -1203) 179682) ((-341 . -1109) T) ((-323 . -368) 179661) ((-413 . -148) 179640) ((-413 . -146) 179619) ((-971 . -1121) 179518) ((-242 . -907) 179450) ((-821 . -1121) 179360) ((-660 . -858) 179344) ((-485 . -610) 179323) ((-556 . -107) 179273) ((-1013 . -382) 179255) ((-1013 . -343) 179237) ((-97 . -1109) T) ((-971 . -23) 179048) ((-483 . -21) T) ((-483 . -25) T) ((-821 . -23) 178918) ((-1186 . -619) 178900) ((-59 . -19) 178884) ((-1186 . -620) 178806) ((-1182 . -732) T) ((-1134 . -732) T) ((-522 . -19) 178790) ((-502 . -19) 178774) ((-59 . -610) 178751) ((-1096 . -1109) T) ((-908 . -102) 178729) ((-860 . -732) T) ((-788 . -1109) T) ((-522 . -610) 178706) ((-502 . -610) 178683) ((-786 . -1109) T) ((-786 . -1074) 178650) ((-467 . -1109) T) ((-460 . -1109) T) ((-592 . -723) 178625) ((-655 . -1109) T) ((-1269 . -47) 178602) ((-1263 . -102) T) ((-1262 . -47) 178572) ((-1241 . -47) 178549) ((-1221 . -174) 178500) ((-1183 . -311) 178479) ((-1177 . -311) 178458) ((-1105 . -622) 178439) ((-1099 . -622) 178420) ((-1089 . -562) 178371) ((-1013 . -907) NIL) ((-1089 . -1231) 178322) ((-676 . -132) T) ((-633 . -1121) T) ((-1082 . -622) 178303) ((-1075 . -622) 178284) ((-1045 . -622) 178265) ((-1028 . -622) 178246) ((-705 . -652) 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174850) ((-227 . -732) T) ((-522 . -620) 174811) ((-522 . -619) 174723) ((-503 . -619) 174655) ((-502 . -620) 174616) ((-502 . -619) 174528) ((-1089 . -368) 174479) ((-40 . -417) 174456) ((-77 . -1227) T) ((-877 . -916) NIL) ((-364 . -333) 174440) ((-364 . -368) T) ((-358 . -333) 174424) ((-358 . -368) T) ((-350 . -333) 174408) ((-350 . -368) T) ((-320 . -288) 174387) ((-108 . -368) T) ((-70 . -1227) T) ((-1241 . -343) 174339) ((-877 . -654) 174284) ((-1241 . -382) 174236) ((-971 . -132) 174091) ((-821 . -132) 173961) ((-965 . -657) 173945) ((-1096 . -174) 173856) ((-965 . -378) 173840) ((-1071 . -800) T) ((-1071 . -797) T) ((-878 . -622) 173738) ((-788 . -174) 173629) ((-786 . -174) 173540) ((-822 . -47) 173502) ((-1071 . -732) T) ((-331 . -495) 173486) ((-959 . -732) T) ((-1290 . -313) 173424) ((-460 . -174) 173335) ((-247 . -290) 173287) ((-1269 . -907) 173200) ((-1262 . -907) 173106) ((-1261 . -1065) 172941) ((-487 . -732) T) ((-1241 . -907) 172774) ((-1240 . -1065) 172582) ((-1221 . -294) 172561) ((-1196 . -1227) T) ((-1193 . -373) T) ((-1192 . -373) T) ((-1155 . -152) 172545) ((-1129 . -102) T) ((-1127 . -1109) T) ((-1089 . -23) T) ((-1089 . -1121) T) ((-1084 . -102) T) ((-1066 . -619) 172512) ((-934 . -962) T) ((-743 . -313) 172450) ((-75 . -1227) T) ((-670 . -387) 172422) ((-171 . -916) 172375) ((-30 . -962) T) ((-112 . -850) T) ((-1 . -619) 172357) ((-1012 . -415) 172329) ((-129 . -657) 172311) ((-50 . -626) 172295) ((-700 . -652) 172230) ((-601 . -907) 172143) ((-444 . -102) T) ((-129 . -378) 172125) ((-142 . -313) NIL) ((-878 . -1058) T) ((-839 . -856) 172104) ((-81 . -1227) T) ((-717 . -294) T) ((-40 . -1067) T) ((-587 . -174) T) ((-524 . -174) T) ((-517 . -619) 172086) ((-171 . -654) 171996) ((-513 . -619) 171978) ((-356 . -148) 171960) ((-356 . -146) T) ((-364 . -1121) T) ((-358 . -1121) T) ((-350 . -1121) T) ((-1013 . -311) T) ((-921 . -311) T) ((-878 . -245) T) ((-108 . -1121) T) ((-878 . -235) 171939) ((-1261 . -111) 171760) ((-1240 . -111) 171549) 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. -562) 165479) ((-254 . -1047) 165306) ((-253 . -1047) 165133) ((-127 . -120) 165117) ((-917 . -1065) 165082) ((-718 . -102) T) ((-705 . -1067) T) ((-603 . -622) 165063) ((-591 . -622) 165044) ((-542 . -624) 164947) ((-348 . -174) T) ((-88 . -619) 164929) ((-153 . -21) T) ((-153 . -25) T) ((-917 . -111) 164885) ((-40 . -723) 164830) ((-876 . -1109) T) ((-670 . -622) 164807) ((-651 . -622) 164788) ((-360 . -622) 164725) ((-357 . -622) 164662) ((-553 . -1109) T) ((-349 . -622) 164599) ((-331 . -620) 164560) ((-331 . -619) 164472) ((-267 . -622) 164225) ((-249 . -622) 164010) ((-1240 . -798) 163963) ((-1240 . -801) 163916) ((-254 . -382) 163885) ((-253 . -382) 163854) ((-660 . -38) 163824) ((-614 . -34) T) ((-488 . -1121) 163734) ((-481 . -34) T) ((-1122 . -132) 163604) ((-971 . -25) 163415) ((-917 . -622) 163365) ((-880 . -619) 163347) ((-971 . -21) 163302) ((-821 . -21) 163212) ((-821 . -25) 163063) ((-1233 . -373) T) ((-629 . -1067) T) ((-1188 . -562) 163042) ((-1182 . -47) 163019) 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. -25) T) ((-1241 . -21) T) ((-1241 . -25) T) ((-1036 . -152) 130825) ((-878 . -826) 130804) ((-878 . -927) T) ((-718 . -290) 130731) ((-602 . -21) T) ((-344 . -652) 130690) ((-602 . -25) T) ((-601 . -21) T) ((-176 . -652) 130607) ((-40 . -732) T) ((-224 . -520) 130540) ((-601 . -25) T) ((-482 . -152) 130524) ((-469 . -152) 130508) ((-928 . -800) T) ((-928 . -732) T) ((-777 . -799) T) ((-777 . -800) T) ((-512 . -1109) T) ((-508 . -1109) T) ((-777 . -732) T) ((-227 . -368) T) ((-1299 . -1060) 130492) ((-1297 . -1060) 130476) ((-1299 . -646) 130446) ((-1166 . -1109) 130424) ((-877 . -1231) T) ((-1297 . -646) 130394) ((-660 . -619) 130376) ((-877 . -562) T) ((-700 . -373) NIL) ((-44 . -1060) 130360) ((-1306 . -622) 130342) ((-1300 . -1109) T) ((-676 . -102) T) ((-364 . -1284) 130326) ((-358 . -1284) 130310) ((-44 . -646) 130294) ((-350 . -1284) 130278) ((-554 . -102) T) ((-526 . -856) 130257) ((-1055 . -1109) T) ((-823 . -458) 130236) ((-153 . -1060) 130220) ((-1055 . -1080) 130149) 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119999) ((-839 . -417) 119983) ((-1129 . -801) T) ((-1129 . -798) T) ((-707 . -1109) T) ((-584 . -619) 119965) ((-384 . -368) T) ((-171 . -499) 119943) ((-224 . -619) 119875) ((-135 . -1109) T) ((-117 . -1109) T) ((-973 . -1227) T) ((-48 . -732) T) ((-1055 . -495) 119840) ((-142 . -431) 119822) ((-142 . -373) T) ((-1036 . -102) T) ((-518 . -515) 119801) ((-718 . -622) 119557) ((-482 . -102) T) ((-469 . -102) T) ((-1043 . -1121) T) ((-1234 . -619) 119539) ((-1191 . -1047) 119475) ((-1184 . -35) 119441) ((-1184 . -95) 119407) ((-1184 . -1215) 119373) ((-1184 . -1212) 119339) ((-1183 . -1212) 119305) ((-1168 . -313) NIL) ((-89 . -402) T) ((-89 . -401) T) ((-1089 . -1161) 119284) ((-1183 . -1215) 119250) ((-1183 . -95) 119216) ((-1043 . -23) T) ((-1183 . -35) 119182) ((-577 . -499) T) ((-1177 . -1212) 119148) ((-1177 . -1215) 119114) ((-1177 . -95) 119080) ((-1177 . -35) 119046) ((-366 . -1121) T) ((-364 . -1161) 119025) ((-358 . -1161) 119004) ((-350 . -1161) 118983) ((-1113 . -290) 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. -1060) 114008) ((-45 . -102) T) ((-823 . -102) T) ((-1188 . -646) 113905) ((-1250 . -25) T) ((-1250 . -21) T) ((-861 . -25) T) ((-44 . -372) 113889) ((-861 . -21) T) ((-737 . -458) 113840) ((-1300 . -619) 113822) ((-1289 . -1060) 113792) ((-1063 . -313) 113730) ((-677 . -1092) T) ((-612 . -1092) T) ((-396 . -1109) T) ((-577 . -25) T) ((-577 . -21) T) ((-182 . -1092) T) ((-162 . -1092) T) ((-157 . -1092) T) ((-155 . -1092) T) ((-1289 . -646) 113700) ((-627 . -1109) T) ((-705 . -893) 113682) ((-1277 . -1227) T) ((-229 . -313) 113620) ((-145 . -373) T) ((-1055 . -620) 113562) ((-1055 . -619) 113505) ((-317 . -916) NIL) ((-1235 . -850) T) ((-705 . -1047) 113450) ((-717 . -927) T) ((-480 . -1231) 113429) ((-1183 . -458) 113408) ((-1177 . -458) 113387) ((-334 . -102) T) ((-878 . -1121) T) ((-323 . -652) 113269) ((-320 . -654) 113090) ((-317 . -654) 113019) ((-480 . -562) 112970) ((-344 . -520) 112936) ((-556 . -152) 112886) ((-40 . -311) T) ((-849 . -619) 112868) ((-707 . -294) T) ((-878 . 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. -1237) 105497) ((-521 . -25) T) ((-501 . -306) T) ((-517 . -23) T) ((-516 . -25) T) ((-514 . -25) T) ((-513 . -23) T) ((-424 . -1060) 105471) ((-413 . -1058) T) ((-323 . -1067) T) ((-700 . -311) T) ((-424 . -646) 105445) ((-108 . -854) T) ((-718 . -732) T) ((-413 . -245) T) ((-413 . -235) 105424) ((-493 . -38) 105374) ((-219 . -38) 105324) ((-480 . -499) 105290) ((-1234 . -373) T) ((-1168 . -1153) T) ((-1110 . -102) T) ((-707 . -619) 105272) ((-707 . -620) 105187) ((-720 . -21) T) ((-720 . -25) T) ((-1144 . -102) T) ((-488 . -652) 104937) ((-135 . -619) 104919) ((-117 . -619) 104901) ((-158 . -25) T) ((-1299 . -1109) T) ((-878 . -645) 104849) ((-1297 . -1109) T) ((-970 . -102) T) ((-741 . -102) T) ((-721 . -102) T) ((-459 . -102) T) ((-822 . -458) 104800) ((-44 . -1109) T) ((-1097 . -856) T) ((-1072 . -313) 104651) ((-670 . -132) T) ((-1063 . -652) 104620) ((-676 . -723) 104604) ((-293 . -1067) T) ((-360 . -132) T) ((-357 . -132) T) ((-349 . -132) T) ((-267 . -132) T) ((-249 . -132) 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-657) 100403) ((-1135 . -646) 100300) ((-1221 . -562) 100279) ((-825 . -391) 100263) ((-717 . -562) T) ((-320 . -891) 100247) ((-320 . -893) 100172) ((-137 . -1227) T) ((-317 . -891) 100133) ((-317 . -893) NIL) ((-805 . -313) 100098) ((-323 . -723) 99939) ((-392 . -391) 99923) ((-328 . -327) 99900) ((-491 . -102) T) ((-480 . -25) T) ((-480 . -21) T) ((-424 . -38) 99874) ((-320 . -1047) 99537) ((-227 . -1212) T) ((-227 . -1215) T) ((-3 . -619) 99519) ((-317 . -1047) 99449) ((-2 . -1109) T) ((-2 . |RecordCategory|) T) ((-839 . -619) 99431) ((-1122 . -1067) 99361) ((-586 . -927) T) ((-570 . -826) T) ((-570 . -927) T) ((-501 . -927) T) ((-137 . -1047) 99345) ((-227 . -95) T) ((-171 . -148) 99324) ((-75 . -447) T) ((0 . -619) 99306) ((-75 . -401) T) ((-171 . -146) 99257) ((-227 . -35) T) ((-49 . -619) 99239) ((-483 . -1067) T) ((-493 . -233) 99221) ((-490 . -977) 99205) ((-488 . -854) 99184) ((-219 . -233) 99166) ((-81 . -447) T) ((-81 . -401) T) ((-1155 . -34) T) ((-821 . -174) 99145) 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-38) 98261) ((-267 . -645) 98209) ((-249 . -645) 98157) ((-707 . -1065) 98144) ((-601 . -1255) 98121) ((-1135 . -288) 98087) ((-323 . -174) 98018) ((-364 . -1109) T) ((-358 . -1109) T) ((-350 . -1109) T) ((-506 . -19) 98000) ((-1129 . -1047) 97982) ((-1111 . -152) 97966) ((-108 . -1109) T) ((-117 . -1065) 97953) ((-717 . -368) T) ((-506 . -610) 97928) ((-707 . -111) 97913) ((-442 . -102) T) ((-882 . -1272) T) ((-252 . -102) T) ((-45 . -1158) 97863) ((-117 . -111) 97848) ((-1302 . -619) 97815) ((-641 . -726) T) ((-613 . -726) T) ((-1302 . -496) 97797) ((-1279 . -619) 97779) ((-1235 . -619) 97761) ((-1233 . -856) T) ((-1221 . -1121) T) ((-821 . -520) 97694) ((-1044 . -1227) T) ((-242 . -1060) 97591) ((-1221 . -23) T) ((-1182 . -458) 97522) ((-950 . -152) 97506) ((-1177 . -313) 97391) ((-1176 . -1109) T) ((-242 . -646) 97333) ((-1168 . -1109) T) ((-1151 . -654) 97307) ((-1135 . -313) 97294) ((-531 . -102) T) ((-526 . -102) 97244) ((-1134 . -458) 97195) ((-1096 . -562) 97126) ((-1096 . -1231) 97105) ((-788 . -1231) 97084) ((-786 . -1231) 97063) ((-62 . -1227) T) ((-483 . -619) 97015) ((-483 . -620) 96937) ((-1089 . -723) 96805) ((-1003 . -1109) T) ((-788 . -562) 96716) ((-786 . -562) 96647) ((-488 . -417) 96616) ((-629 . -927) 96595) ((-460 . -1231) 96574) ((-737 . -313) 96561) ((-707 . -622) 96533) ((-404 . -619) 96515) ((-681 . -520) 96448) ((-670 . -25) T) ((-670 . -21) T) ((-460 . -562) 96379) ((-360 . -25) T) ((-360 . -21) T) ((-118 . -927) T) ((-118 . -826) NIL) ((-357 . -25) T) ((-357 . -21) T) ((-349 . -25) T) ((-349 . -21) T) ((-267 . -25) T) ((-267 . -21) T) ((-249 . -25) T) ((-249 . -21) T) ((-83 . -389) T) ((-83 . -401) T) ((-135 . -622) 96361) ((-117 . -622) 96333) ((-1013 . -1060) 96283) ((-1013 . -646) 96233) ((-950 . -989) 96217) ((-921 . -646) 96169) ((-921 . -1060) 96121) ((-917 . -21) T) ((-917 . -25) T) ((-878 . -856) 96072) ((-872 . -654) 96032) ((-717 . -1121) T) ((-717 . -23) T) ((-707 . -1058) T) ((-293 . -174) T) ((-707 . -235) T) ((-315 . 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88680) ((-483 . -1065) 88645) ((-664 . -132) T) ((-627 . -622) 88614) ((-1122 . -520) 88547) ((-341 . -132) T) ((-171 . -408) 88526) ((-488 . -723) 88468) ((-821 . -290) 88445) ((-483 . -111) 88401) ((-659 . -1067) T) ((-822 . -1060) 88244) ((-1288 . -1092) T) ((-1250 . -458) 88175) ((-822 . -646) 88024) ((-1287 . -1092) T) ((-1096 . -132) T) ((-1063 . -723) 87966) ((-788 . -132) T) ((-786 . -132) T) ((-577 . -458) T) ((-1036 . -520) 87899) ((-627 . -1058) T) ((-598 . -1109) T) ((-539 . -175) T) ((-467 . -132) T) ((-460 . -132) T) ((-1008 . -1227) 87868) ((-45 . -1109) T) ((-390 . -723) 87838) ((-823 . -1109) T) ((-482 . -520) 87771) ((-469 . -520) 87704) ((-1302 . -622) 87686) ((-459 . -372) 87656) ((-45 . -616) 87635) ((-320 . -306) T) ((-483 . -622) 87585) ((-1241 . -313) 87470) ((-676 . -619) 87432) ((-59 . -856) 87411) ((-1013 . -406) 87393) ((-554 . -619) 87375) ((-805 . -652) 87334) ((-821 . -610) 87311) ((-522 . -856) 87290) ((-502 . -856) 87269) ((-40 . -1231) T) ((-1008 . 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-313) 81728) ((-970 . -417) 81712) ((-705 . -1231) T) ((-638 . -290) 81665) ((-1096 . -645) 81613) ((-788 . -645) 81561) ((-786 . -645) 81509) ((-348 . -132) T) ((-293 . -619) 81491) ((-912 . -1109) T) ((-705 . -562) T) ((-130 . -622) 81473) ((-876 . -1121) T) ((-460 . -645) 81421) ((-912 . -910) 81405) ((-384 . -458) T) ((-493 . -1109) T) ((-950 . -313) 81343) ((-707 . -654) 81330) ((-555 . -850) T) ((-219 . -1109) T) ((-320 . -927) 81309) ((-317 . -927) T) ((-317 . -826) NIL) ((-396 . -726) T) ((-876 . -23) T) ((-117 . -654) 81296) ((-480 . -146) 81275) ((-424 . -417) 81259) ((-480 . -148) 81238) ((-110 . -495) 81220) ((-315 . -622) 81201) ((-2 . -619) 81183) ((-188 . -102) T) ((-1168 . -19) 81165) ((-1168 . -610) 81140) ((-664 . -21) T) ((-664 . -25) T) ((-599 . -1153) T) ((-1122 . -290) 81117) ((-341 . -25) T) ((-341 . -21) T) ((-242 . -652) 80867) ((-501 . -368) T) ((-1292 . -38) 80837) ((-1182 . -1060) 80660) ((-1151 . -1227) T) ((-1134 . -1060) 80503) ((-860 . -1060) 80487) 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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 5411c9f9..1a1ae0b1 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3481463042) +(30 . 3481665218) (4455 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -484,662 +484,662 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |writable?| |base| |parameters| |explimitedint| - |heap| |rightLcm| |returns| |denom| |solid| |innerEigenvectors| - |roughEqualIdeals?| |lintgcd| |subQuasiComponent?| |mapExponents| - |getSyntaxFormsFromFile| |lexico| |universe| |univariateSolve| - |f04arf| |generate| |patternVariable| |green| |primaryDecomp| - |modulus| |idealiserMatrix| |real?| |cond| |pi| |quasiRegular?| - |linearPolynomials| |OMread| |startTableGcd!| |logpart| - |pseudoRemainder| |part?| |integralBasis| |cap| |gderiv| |log10| - |increase| |infinity| |fillPascalTriangle| |nativeModuleExtension| - |incrementBy| |s17ajf| |index?| |fglmIfCan| |rightRank| |redmat| - |perfectNthPower?| |diagonals| |bitand| |d01ajf| |messagePrint| - |transcendenceDegree| |expand| |nextColeman| |tan2trig| - |useSingleFactorBound| |usingTable?| |createRandomElement| |f01bsf| - |froot| |cyclotomicDecomposition| |bitior| |fi2df| |bandedJacobian| - |aCubic| |filterWhile| |length| |map| |complementaryBasis| |simpson| - |formula| |selectMultiDimensionalRoutines| |difference| |decompose| - |d01akf| |cosIfCan| |region| |dihedral| |kernel| |setTex!| - |filterUntil| |viewWriteDefault| |scripts| |member?| |Beta| - |isQuotient| |droot| |factorsOfCyclicGroupSize| |rightDivide| - |shiftLeft| |outerProduct| |jokerMode| |draw| |lifting| |OMgetFloat| - |e02dff| |select| |s17agf| |controlPanel| |leadingBasisTerm| - |maxRowIndex| |lazyPrem| |antiAssociative?| |symbol| |getIdentifier| - |solid?| |mathieu23| |redPo| |meshFun2Var| |encodingDirectory| - |integralAtInfinity?| |currentEnv| |showTheFTable| - |indicialEquationAtInfinity| |minset| |argscript| |expression| - |polyRicDE| |wreath| |tanSum| |lexTriangular| |myDegree| |normalDenom| - |d02gbf| |setScreenResolution| |commaSeparate| |pastel| |nrows| - |changeThreshhold| |integer| |appendPoint| |arguments| |associative?| - |just| |maxdeg| |viewThetaDefault| |convert| |retractable?| - |lowerCase!| |previous| |max| |ncols| |drawCurves| |boundOfCauchy| - |ReduceOrder| |linSolve| |makeObject| |f2st| |extendedEuclidean| - |integralMatrixAtInfinity| |decomposeFunc| |roughBasicSet| |epilogue| - |height| |permutation| |OMlistSymbols| |rootProduct| |clipParametric| - |trace2PowMod| |qsetelt| |coef| |subTriSet?| |pointData| |sts2stst| ** - |pushdterm| |integrate| |setLength!| |monomial?| - |resultantReduitEuclidean| |lineColorDefault| |makeGraphImage| - |xRange| |unitNormal| |trivialIdeal?| |makeRecord| |OMgetEndAtp| - |diagonal| |showTheSymbolTable| |pushup| |fortranTypeOf| - |factorOfDegree| |norm| |imagJ| |yRange| |interpolate| |padecf| - |powern| |continuedFraction| |vectorise| |divisors| |cyclic?| - |symmetricPower| |abs| |nextPartition| |zRange| |listOfLists| - |principal?| |dAndcExp| |lfinfieldint| |tanh2coth| |symbolIfCan| - |e01bef| |stripCommentsAndBlanks| |extractTop!| |selectfirst| - |OMreceive| |map!| |separateDegrees| |label| |lllp| |upperCase!| - |cPower| |upperBound| |writeBytes!| |selectAndPolynomials| - |parametersOf| |algebraicVariables| |lo| |viewZoomDefault| - |beauzamyBound| |qsetelt!| |e04mbf| |inf| |e01sff| |zeroDimPrimary?| - |qPot| |ldf2vmf| |duplicates| |numericalOptimization| |seed| |module| - |incr| |modifyPointData| |rationalPoint?| |df2fi| |traceMatrix| - |iiasin| |createNormalPoly| |initial| |charClass| |push| - |doubleComplex?| |jacobian| |finite?| |complexEigenvalues| |cCsc| - |e02agf| |OMunhandledSymbol| |symbol?| |rational| Y - |conditionsForIdempotents| |getOrder| |genericRightNorm| |isImplies| - |routines| |extendedResultant| |primextendedint| |ricDsolve| |vark| - |rquo| |extract!| |edf2ef| |iisech| |nextPrime| |sinhIfCan| - |algebraicCoefficients?| |OMputApp| |internal?| - |useEisensteinCriterion?| |d01anf| |functionIsFracPolynomial?| - |maxColIndex| |normalDeriv| |henselFact| |powerAssociative?| |acsch| - |normInvertible?| |lambert| |viewport3D| |s18def| |readLine!| - |cyclotomicFactorization| |youngGroup| |constructor| - |complexElementary| |acotIfCan| |LazardQuotient| |e02daf| |tanhIfCan| - |imaginary| |absolutelyIrreducible?| |unparse| |BumInSepFFE| |nthCoef| - |nothing| |degree| |primintegrate| |dimensionsOf| |identification| - |tail| |option| |complexEigenvectors| |sorted?| |hasoln| - |identitySquareMatrix| |writeInt8!| |showSummary| |rules| |d02kef| - |s18dcf| |critM| |evaluateInverse| - |rewriteIdealWithQuasiMonicGenerators| |less?| |patternMatch| - |nodeOf?| |mapUnivariateIfCan| |dmp2rfi| - |setLegalFortranSourceExtensions| |direction| |nextPrimitivePoly| - |linearDependence| |quickSort| |double?| |computeBasis| - |stopTableGcd!| |regime| |subset?| |showAttributes| |exprToGenUPS| - |clearTheFTable| |balancedBinaryTree| |computePowers| - |leftRegularRepresentation| |iomode| |belong?| |symFunc| - |pleskenSplit| |diagonal?| |leadingIndex| |innerSolve| |separate| - |intPatternMatch| |rightTrim| |numberOfIrreduciblePoly| |leftRecip| - |numericIfCan| |overset?| |halfExtendedSubResultantGcd2| - |LagrangeInterpolation| |printInfo!| |figureUnits| |backOldPos| - |argument| |quartic| |leftTrim| |OMputEndObject| |unknown| |unmakeSUP| - |univariate?| |sort!| |limitedint| |leftNorm| |component| - |tableForDiscreteLogarithm| |OMputAtp| |zerosOf| |credPol| - |symmetricSquare| |reduceLODE| |localIntegralBasis| |constantOpIfCan| - |maxint| |closeComponent| |extendIfCan| F |nullity| |realSolve| - |e02zaf| |tube| F2FG |superHeight| |taylorRep| |duplicates?| |pow| - |swap!| |mainCoefficients| |mapExpon| |OMgetType| |maxIndex| - |addMatchRestricted| |iidprod| |monicDecomposeIfCan| |floor| - |equality| |gcdcofact| |iicos| |coerceL| |say| |chebyshevU| - |setfirst!| |alphabetic| |intersect| |stiffnessAndStabilityOfODEIF| - |flexible?| |rationalIfCan| |function| |f02akf| |atoms| |remove| - |imagj| |plot| |perfectNthRoot| |shape| |uncouplingMatrices| - |maxPoints| |linearAssociatedLog| |tan2cot| |basisOfMiddleNucleus| - |airyAi| |fTable| |check| |monomial| |setCondition!| |mkIntegral| - |getProperties| |rightGcd| |bat| |writeLine!| |polarCoordinates| - |fortranComplex| |getProperty| |removeSinSq| |open| |LyndonBasis| - |multivariate| |last| |eval| |sh| |assoc| |irreducible?| |redPol| - |multiset| |hermiteH| |iiasech| |secIfCan| |shellSort| |modularFactor| - |UP2ifCan| |OMopenFile| |splitConstant| |null| |variables| |result| - |setStatus| |initiallyReduce| |startStats!| |generalTwoFactor| - |bezoutMatrix| |sn| |lieAlgebra?| |e02def| |totalGroebner| |pattern| - |not| |factorFraction| |cyclotomic| |weierstrass| |reset| |lookup| - |stoseInvertibleSetsqfreg| |satisfy?| |expandTrigProducts| - |bezoutDiscriminant| |iiacos| |repeatUntilLoop| |explicitEntries?| - |and| |extractClosed| |iisqrt3| |reverseLex| |fortranDoubleComplex| - |bitTruth| |outputArgs| |red| |swapColumns!| |operations| |iicsch| - |leadingTerm| |numberOfComputedEntries| |or| |minRowIndex| |isTimes| - |pop!| |write| |linearPart| |PollardSmallFactor| |computeInt| - |userOrdered?| |f01brf| |dimension| |scalarTypeOf| |normalize| - |optional?| |xor| |mathieu12| |sturmVariationsOf| |save| - |fortranCarriageReturn| |dimensions| |radPoly| |cycles| |setColumn!| - |hermite| |elementary| |complexLimit| |message| |getOperator| |f04asf| - |case| |taylor| |squareFreePolynomial| |LyndonCoordinates| |pr2dmp| - |mergeFactors| |nextsousResultant2| |OMputEndError| |close!| |diag| - |normal?| |graphs| |overlabel| |Zero| |laurent| |OMputAttr| |remove!| - |internalAugment| |exprex| |chainSubResultants| |inspect| |OMgetBVar| - |puiseux| |One| |firstUncouplingMatrix| |geometric| |OMgetAttr| - |minrank| |power| |listLoops| |complexZeros| |intermediateResultsIF| - |bernoulli| |aLinear| |ceiling| |specialTrigs| |subPolSet?| |minimize| - |delay| |getCode| LODO2FUN |ref| |hi| |cyclicCopy| |complexRoots| - |realElementary| |hessian| |rootKerSimp| |conical| |lcm| |besselJ| - |lifting1| |inv| |matrixGcd| |removeRoughlyRedundantFactorsInPols| - |genus| |failed?| |createLowComplexityTable| |completeHensel| |s18adf| - |prime?| |ground?| |constant| |f04qaf| |screenResolution3D| - |useEisensteinCriterion| |besselY| |sncndn| |extractPoint| |nextItem| - |flexibleArray| |OMputEndBind| |ground| |fullDisplay| |repSq| - |algebraic?| |append| |solveRetract| |internalInfRittWu?| - |pointColorDefault| |open?| |style| |makeFloatFunction| |setOfMinN| - |lSpaceBasis| |contains?| |OMreadFile| |pile| |divergence| - |leadingMonomial| |gcd| |elt| |relativeApprox| |subspace| |summation| - |createNormalPrimitivePoly| |elColumn2!| |stopMusserTrials| |moebius| - |d01aqf| |enqueue!| |outputAsTex| |stosePrepareSubResAlgo| |false| - |leadingCoefficient| |alternatingGroup| |changeBase| |randomR| - |stopTableInvSet!| |setProperty| |discreteLog| |iiasinh| |OMputError| - |possiblyInfinite?| |listOfMonoms| |subResultantsChain| |in?| - |primitiveMonomials| |output| |atanhIfCan| |sqfrFactor| - |stoseInvertibleSetreg| |e02bef| |stoseLastSubResultant| - |quasiRegular| |readInt8!| |useNagFunctions| |firstNumer| - |horizConcat| |OMgetApp| |reductum| |subCase?| |getPickedPoints| - |alphanumeric?| |nthExpon| |definingEquations| |inverseColeman| |pdct| - |quotient| |mainDefiningPolynomial| |compBound| |normalizedDivide| - |sumSquares| |contractSolve| |powerSum| |mindeg| |bezoutResultant| - |reducedQPowers| |numberOfHues| |hcrf| |coth2tanh| |transform| - |singRicDE| |asimpson| |setVariableOrder| |entry?| |d01gbf| |power!| - |integer?| |algebraicSort| |associatedSystem| |denominator| - |inHallBasis?| |quasiAlgebraicSet| |rationalFunction| |pseudoDivide| - |separant| |palgRDE| |numberOfComponents| |palginfieldint| - |gcdPrimitive| |basisOfRightNucleus| |createLowComplexityNormalBasis| - |children| |cycleSplit!| |univcase| |isNot| |taylorQuoByVar| - |categoryMode| |iiacosh| |nonLinearPart| |rischDEsys| |doubleDisc| - |numberOfComposites| |reducedDiscriminant| |cfirst| |numerator| - |extractIndex| |integralMatrix| |shuffle| |LiePoly| |outputList| |Nul| - |iisec| |build| |setValue!| |rightAlternative?| |normalizeIfCan| - |s13adf| |OMputBind| |substring?| |baseRDEsys| |putProperties| - |s17dlf| |univariatePolynomials| |SturmHabichtMultiple| |readByte!| - |setelt!| |squareTop| |shufflein| |pointColorPalette| |digamma| - |rightTraceMatrix| |graphStates| |nor| |sparsityIF| |poisson| - |reduceByQuasiMonic| |stoseInvertible?reg| |llprop| |mainKernel| - |quoted?| |makeSketch| |scaleRoots| |preprocess| |suffix?| |leftLcm| - |plusInfinity| |reciprocalPolynomial| |palgint| |primeFrobenius| - |c05adf| |signatureAst| |OMsupportsCD?| |endSubProgram| - |LazardQuotient2| |linearAssociatedExp| |genericRightTraceForm| - |remainder| |selectODEIVPRoutines| |minusInfinity| |changeNameToObjf| - |qinterval| |OMclose| |lfintegrate| |cAcosh| |infLex?| - |readLineIfCan!| |key?| |over| |selectOrPolynomials| |prefix?| - |cot2tan| |balancedFactorisation| |basisOfCommutingElements| - |rightTrace| |selectPolynomials| |monicLeftDivide| |recip| |palgint0| - |addMatch| |sylvesterSequence| |integers| |indiceSubResultant| - |makeViewport2D| |iibinom| |setleaves!| |gcdprim| |mapBivariate| |Ci| - |besselI| |key| |cyclicParents| |diff| |external?| |moreAlgebraic?| - |nonSingularModel| |ip4Address| |d03faf| |reindex| |bipolar| |cAtanh| - |palgLODE0| |Si| |invertibleElseSplit?| |lastSubResultantElseSplit| - |lazyPseudoDivide| |tab| |s17aff| |moduloP| |npcoef| |factorials| - |ef2edf| |e01bff| |Lazard| |filename| |completeEchelonBasis| - |infieldint| |whatInfinity| |doublyTransitive?| |conditionP| |orbit| - |tubePointsDefault| |type| |eigenvalues| |weights| |e04ucf| - |subNodeOf?| |isList| |fixPredicate| |primitivePart!| |returnType!| - |leftMult| |removeRoughlyRedundantFactorsInPol| |mapMatrixIfCan| - |numberOfFractionalTerms| |ListOfTerms| |brillhartIrreducible?| - |coord| |s19aaf| |parse| |multiplyExponents| |LyndonWordsList1| - |viewWriteAvailable| |reify| |environment| |permutationRepresentation| - |infix?| |removeZeroes| |pushNewContour| |bfKeys| |rootRadius| |next| - |clipPointsDefault| |indiceSubResultantEuclidean| |c05nbf| - |strongGenerators| |createPrimitiveElement| |modularGcd| |mask| - |atrapezoidal| |componentUpperBound| |genericLeftNorm| |iicoth| - |OMputVariable| |constantToUnaryFunction| |lazyPquo| - |removeIrreducibleRedundantFactors| |wholeRadix| |ranges| - |lazyPseudoRemainder| |f01rcf| |imagk| |determinant| |pointLists| - |lfextlimint| |zeroDimensional?| |lazyIntegrate| |e04ycf| |subHeight| - |scanOneDimSubspaces| |nextLatticePermutation| |clearTheIFTable| - |scripted?| |triangulate| |setErrorBound| |isEquiv| |sPol| |mpsode| - |f01rdf| |quasiMonic?| |minPoly| |representationType| |findBinding| - |fractionFreeGauss!| EQ |e04gcf| |basisOfLeftAnnihilator| - |computeCycleEntry| |s01eaf| |coth2trigh| |rroot| |move| |reflect| - |checkPrecision| |child?| |augment| |upDateBranches| - |restorePrecision| |basisOfNucleus| |s19abf| |lhs| |taylorIfCan| - |supRittWu?| |expandPower| |zero?| |primextintfrac| |FormatArabic| - |imagI| |generalLambert| |node?| |mapDown!| |leviCivitaSymbol| - |monicDivide| |rightZero| |rhs| |setImagSteps| |exponential| - |multinomial| |oddlambert| |insertBottom!| |pushdown| |solveid| - |iipow| |basis| |OMgetEndApp| |OMgetEndAttr| |binary| |whitePoint| - |copy!| |collectUpper| |topFortranOutputStack| |sizePascalTriangle| - |escape| GF2FG |doubleFloatFormat| |intensity| |rischDE| - |fixedPointExquo| |imagE| |c06ecf| |collect| |rationalPower| |psolve| - |outlineRender| |OMgetError| |range| |intChoose| |associator| |back| - |predicates| |quotientByP| |nextNormalPoly| |bitLength| |kmax| - |setScreenResolution3D| |showTheRoutinesTable| - |getMultiplicationTable| |index| |f01qcf| |OMencodingBinary| - |coshIfCan| |stoseInvertibleSet| |wholeRagits| |solve| |laguerre| - |hdmpToDmp| |f07fdf| |coleman| |variationOfParameters| |rule| |f01maf| - |sequences| |particularSolution| |deleteRoutine!| - |evenInfiniteProduct| |OMgetEndBind| |numberOfFactors| |currentScope| - |iprint| |leftRemainder| |pointColor| |accuracyIF| |branchIfCan| - |rotate| |compactFraction| |subResultantGcdEuclidean| |Frobenius| - |halfExtendedResultant2| |repeating?| |coordinate| |pointPlot| - |createZechTable| |exprHasLogarithmicWeights| |bottom!| |getlo| |unit| - |pair| |ridHack1| |eyeDistance| |SFunction| |homogeneous?| |s19acf| - |c06frf| |value| |curve| |structuralConstants| |mapUp!| - |unrankImproperPartitions0| |hexDigit| |cSinh| |resetAttributeButtons| - |OMgetEndBVar| |distdfact| |slex| |OMgetEndObject| |whileLoop| - |tanintegrate| |d01asf| |totalDifferential| |closed?| |approximants| - |putProperty| |number?| |radicalEigenvector| |leadingIdeal| - |extractBottom!| |implies| |changeMeasure| |intcompBasis| - |sturmSequence| |numberOfOperations| |hue| |wronskianMatrix| |product| - |bombieriNorm| |entry| |cSin| |dictionary| |subResultantGcd| - |setprevious!| |makeTerm| |curryRight| |listYoungTableaus| |f02adf| - |head| |stFunc1| |plotPolar| |setRealSteps| |topPredicate| |rootPower| - |complexIntegrate| |macroExpand| |f04mcf| |sub| |writeByte!| - |incrementKthElement| |s18aff| |karatsuba| |triangular?| |buildSyntax| - |cAcoth| |root?| |voidMode| |startTableInvSet!| |mapGen| - |antiCommutator| |uniform| |inconsistent?| |zeroSquareMatrix| - |saturate| |leftUnits| |setvalue!| |schwerpunkt| |reverse| |monic?| - |OMencodingXML| |connect| |shanksDiscLogAlgorithm| |integral| 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- |innerSolve1| |padicFraction| |toScale| |bubbleSort!| |linkToFortran| - |isMult| |rightFactorIfCan| |changeName| |polyRDE| |normal01| - |derivative| |testDim| |cAsech| |f01ref| |getButtonValue| |lyndon?| - |cup| |readIfCan!| |quadraticForm| |scan| |cCot| - |multiplyCoefficients| |d01alf| |e02bcf| |exponentialOrder| - |prepareDecompose| |hMonic| |parts| |OMputEndBVar| |s20adf| |terms| - |bigEndian| |legendreP| |youngDiagram| |e02akf| - |degreeSubResultantEuclidean| |primitiveElement| |socf2socdf| - |delete!| |genericLeftDiscriminant| |pack!| |firstSubsetGray| - |explicitlyEmpty?| |rotatey| |positive?| |rename| |generic| |curve?| - SEGMENT |makeViewport3D| |error| |curryLeft| |biRank| - |removeConstantTerm| |port| |cotIfCan| |primPartElseUnitCanonical| - |swapRows!| |exQuo| |cAtan| |quote| |leadingSupport| |assert| - |regularRepresentation| |normDeriv2| |c06eaf| |getVariableOrder| - |exactQuotient| |wordInStrongGenerators| |computeCycleLength| - |stFunc2| |maximumExponent| |binaryTournament| |prinpolINFO| - |elseBranch| |t| |outputAsScript| |rationalApproximation| - |quadraticNorm| |arbitrary| |overbar| |smith| |tower| |setFieldInfo| - |bumptab1| |iisin| |quoByVar| |semiResultantEuclidean1| - |modularGcdPrimitive| |loadNativeModule| |sumOfDivisors| |graphCurves| - |cAsinh| |normalElement| |showTheIFTable| |leftOne| |setLabelValue| - |d02bhf| |dn| |inverse| |rootNormalize| |divide| |discriminant| - |interactiveEnv| |leftGcd| |slash| |algebraicDecompose| |s17acf| - |OMopenString| |leftAlternative?| |iiabs| |f07adf| |realRoots| - |fortranLiteralLine| |palgextint| |leftRank| |zeroVector| |elRow2!| - |findCycle| |hypergeometric0F1| |midpoints| |iiacsc| |raisePolynomial| - |minGbasis| |f07aef| |lookupFunction| |removeSinhSq| |adjoint| - |complexNumeric| |isobaric?| |sech2cosh| |block| |f01qdf| |dmpToHdmp| - |bivariate?| |rotatez| |upperCase| |cons| |rewriteIdealWithRemainder| - |acothIfCan| |const| |f2df| |dmpToP| |solve1| |kernels| - |trigs2explogs| |e02ddf| |nextPrimitiveNormalPoly| |step| - |viewSizeDefault| |hostByteOrder| |arrayStack| |tableau| - |setPrologue!| |operator| |rk4qc| |assign| |isAbsolutelyIrreducible?| - |fmecg| |f04jgf| |randomLC| |movedPoints| |operators| |insert!| - |hspace| |character?| |float?| |collectQuasiMonic| |applyRules| - |rotatex| |critMTonD1| |rightOne| |univariate| |prolateSpheroidal| - |squareFreeLexTriangular| |iteratedInitials| |getConstant| |nullSpace| - |laguerreL| |selectSumOfSquaresRoutines| |deepestInitial| |coerce| - |comment| |tRange| |alternative?| |thetaCoord| |OMputEndApp| - |eigenMatrix| |readInt16!| |vertConcat| |setPredicates| |construct| - |normFactors| |basisOfRightNucloid| |source| |createThreeSpace| - |radix| |problemPoints| |separateFactors| UTS2UP |factor| - |integralRepresents| |kovacic| |internalIntegrate0| |deriv| - |permutations| |fullPartialFraction| |KrullNumber| |rightQuotient| - |sqrt| |var1Steps| |infieldIntegrate| |moduleSum| |s19adf| - |divideIfCan| |reducedForm| |is?| |qelt| |colorDef| |real| |aromberg| - |squareMatrix| |radicalOfLeftTraceForm| |cTan| |critpOrder| |contours| - |bounds| |imag| |jordanAdmissible?| |currentCategoryFrame| - |clipWithRanges| |linear?| |logIfCan| |cCos| |mappingMode| - |extensionDegree| |directProduct| |target| |compose| |viewpoint| - |ipow| |singularAtInfinity?| |closed| |lyndon| |mainMonomials| - |cycleTail| |logical?| |resize| |rightMinimalPolynomial| |rootBound| - |zeroMatrix| |makeMulti| |seriesToOutputForm| |setMaxPoints3D| - |iCompose| |one?| |brace| |isOp| |ptree| |cycleElt| |eigenvector| - |kind| |corrPoly| |inputOutputBinaryFile| |lyndonIfCan| - |leftScalarTimes!| |d01fcf| |destruct| |s17dgf| |lastSubResultant| - |basisOfLeftNucleus| |splitNodeOf!| |completeEval| |op| |leastPower| - |s13acf| |oddInfiniteProduct| |basisOfCenter| |principalAncestors| - |OMencodingUnknown| |multiEuclidean| |cAcot| |innerint| - |internalZeroSetSplit| |s17def| |round| |resetVariableOrder| |ravel| - |outputFloating| |SturmHabichtSequence| |multiple?| |infiniteProduct| - |rk4a| |debug3D| |printCode| |extractIfCan| |symmetricTensors| - |lieAdmissible?| |symmetricRemainder| |plus!| |reshape| |addBadValue| - |badValues| |denomLODE| |divideExponents| |acscIfCan| |setelt| - |magnitude| |getExplanations| |generalSqFr| |perfectSquare?| - |solveLinearPolynomialEquationByRecursion| - |factorSquareFreePolynomial| |distribute| |elaborateFile| - |removeCosSq| |prinb| |contract| |elem?| |exprToXXP| |minPoints| - |normalise| |row| |measure| |recoverAfterFail| |copy| |rootOf| - |OMgetSymbol| |nonQsign| |squareFreeFactors| |extend| - |clearTheSymbolTable| |union| |closedCurve| |pToHdmp| |rur| - |OMmakeConn| |createIrreduciblePoly| |replace| |rightUnits| - |quadratic| |orthonormalBasis| |cyclePartition| |repeating| |c06gbf| - |tanNa| |OMgetObject| |bipolarCylindrical| |leadingExponent| |sign| - |f04atf| |update| |triangularSystems| |completeSmith| |inrootof| - |purelyAlgebraic?| |s14abf| |autoCoerce| |laurentRep| |leftZero| - |unitsColorDefault| |sortConstraints| |characteristicSet| |c06fuf| - |firstDenom| |ran| |meatAxe| |equiv| |fortranLogical| - |splitDenominator| |every?| |internalIntegrate| |infix| - |rightExactQuotient| |diagonalMatrix| |clearDenominator| - |semiLastSubResultantEuclidean| |BasicMethod| |insertMatch| - |cartesian| |mainExpression| |nand| |sort| |weakBiRank| |jacobi| - |airyBi| |ideal| |ramified?| |ramifiedAtInfinity?| |bringDown| |prem| - |reduced?| |antisymmetric?| |setleft!| |lowerCase| |invertIfCan| - |showFortranOutputStack| |readUInt32!| |numberOfMonomials| |imagi| - |rank| |position| |cAcsc| |select!| |atanIfCan| |largest| |digits| - |numerators| |lexGroebner| |match?| |bindings| |setsubMatrix!| - |iisqrt2| |shrinkable| |extendedIntegrate| |rootPoly| |dequeue!| - |digit?| |completeHermite| |charthRoot| |definingInequation| - |deepExpand| |arity| |normalizeAtInfinity| |random| |middle| |iiperm| - |nextSublist| |fractRadix| |nthExponent| |parabolic| |sinhcosh| - |numberOfDivisors| |times!| |irreducibleFactor| |makeCos| - |polynomialZeros| |Is| |iiasec| |OMcloseConn| |outputBinaryFile| - |processTemplate| |commutativeEquality| |setrest!| - |eisensteinIrreducible?| |vedf2vef| |harmonic| |iFTable| |fprindINFO| - |viewPosDefault| |OMgetBind| |toseLastSubResultant| |mapSolve| - |approxSqrt| |fortranReal| |tanh2trigh| |postfix| |ocf2ocdf| |declare| - |dual| |unprotectedRemoveRedundantFactors| |distance| - |inverseIntegralMatrix| |isOpen?| |prod| |atom?| |minPoints3D| - |setMinPoints3D| |numberOfVariables| |decreasePrecision| |e02ajf| - |mathieu24| |rename!| |increment| |parseString| |monomRDEsys| - |inverseLaplace| |numFunEvals3D| |errorInfo| |leastMonomial| |decimal| - |elliptic?| |asinhIfCan| |associates?| |tanh| |diophantineSystem| - |optpair| |setClosed| |rangePascalTriangle| - |factorSquareFreeByRecursion| |SturmHabichtCoefficients| |digit| - |iitanh| |arg1| |coth| |yCoord| |simpleBounds?| - |rootOfIrreduciblePoly| |close| |lquo| |singleFactorBound| |minIndex| - |cyclicGroup| |edf2fi| |btwFact| |arg2| |sech| |randnum| |cothIfCan| - |lfunc| |rootDirectory| |identityMatrix| |hasTopPredicate?| - |binaryTree| |csch| |addPoint2| |rightExtendedGcd| |pade| |before?| - |callForm?| |imagK| |subresultantSequence| |display| |setchildren!| - |bright| |setPosition| |physicalLength!| |conditions| |endOfFile?| - |asinh| |enterInCache| |nthr| |stirling2| |groebner| |factorial| - |e02bbf| |color| |leftDiscriminant| |match| |leftExtendedGcd| - |polCase| |acosh| RF2UTS |stop| |fortranLinkerArgs| - |resultantEuclidean| |primes| |algebraicOf| |read!| |algintegrate| - |precision| |odd?| |atanh| |shade| |var2StepsDefault| |makeFR| - |showAll?| |coordinates| |polygon?| |nthRoot| |li| |bothWays| - |resultantnaif| |acoth| |commonDenominator| |linearlyDependentOverZ?| - |super| |host| |LyndonWordsList| |prindINFO| |setStatus!| - |clearTable!| |multiEuclideanTree| |prevPrime| |coerceS| |asech| - |e02bdf| |sin?| |finiteBasis| |input| |perfectSqrt| |constantLeft| - |lift| |categoryFrame| |euclideanNormalForm| |f04maf| |dot| |mat| - |inc| |df2st| |iExquo| |library| |linears| |pushuconst| |reduce| - |moebiusMu| |expenseOfEvaluationIF| |multiple| |trapezoidalo| - |constDsolve| |e02dcf| |nullary?| |log2| |comparison| |rubiksGroup| - |unit?| |leaves| |polyPart| |lazyVariations| |applyQuote| |wholePart| - |null?| |stoseInternalLastSubResultant| |initTable!| |xn| |expt| - |maxPoints3D| |palgintegrate| |fortranCompilerName| |toseInvertible?| - |mainValue| |euclideanGroebner| |totolex| |rightMult| |e04dgf| - |partialQuotients| |standardBasisOfCyclicSubmodule| |fortranDouble| - |setTopPredicate| |rootsOf| |getBadValues| |set| |diagonalProduct| - |nextIrreduciblePoly| |noValueMode| |removeSuperfluousQuasiComponents| - |powmod| |binaryFunction| |ruleset| |exactQuotient!| |conjugate| - |fortran| |id| |consnewpol| |isConnected?| |readUInt8!| |externalList| - |deleteProperty!| |quasiMonicPolynomials| |box| |coerceImages| - |acschIfCan| |aQuadratic| |inRadical?| |lazy?| |tensorProduct| - |trueEqual| |bit?| |rombergo| |toroidal| |fill!| |simplifyLog| - |isAtom| |test| |listexp| |table| |octon| |factorList| |s14baf| - |trunc| |c06ekf| |suchThat| |invmultisect| |makeSUP| |gensym| |insert| - |new| |prefixRagits| |internalDecompose| |addPointLast| |pomopo!| - |getMeasure| |ratDenom| |obj| |capacity| |sumOfKthPowerDivisors| - |s17adf| |putGraph| |basisOfRightAnnihilator| |cscIfCan| |content| - |functionIsOscillatory| |any| |mkcomm| |nextSubsetGray| |cache| - |OMputObject| |iiatanh| |mvar| |monomRDE| |lex| |mapdiv| - |goodnessOfFit| |genericLeftMinimalPolynomial| |f04mbf| |triangSolve| - |decrease| |delete| |eq| |linearDependenceOverZ| |signature| - |expenseOfEvaluation| |position!| |prefix| |putColorInfo| - |trailingCoefficient| |cycleEntry| |bernoulliB| |mathieu22| - |shiftRight| |predicate| |byte| |iter| |janko2| |sinh2csch| |basicSet| - |anticoord| |symmetric?| |evenlambert| |mappingAst| |elaborate| - |recolor| |mathieu11| |outputMeasure| |makeop| |weight| |option?| - |makeEq| |sup| |f02bjf| |subst| |highCommonTerms| - |extendedSubResultantGcd| |sizeLess?| |rspace| |OMbindTCP| |coerceP| - |degreeSubResultant| |column| |split| |s17aef| |resetBadValues| - |hasSolution?| |mergeDifference| |OMputBVar| |collectUnder| - |getOperands| |rangeIsFinite| |c06gsf| |bag| |reduction| |normalForm| - |iterationVar| |sqfree| |antisymmetricTensors| |eulerPhi| |script| - |OMputString| |removeRedundantFactors| |permutationGroup| - |setMinPoints| |radicalSimplify| |changeWeightLevel| - |wordInGenerators| |leaf?| |primitivePart| |e02gaf| |low| - |axesColorDefault| |left| |useSingleFactorBound?| |makeSeries| - |presuper| |cross| |retractIfCan| |lowerCase?| |safeCeiling| |s17dhf| - |flatten| |cAcos| |/\\| |complexForm| |powers| |right| |int| - |create3Space| |drawStyle| |tryFunctionalDecomposition?| |mix| |ord| - |coefficients| |objects| |tex| |relationsIdeal| |factorSFBRlcUnit| - |\\/| |generalInfiniteProduct| |numer| |unitVector| |scale| - |fortranCharacter| |groebner?| |lagrange| |nil| |infinite| + |Record| |Union| |raisePolynomial| |rationalPoints| |reduction| + |whileLoop| |imagj| |leftFactor| |denom| |irreducibleFactor| + |doubleResultant| |digamma| |leftTrace| |minGbasis| |normalForm| + |plot| |tanintegrate| |possiblyNewVariety?| |makeCos| |generate| + |rightTraceMatrix| |numericalIntegration| |ffactor| |f07aef| + |iterationVar| |cond| |HenselLift| |perfectNthRoot| |d01asf| |pi| + |polynomialZeros| |nthRootIfCan| |graphStates| |lookupFunction| + |solveInField| |sqfree| |totalDifferential| |log10| |shape| |infinity| + |viewDefaults| |Is| |incrementBy| |nor| |e01sef| |cCsch| + |removeSinhSq| |antisymmetricTensors| |uncouplingMatrices| |bitand| + |replaceKthElement| |closed?| |iiasec| |expand| |sparsityIF| + |OMreadStr| |unvectorise| |adjoint| |messagePrint| |eulerPhi| + |flatten| |maxPoints| |bitior| |setButtonValue| |approximants| + |OMcloseConn| |filterWhile| |map| |isobaric?| |OMgetAtp| |poisson| + |internalSubQuasiComponent?| |transcendenceDegree| |OMputString| + |checkForZero| |linearAssociatedLog| |putProperty| |kernel| + |outputBinaryFile| |filterUntil| |connectTo| |isQuotient| + |reduceByQuasiMonic| |sech2cosh| |squareFreePart| + |removeRedundantFactors| |draw| |comment| |tan2cot| |number?| |updatD| + |processTemplate| |select| |even?| |stoseInvertible?reg| |block| + |hostPlatform| |permutationGroup| |symbol| |basisOfMiddleNucleus| + |zeroDimPrime?| |outputList| |radicalEigenvector| + |commutativeEquality| |currentEnv| |difference| |e01daf| |llprop| + |f01qdf| |romberg| |setMinPoints| |expression| |airyAi| |leadingIdeal| + |d01apf| |setrest!| |decompose| |mainKernel| |OMwrite| |dmpToHdmp| + |transcendentalDecompose| |radicalSimplify| |integer| |fTable| + |extractBottom!| |roughBase?| |eisensteinIrreducible?| |convert| + |d01akf| |quoted?| |numberOfChildren| |divisor| |bivariate?| + |changeWeightLevel| |setClipValue| |check| |makeObject| |implies| + |vedf2vef| |makeSketch| |cosIfCan| |height| |closedCurve?| |rotatez| + |minColIndex| |wordInGenerators| |meshPar2Var| |setCondition!| + |changeMeasure| |coef| |harmonic| ** |scaleRoots| |setEmpty!| + |expintfldpoly| |upperCase| |parents| |leaf?| |mkIntegral| + |intcompBasis| |frobenius| |iFTable| |makeRecord| |kroneckerDelta| + |preprocess| |skewSFunction| |rewriteIdealWithRemainder| + |primitivePart| |outerProduct| |getProperties| |sturmSequence| + |removeRedundantFactorsInPols| |fprindINFO| |leftLcm| |vspace| + |acothIfCan| |argumentList!| |e02gaf| |rightGcd| |numberOfOperations| + |csc2sin| |viewPosDefault| |reciprocalPolynomial| |subresultantVector| + |const| |bracket| |low| |bat| |validExponential| |hue| |OMgetBind| + |label| |palgint| |selectIntegrationRoutines| |f2df| |torsion?| + |axesColorDefault| |lo| |writeLine!| |cAcsch| |wronskianMatrix| + |toseLastSubResultant| |sumOfSquares| |primeFrobenius| |compdegd| + |dmpToP| |useSingleFactorBound?| |incr| |polarCoordinates| + |semiIndiceSubResultantEuclidean| |product| |mapSolve| |initial| + |someBasis| |solve1| |c05adf| |acsch| |concat!| |makeSeries| + |fortranComplex| |bombieriNorm| |insertionSort!| |approxSqrt| Y + |degreePartition| |signatureAst| |trigs2explogs| + |countRealRootsMultiple| |presuper| |getProperty| |cSin| |d02raf| + |fortranReal| |OMsupportsCD?| |headRemainder| |sizeMultiplication| + |e02ddf| |cross| |removeSinSq| |dictionary| |makeYoungTableau| + |tanh2trigh| |doubleRank| |endSubProgram| |nextPrimitiveNormalPoly| + |copyInto!| |lowerCase?| |LyndonBasis| |edf2efi| |subResultantGcd| + |postfix| |countable?| |LazardQuotient2| |viewSizeDefault| + |RemainderList| |constructor| |safeCeiling| |sh| |setprevious!| + |f01qef| |ocf2ocdf| |linearAssociatedExp| |antiCommutative?| |mesh| + |hostByteOrder| |nothing| |s17dhf| |irreducible?| |gbasis| |makeTerm| + |tail| |option| |dual| |arrayStack| |showSummary| + |genericRightTraceForm| |medialSet| |supersub| |rules| |cAcos| + |redPol| |curryRight| |laurentIfCan| + |unprotectedRemoveRedundantFactors| |bandedJacobian| |e02aef| + |remainder| |radicalRoots| |tableau| |complexForm| |multiset| |f02bbf| + |listYoungTableaus| |distance| |hexDigit?| |s13aaf| + |selectODEIVPRoutines| |aCubic| |showAttributes| |setPrologue!| + |powers| |macroExpand| |hermiteH| |knownInfBasis| |f02adf| + |inverseIntegralMatrix| |changeNameToObjf| |se2rfi| |groebgen| |rk4qc| + |create3Space| |rightTrim| |iiasech| |head| + |stoseIntegralLastSubResultant| |isOpen?| |qinterval| + |generateIrredPoly| |toseInvertibleSet| |assign| |rank| |drawStyle| + |leftTrim| |yCoordinates| |unknown| |stFunc1| |prod| |pascalTriangle| + |OMclose| |listConjugateBases| |isAbsolutelyIrreducible?| + |tryFunctionalDecomposition?| |asin| |direction| |plotPolar| + |createRandomElement| |sec2cos| |atom?| |lift| |lfintegrate| |c02agf| + |pToDmp| |fmecg| |mix| F |nextPrimitivePoly| |acos| |setRealSteps| + |createPrimitiveNormalPoly| |f01bsf| |minPoints3D| |sort| |reduce| + |complementaryBasis| |cAcosh| |transcendent?| |entries| |f04jgf| |ord| + |linearDependence| |atan| |OMgetInteger| |topPredicate| + |setMinPoints3D| |say| |randomLC| |f04axf| |coefficients| |quickSort| + |acot| |rootPower| |elliptic| |linear| |numberOfVariables| + |horizConcat| |remove| |function| |removeRedundantFactorsInContents| + |alternating| |writable?| |movedPoints| |relationsIdeal| |double?| + |asec| |complexIntegrate| |resultantReduit| |decreasePrecision| + |generalizedInverse| |OMgetApp| |monomial| |operators| |explimitedint| + |setAdaptive3D| |open| |factorSFBRlcUnit| |computeBasis| |acsc| + |outputSpacing| |leftPower| |f04mcf| |polynomial| |e02ajf| |random| + |multivariate| |last| |subCase?| |eval| |heap| |reducedSystem| |lists| + |insert!| |generalInfiniteProduct| |stopTableGcd!| |sinh| |assoc| + |null| |mathieu24| |semiDiscriminantEuclidean| |variables| + |getPickedPoints| |result| |rightLcm| |hspace| |refine| |unitVector| + |regime| |cosh| |dihedralGroup| |froot| |intensity| |rename!| + |pattern| |not| |alphanumeric?| |typeLists| |returns| |reset| + |character?| |probablyZeroDim?| |scale| |subset?| |tanh| |rischDE| + |simplify| |increment| |and| |nthExpon| |gcdPolynomial| |solid| + |divisorCascade| |float?| |fortranCharacter| |exprToGenUPS| |coth| + |s14aaf| |fixedPointExquo| |parseString| |operations| |or| |orbits| + |definingEquations| |write| |innerEigenvectors| |groebner?| + |clearTheFTable| |sech| |depth| |makeCrit| |imagE| |monomRDEsys| + |rotatey| |xor| |removeSquaresIfCan| |inverseColeman| |save| |d01amf| + |roughEqualIdeals?| |lagrange| |balancedBinaryTree| |csch| + |monomialIntegrate| |c06ecf| |inverseLaplace| |message| |df2mf| |case| + |pdct| |taylor| |leadingCoefficientRicDE| |positive?| |lintgcd| + |computePowers| |asinh| |factorPolynomial| |collect| |byte| + |numFunEvals3D| |quotient| |Zero| |bitCoef| |laurent| |rename| UP2UTS + |subQuasiComponent?| |leftRegularRepresentation| |acosh| + |integralLastSubResultant| |rationalPower| |stop| |irCtor| |One| + |mainDefiningPolynomial| |puiseux| |colorFunction| |generic| + |mapExponents| |iomode| |atanh| |psolve| |deref| |leftZero| + |compBound| |c05pbf| |OMParseError?| |curve?| |getSyntaxFormsFromFile| + |formula| |belong?| |acoth| |hi| |outlineRender| |squareFree| + |unitsColorDefault| |dioSolve| |lcm| |normalizedDivide| |inv| + |cot2trig| |makeViewport3D| |lexico| |asech| |symFunc| + |drawComplexVectorField| |OMgetError| |sortConstraints| |ground?| + |sumSquares| |semiResultantEuclideannaif| |curveColorPalette| + |curryLeft| |universe| |pleskenSplit| |range| |tubePlot| + |characteristicSet| |constant| |ground| |append| + |semiDegreeSubResultantEuclidean| |contractSolve| |biRank| |scopes| + |sumOfKthPowerDivisors| |univariateSolve| |multiple| |diagonal?| + |intChoose| |noKaratsuba| |c06fuf| |zeroOf| |powerSum| |elt| + |leadingMonomial| |gcd| |removeConstantTerm| |OMgetVariable| |f04arf| + |s17adf| |applyQuote| |leadingIndex| |associator| |nrows| |ode1| + |firstDenom| |int| |conjunction| |false| |leadingCoefficient| |mindeg| + |littleEndian| |cotIfCan| |putGraph| |patternVariable| + |createMultiplicationTable| |innerSolve| |back| |ncols| |ran| + |bezoutResultant| |primitiveMonomials| |zCoord| |output| + |primPartElseUnitCanonical| |monicModulo| |basisOfRightAnnihilator| + |green| |separate| |predicates| |binomial| |meatAxe| |reducedQPowers| + |eulerE| |reductum| |constantOperator| |swapRows!| |primaryDecomp| + |cscIfCan| |intPatternMatch| |ruleset| |shallowExpand| |quotientByP| + |equiv| |numberOfHues| |showArrayValues| |hclf| |exQuo| |content| + |modulus| |numberOfIrreduciblePoly| |nextNormalPoly| |qualifier| + |fortranLogical| |hcrf| |subSet| |cAtan| |square?| + |functionIsOscillatory| |idealiserMatrix| |leftRecip| + |increasePrecision| |bitLength| |splitDenominator| + |integralBasisAtInfinity| |coth2tanh| |quote| |high| |mkcomm| |real?| + |numericIfCan| |suchThat| |kmax| |laplacian| |every?| |lfextendedint| + |transform| |sdf2lst| |leadingSupport| |nextSubsetGray| + |quasiRegular?| |overset?| |d02ejf| |setScreenResolution3D| + |internalIntegrate| |bfEntry| |singRicDE| |regularRepresentation| + |genericRightDiscriminant| |OMputObject| |linearPolynomials| + |cyclotomicDecomposition| |halfExtendedSubResultantGcd2| |invmod| + |showTheRoutinesTable| |infix| |genericPosition| |asimpson| + |normDeriv2| |ode2| |iiatanh| |OMread| |partialNumerators| + |LagrangeInterpolation| |fi2df| |getMultiplicationTable| + |rightExactQuotient| |rightFactorCandidate| |setVariableOrder| + |insertRoot!| |c06eaf| |mvar| |startTableGcd!| |printInfo!| + |functorData| |f01qcf| |diagonalMatrix| |entry?| |supDimElseRittWu?| + |acosIfCan| |getVariableOrder| |logpart| |monomRDE| |figureUnits| + |plusInfinity| |OMencodingBinary| |rotate!| |clearDenominator| + |shiftRoots| |d01gbf| |bivariatePolynomials| |exactQuotient| |lex| + |pseudoRemainder| |backOldPos| |minusInfinity| |coshIfCan| |tab1| + |semiLastSubResultantEuclidean| |updatF| |power!| |tablePow| + |wordInStrongGenerators| |mapdiv| |part?| |argument| |basisOfCentroid| + |stoseInvertibleSet| |BasicMethod| |integer?| |superscript| + |computeCycleLength| |rightCharacteristicPolynomial| |goodnessOfFit| + |integralBasis| |quartic| |rowEch| |wholeRagits| |insertMatch| |key| + |ptFunc| |algebraicSort| |irreducibleRepresentation| |stFunc2| + |genericLeftMinimalPolynomial| |OMputEndObject| |expressIdealMember| + |solve| |cartesian| |associatedSystem| |hconcat| |maximumExponent| + |ParCondList| |f04mbf| |unmakeSUP| |laguerre| + |selectOptimizationRoutines| |mainExpression| |filename| |denominator| + |quatern| |binaryTournament| |lazyPremWithDefault| |triangSolve| + |type| |univariate?| |tanQ| |hdmpToDmp| |nand| |inHallBasis?| + |OMputFloat| |iilog| |prinpolINFO| |decrease| |sort!| |f07fdf| + |setMaxPoints| |weakBiRank| |parse| |maxrank| |quasiAlgebraicSet| + |size?| |elseBranch| |linearDependenceOverZ| |limitedint| |forLoop| + |coleman| |jacobi| |next| |minimalPolynomial| |rationalFunction| + |stopTable!| |outputAsScript| |expenseOfEvaluation| |leftNorm| + |c06gqf| |variationOfParameters| |airyBi| |iflist2Result| + |pseudoDivide| |rationalApproximation| |more?| |position!| |component| + |getRef| |f01maf| |ideal| |separant| |iiacsch| |quadraticNorm| + |reseed| |cap| |putColorInfo| |tableForDiscreteLogarithm| |evaluate| + |sequences| |ramified?| |palgRDE| |startTable!| |arbitrary| |identity| + |trailingCoefficient| EQ |OMputAtp| |ScanArabic| |particularSolution| + |ramifiedAtInfinity?| |setright!| |numberOfComponents| |overbar| + |semiResultantEuclidean2| |cycleEntry| |zerosOf| + |leftMinimalPolynomial| |deleteRoutine!| |bringDown| |lhs| + |palginfieldint| FG2F |quotedOperators| |smith| |bernoulliB| |credPol| + |mainForm| |evenInfiniteProduct| |prem| |rhs| |gcdPrimitive| + |rewriteIdealWithHeadRemainder| |Aleph| |setFieldInfo| |mathieu22| + |symmetricSquare| |goto| |OMgetEndBind| |reduced?| + |basisOfRightNucleus| |pdf2ef| |splitLinear| |bumptab1| |shiftRight| + |reduceLODE| |numberOfFactors| |fixedPoints| |antisymmetric?| + |createLowComplexityNormalBasis| |isPlus| |binding| |iisin| |janko2| + |localIntegralBasis| |splitSquarefree| |currentScope| |setleft!| + |generalizedContinuumHypothesisAssumed?| |children| |omError| + |quoByVar| |sinh2csch| |constantOpIfCan| |rootSimp| |iprint| + |lowerCase| |index| |s21bbf| |cycleSplit!| |semiResultantEuclidean1| + |fractionPart| |basicSet| |maxint| |rule| |distFact| |leftRemainder| + |invertIfCan| |alphabetic?| |univcase| |modularGcdPrimitive| + |totalLex| |anticoord| |closeComponent| |pointColor| |modifyPoint| + |showFortranOutputStack| |f02abf| |isNot| |unitCanonical| + |sumOfDivisors| |symmetric?| |extendIfCan| |accuracyIF| |fibonacci| + |readUInt32!| |pair| |monomialIntPoly| |taylorQuoByVar| |csubst| + |graphCurves| |evenlambert| |value| |nullity| |expintegrate| + |branchIfCan| |numberOfMonomials| |categoryMode| |split!| |cAsinh| + |characteristicSerie| |mappingAst| |realSolve| |subMatrix| |rotate| + |imagi| |iiacosh| |seriesSolve| |generalizedEigenvector| + |normalElement| |elaborate| |datalist| |e02zaf| |compactFraction| + |mainMonomial| |cAcsc| |nonLinearPart| |lowerBound| |showTheIFTable| + |constant?| |recolor| |entry| |tube| |subResultantGcdEuclidean| + |getGraph| |select!| |rischDEsys| |loopPoints| |leftOne| |complement| + |mathieu11| |radicalSolve| |Frobenius| |atanIfCan| |doubleDisc| + |cycleLength| |setLabelValue| |pseudoQuotient| |outputMeasure| + |primextendedint| |c06gcf| |halfExtendedResultant2| |largest| + |idealSimplify| |numberOfComposites| |d02bhf| |f07fef| |sn| |makeop| + |ricDsolve| |exponential1| |repeating?| |digits| |setProperties| + |reducedDiscriminant| |dn| |rarrow| |weight| |vark| |reverse| + |coordinate| |birth| |numerators| |e02adf| |inverse| |option?| |rquo| + |pointPlot| |makingStats?| |lexGroebner| |call| |f04qaf| + |viewPhiDefault| |rootNormalize| |univariatePolynomial| |makeEq| + |extract!| |graeffe| |createZechTable| |bindings| |screenResolution3D| + |mainPrimitivePart| |c06ebf| |divide| |sup| |edf2ef| + |exprHasLogarithmicWeights| |e01bgf| |s17ajf| |setsubMatrix!| |iroot| + |useEisensteinCriterion| |tubePoints| |discriminant| |f02bjf| |iisech| + |index?| |iisqrt2| |tree| |e02ahf| |besselY| |interactiveEnv| + |mapUnivariate| |highCommonTerms| |nextPrime| |fortranInteger| + |isEquiv| |shrinkable| |sncndn| |rightUnit| |meshPar1Var| |leftGcd| + |extendedSubResultantGcd| |sinhIfCan| |sPol| |integerIfCan| + |extendedIntegrate| |binarySearchTree| |extractPoint| |matrixConcat3D| + |slash| |sizeLess?| |algebraicCoefficients?| |noLinearFactor?| + |mpsode| |rootPoly| |groebSolve| |nextItem| |typeForm| |rspace| + |OMputApp| |rischNormalize| |f01rdf| |dequeue!| |flexibleArray| + |errorKind| |readUInt16!| |traverse| |OMbindTCP| |internal?| + |quasiMonic?| |extractSplittingLeaf| |completeHermite| |subtractIfCan| + |OMputEndBind| |positiveRemainder| |defineProperty| |coerceP| + |useEisensteinCriterion?| |minPoly| |unitNormalize| |generator| + |charthRoot| |fullDisplay| |changeVar| |patternMatchTimes| + |countRealRoots| |representationType| |degreeSubResultant| |search| + |d01anf| |f02awf| |keys| |singular?| |repSq| |nary?| |factorsOfDegree| + |column| |functionIsFracPolynomial?| |rem| + |semiSubResultantGcdEuclidean1| |findBinding| |lieAdmissible?| + |sinIfCan| |region| |rdregime| |algebraic?| |exponents| |s17ahf| + |split| |quo| |maxColIndex| |fractionFreeGauss!| |d01bbf| + |symmetricRemainder| |simplifyExp| |dihedral| |inputBinaryFile| + |HermiteIntegrate| |solveRetract| |mesh?| |stack| |s17aef| + |normalDeriv| |e04gcf| |bat1| |exprHasAlgebraicWeight| |plus!| + |setTex!| |internalLastSubResultant| |internalInfRittWu?| + |exprHasWeightCosWXorSinWX| |push!| |div| |henselFact| + |basisOfLeftAnnihilator| |s18acf| |jacobiIdentity?| |addBadValue| + |virtualDegree| |viewWriteDefault| |negative?| |pointColorDefault| + |acoshIfCan| |condition| |fortranCompilerName| |powerAssociative?| + |exquo| |computeCycleEntry| |divideIfCan!| |palglimint0| |badValues| + |member?| |returnTypeOf| |open?| |setEpilogue!| |infRittWu?| + |toseInvertible?| |normInvertible?| ~= + |solveLinearPolynomialEquationByFractions| |s01eaf| |d02gaf| + |denomLODE| |Beta| |style| |OMencodingSGML| |OMsend| |bivariateSLPEBR| + |mainValue| |#| |dim| |lambert| |deepestTail| |coth2trigh| + |dualSignature| |divideExponents| |droot| |makeFloatFunction| + |uniform01| |invertible?| |nlde| |euclideanGroebner| ~ |viewport3D| + |rroot| |composites| |idealiser| |acscIfCan| |concat| + |factorsOfCyclicGroupSize| |exp1| |setOfMinN| |normalized?| |inR?| + |diagonals| |totolex| |newReduc| |s18def| |move| |matrix| |algint| + |magnitude| |lSpaceBasis| |rightDivide| |nextNormalPrimitivePoly| + |bandedHessian| |d01ajf| |cubic| |rightMult| |readLine!| |reflect| + |f02aaf| |getExplanations| |viewDeltaYDefault| |contains?| |shiftLeft| + |clearCache| |explicitlyFinite?| |dequeue| |surface| |e04dgf| + |cyclotomicFactorization| |symbolTable| |presub| |child?| |Gamma| + |generalSqFr| |jokerMode| |laplace| |OMreadFile| |innerSolve1| + |UpTriBddDenomInv| |partialQuotients| |youngGroup| + |selectNonFiniteRoutines| |augment| |thenBranch| |perfectSquare?| + |lifting| |pile| |lastSubResultantEuclidean| |padicFraction| + |subResultantChain| |standardBasisOfCyclicSubmodule| |att2Result| + |complexElementary| |symmetricProduct| |upDateBranches| + |pushFortranOutputStack| |solveLinearPolynomialEquationByRecursion| + |char| |OMgetFloat| |cRationalPower| |divergence| |toScale| |setlast!| + |fortranDouble| |failed| |level| |popFortranOutputStack| |acotIfCan| + |d02bbf| |restorePrecision| |factorSquareFreePolynomial| + |roughUnitIdeal?| |e02dff| |paren| |relativeApprox| |unravel| + |bubbleSort!| |setTopPredicate| |basisOfNucleus| |LazardQuotient| + |central?| |readable?| |distribute| |outputAsFortran| |s17agf| + |cyclicSubmodule| |subspace| |parabolicCylindrical| |linkToFortran| + |rootsOf| |e02daf| |s19abf| |pole?| |elaborateFile| |limitedIntegrate| + |controlPanel| |summation| |eigenvectors| |isMult| |nil?| + |getBadValues| |tanhIfCan| |s17dcf| |taylorIfCan| |expint| + |removeCosSq| |leadingBasisTerm| |createNormalPrimitivePoly| |f04faf| + |leftDivide| |rightFactorIfCan| |diagonalProduct| |imaginary| + |wordsForStrongGenerators| |supRittWu?| |prinb| |An| + |basisOfLeftNucloid| |maxRowIndex| |elColumn2!| + |semiSubResultantGcdEuclidean2| |changeName| |compile| + |nextIrreduciblePoly| |absolutelyIrreducible?| |B1solve| |expandPower| + |contract| |expandLog| |stopMusserTrials| |chineseRemainder| + |lazyPrem| |isExpt| |selectMultiDimensionalRoutines| |float| |polyRDE| + |nextColeman| |noValueMode| |unparse| |zero?| |deepCopy| |elem?| + |pair?| |clipBoolean| |antiAssociative?| |moebius| + |resultantEuclideannaif| |normal01| |tan2trig| + |removeSuperfluousQuasiComponents| |simplifyPower| |BumInSepFFE| + |primextintfrac| |second| |exprToXXP| |partialFraction| + |getIdentifier| |d01aqf| |mainVariable?| |derivative| + |leftRankPolynomial| |powmod| |nthCoef| |FormatArabic| + |removeSuperfluousCases| |third| |getDatabase| |minPoints| + |alphanumeric| |solid?| |categories| |enqueue!| |testDim| |varselect| + |binaryFunction| |degree| |constantRight| |imagI| |normalise| + |enterPointData| |setRow!| |mathieu23| |blue| |outputAsTex| |cAsech| + |void| |exactQuotient!| |primintegrate| |e01bhf| |generalLambert| + |gramschmidt| |row| |redPo| |string?| |stosePrepareSubResAlgo| + |genericRightMinimalPolynomial| |f01ref| |conjugate| |dimensionsOf| + |rowEchelonLocal| |node?| |setAttributeButtonStep| |measure| |expr| + |meshFun2Var| |alternatingGroup| |printTypes| |getButtonValue| + |OMconnectTCP| |consnewpol| |identification| |mapDown!| |cycle| + |recoverAfterFail| |coefficient| |encodingDirectory| |substring?| + |changeBase| |positiveSolve| |lyndon?| |removeCoshSq| |isConnected?| + |complexEigenvectors| |leviCivitaSymbol| |s21bcf| |frst| |rootOf| + |integralAtInfinity?| |randomR| |mapmult| GE |cup| |zag| |readUInt8!| + |sorted?| |currentSubProgram| |monicDivide| |OMgetSymbol| |hdmpToP| + |chvar| |showTheFTable| |suffix?| |log| |stopTableInvSet!| GT + |setFormula!| |readIfCan!| |externalList| |hasoln| |rightZero| + |Hausdorff| |internalSubPolSet?| |nonQsign| |variable| |setProperty| + |indicialEquationAtInfinity| |goodPoint| LE |relerror| |quadraticForm| + |deleteProperty!| |setImagSteps| |identitySquareMatrix| + |leastAffineMultiple| |discreteLog| |OMsupportsSymbol?| + |squareFreeFactors| |iterators| BY |minset| |prefix?| |coefChoose| LT + |removeDuplicates!| |scan| |quasiMonicPolynomials| |writeInt8!| + |exponential| |graphState| |quadratic?| |extend| |iiasinh| |argscript| + |fracPart| |cCot| |weighted| |delta| |coerceImages| |d02kef| + |multinomial| |notelem| |eof?| |clearTheSymbolTable| |polyRicDE| + |OMputError| |mirror| |chiSquare| |multiplyCoefficients| |acschIfCan| + |s18dcf| |complexNormalize| |oddlambert| |abelianGroup| |closedCurve| + |wreath| |iiatan| |possiblyInfinite?| |modTree| |d01alf| |aQuadratic| + |critM| |insertBottom!| |reverse!| |iiacoth| |pToHdmp| |tanSum| + |printStatement| |listOfMonoms| |exprToUPS| |e02bcf| |inRadical?| + |evaluateInverse| |mkPrim| |pushdown| |ScanFloatIgnoreSpacesIfCan| + |rur| |lexTriangular| |realEigenvectors| |subResultantsChain| + |exponentialOrder| |axes| |lazy?| + |rewriteIdealWithQuasiMonicGenerators| |unknownEndian| |solveid| + |binomThmExpt| |OMmakeConn| |myDegree| |infix?| |in?| |resultant| + |indices| |prepareDecompose| |tensorProduct| NOT |less?| |iipow| + |light| |createIrreduciblePoly| |UnVectorise| |mask| |normalDenom| + |primlimintfrac| |atanhIfCan| |hMonic| |c06fpf| |trueEqual| OR + |patternMatch| |basis| |asecIfCan| |cSech| |replace| |pdf2df| |d02gbf| + |sqfrFactor| |lambda| |primlimitedint| |OMputEndBVar| |bit?| AND + |nodeOf?| |drawToScale| |OMgetEndApp| |rightUnits| |infinite?| + |stoseInvertibleSetreg| |quasiComponent| |partialDenominators| + |s20adf| |rombergo| |mapUnivariateIfCan| |commutator| |OMgetEndAttr| + |queue| |quadratic| |iifact| |e02bef| |indicialEquations| |terms| + |toroidal| |dmp2rfi| |setnext!| |binary| |orthonormalBasis| + |LiePolyIfCan| |checkPrecision| |outputGeneral| + |stoseLastSubResultant| |bigEndian| |s15aef| |fill!| |debug| + |setLegalFortranSourceExtensions| |whitePoint| |subscript| |rootSplit| + |cyclePartition| |s20acf| |quasiRegular| |legendreP| |qqq| + |simplifyLog| D |safeFloor| |copy!| |musserTrials| |repeating| + |readInt8!| |latex| |directSum| |youngDiagram| |isAtom| + |nextPartition| |discriminantEuclidean| |collectUpper| |c06gbf| + |Lazard2| |useNagFunctions| |po| |e02akf| |cosSinInfo| |listexp| + |listOfLists| |topFortranOutputStack| |OMputSymbol| + |coerceListOfPairs| |tanNa| |combineFeatureCompatibility| |firstNumer| + |degreeSubResultantEuclidean| |components| |octon| |principal?| + |sizePascalTriangle| |minimumDegree| |OMgetObject| |headReduce| + |primitiveElement| |merge| |factorList| |dAndcExp| |escape| + |generalPosition| |bipolarCylindrical| |totalfract| |elementary| + |insertTop!| |socf2socdf| |polygamma| |s14baf| |lfinfieldint| * + |readInt32!| GF2FG |leadingExponent| |hasPredicate?| |complexLimit| + |rightPower| |delete!| |showRegion| |trunc| |tanh2coth| |minus!| + |doubleFloatFormat| |safetyMargin| |sign| |f02ajf| |getOperator| + |genericLeftDiscriminant| |nsqfree| |c06ekf| |optimize| |symbolIfCan| + |f04atf| |mainContent| |f04asf| |sample| |pack!| |wrregime| |center| + |invmultisect| |anfactor| |e01bef| |e04ucf| = |branchPoint?| + |triangularSystems| |copies| |squareFreePolynomial| |properties| + |firstSubsetGray| |f01mcf| |makeSUP| |print| |stripCommentsAndBlanks| + |rk4| |subNodeOf?| |element?| |completeSmith| |LyndonCoordinates| + |nodes| |translate| |explicitlyEmpty?| |complete| |gensym| |resolve| + |ratPoly| |extractTop!| < |isList| |inrootof| |cExp| |heapSort| + |pr2dmp| |prefixRagits| |localAbs| |selectfirst| > |fixPredicate| + |physicalLength| |purelyAlgebraic?| |mergeFactors| |OMputInteger| + |cSec| |prime| |internalDecompose| |OMreceive| <= |radicalEigenvalues| + |primitivePart!| |s14abf| |symbolTableOf| |nextsousResultant2| |tanAn| + |rightNorm| |typeList| |printInfo| |gderiv| |addPointLast| + |separateDegrees| |s15adf| >= |returnType!| |e01saf| |laurentRep| + |iiacot| |OMputEndError| |f02aef| |ParCond| |increase| |pomopo!| + |lllp| |leftMult| |qroot| |close!| |e04jaf| |gcdcofactprim| + |viewport2D| |getMeasure| |upperCase!| + |removeRoughlyRedundantFactorsInPol| |aQuartic| |ldf2lst| |cCos| + |diag| |OMgetEndError| |palglimint| |approxNthRoot| |ratDenom| |has?| + |cPower| |mapMatrixIfCan| + |mappingMode| |partition| |irForm| + |normal?| |true| |univariatePolynomialsGcds| |useSingleFactorBound| + |e01sbf| |capacity| - |upperBound| |numberOfFractionalTerms| + |fractRagits| |order| |extensionDegree| |sylvesterMatrix| |f02wef| + |graphs| |usingTable?| |solveLinearlyOverQ| |interpret| + |brillhartTrials| |mantissa| |writeBytes!| / |ListOfTerms| |compose| + |inGroundField?| |rightRemainder| |overlabel| |jordanAlgebra?| + |karatsubaOnce| |read!| |selectAndPolynomials| |brillhartIrreducible?| + |extendedint| |twist| |viewpoint| |rightRankPolynomial| |OMputAttr| + |ScanRoman| |OMlistCDs| |category| |algintegrate| |nil| |parametersOf| + |coord| |OMconnOutDevice| |ipow| |createPrimitivePoly| |dark| + |remove!| |localUnquote| |listRepresentation| |domain| |odd?| + |algebraicVariables| |s19aaf| |generic?| |singularAtInfinity?| + |leftFactorIfCan| |OMsetEncoding| |internalAugment| |legendre| + |disjunction| |package| |shade| |init| |viewZoomDefault| + |halfExtendedSubResultantGcd1| |multiplyExponents| |closed| + |torsionIfCan| |shift| |zeroDim?| |exprex| |numberOfCycles| + |selectsecond| |var2StepsDefault| |beauzamyBound| |approximate| + |LyndonWordsList1| |trim| |curveColor| |lyndon| |ddFact| + |chainSubResultants| |outputForm| |unexpand| |makeFR| |complex| + |e04mbf| |explogs2trigs| |viewWriteAvailable| |rowEchLocal| + |mainMonomials| |inspect| |OMUnknownSymbol?| |pureLex| |allRootsOf| + |showAll?| |inf| |reify| |solveLinearPolynomialEquation| |list?| + |cycleTail| |show| |OMgetBVar| |purelyAlgebraicLeadingMonomial?| + |showIntensityFunctions| |zeroSetSplit| |coordinates| |property| + |upperCase?| |e01sff| |environment| |varList| |logical?| + |stoseInvertible?| |denominators| |firstUncouplingMatrix| |recur| + |ratDsolve| |polygon?| |zeroDimPrimary?| |newLine| + |permutationRepresentation| |algDsolve| |resize| |trace| |geometric| + |printStats!| |printingInfo?| |initials| |nthRoot| |qPot| |empty| + |removeZeroes| |rightMinimalPolynomial| |realEigenvalues| |ignore?| + |top!| |OMgetAttr| |nullary| |parts| |bothWays| |units| |ldf2vmf| + |exponent| |pushNewContour| |localReal?| |rootBound| |minrank| + |interReduce| |drawComplex| |expextendedint| |resultantnaif| + |duplicates| |bfKeys| |df2ef| |imports| |zeroMatrix| |retract| |exp| + |branchPointAtInfinity?| |power| |finiteBound| |stoseSquareFreePart| + |commonDenominator| |numericalOptimization| |rootRadius| |factorset| + |makeMulti| |factorSquareFree| |GospersMethod| |listLoops| |any?| + |truncate| |linearlyDependentOverZ?| |seed| |createNormalElement| + |clipPointsDefault| |iiGamma| |seriesToOutputForm| |complexZeros| + |plenaryPower| |swap| |leftQuotient| |host| |module| |flagFactor| + |indiceSubResultantEuclidean| |setMaxPoints3D| |setOrder| + |intermediateResultsIF| |bumprow| |lazyEvaluate| |characteristic| + |LyndonWordsList| |code| |modifyPointData| |rightScalarTimes!| + |c05nbf| |iCompose| |initiallyReduced?| |PDESolve| |bernoulli| + |unary?| |semicolonSeparate| |prindINFO| |qelt| |rationalPoint?| + |strongGenerators| |primPartElseUnitCanonical!| |one?| |totalDegree| + |aLinear| |coHeight| |linearlyDependent?| |ScanFloatIgnoreSpaces| + |qsetelt| |setStatus!| |df2fi| |integralDerivationMatrix| + |createPrimitiveElement| |isOp| |bumptab| |freeOf?| |ceiling| + |groebnerIdeal| |cos2sec| |clearTable!| |xRange| |traceMatrix| + |modularGcd| |sechIfCan| |cycleElt| |hitherPlane| |specialTrigs| + |setref| |oblateSpheroidal| |e04naf| |multiEuclideanTree| |yRange| + |iiasin| |getStream| |atrapezoidal| |eigenvector| |front| + |OMUnknownCD?| |subPolSet?| |genericLeftTraceForm| |twoFactor| + |prevPrime| |zRange| |dom| |createNormalPoly| |Ei| |plus| + |componentUpperBound| |corrPoly| |mdeg| |minimize| |addiag| |find| + |writeUInt8!| |map!| |coerceS| |charClass| |genericLeftNorm| + |simpsono| |getMultiplicationMatrix| |inputOutputBinaryFile| |rst| + |delay| |f02agf| |f04adf| |qsetelt!| |e02bdf| |push| |iicoth| |s17akf| + |associatedEquations| |lyndonIfCan| |linearMatrix| |getCode| + |screenResolution| |stronglyReduce| |sin?| |doubleComplex?| + |OMputVariable| |isAnd| |leftScalarTimes!| |padicallyExpand| + |stirling1| |gethi| LODO2FUN |top| |hasHi| |finiteBasis| + |constantToUnaryFunction| |jacobian| |times| |definingPolynomial| + |d01fcf| |OMserve| |dflist| |ref| |iicsc| |roman| |perfectSqrt| + |title| |comp| |finite?| |subscriptedVariables| |lazyPquo| |s17dgf| + |permanent| |generalizedEigenvectors| |status| |cyclicCopy| |fortran| + |eq?| |polar| |constantLeft| |fglmIfCan| |systemCommand| |s21bdf| + |complexEigenvalues| |lastSubResultant| + |removeIrreducibleRedundantFactors| |cosh2sech| |options| |continue| + |noncommutativeJordanAlgebra?| |complexRoots| |expIfCan| |child| + |categoryFrame| |rightRank| |cCsc| |getGoodPrime| |wholeRadix| + |basisOfLeftNucleus| |cLog| |realElementary| |leftExactQuotient| + |rightRegularRepresentation| |adaptive| |euclideanNormalForm| |e| + |ranges| |erf| |e02agf| |RittWuCompare| |monom| |lowerPolynomial| + |splitNodeOf!| |node| |mapCoef| |hessian| |stoseInvertible?sqfreg| + |s21baf| |list| |f04maf| |completeEval| |lazyPseudoRemainder| + |OMunhandledSymbol| |normal| |adaptive3D?| |empty?| |string| + |rootKerSimp| |expPot| |karatsubaDivide| |complexNumericIfCan| |car| + |dot| |symbol?| |var2Steps| |f01rcf| |leastPower| + |monicRightFactorIfCan| |conical| |iicot| |certainlySubVariety?| + |bsolve| |cdr| |mat| |tubeRadius| |dilog| |rational| |common| |imagk| + |packageCall| |s13acf| |attributeData| |createMultiplicationMatrix| + |besselJ| |setDifference| |shallowCopy| |df2st| + |conditionsForIdempotents| |sin| |invertibleSet| |determinant| + |oddInfiniteProduct| |lighting| |setIntersection| |lifting1| + |resetNew| |numFunEvals| |mainCharacterization| |iExquo| |cos| + |getOrder| |functionIsContinuousAtEndPoints| |pointLists| + |basisOfCenter| |xCoord| |paraboloidal| |matrixGcd| |parametric?| + |makeSin| |setUnion| |linears| |genericRightNorm| |tan| |lfextlimint| + |dimensionOfIrreducibleRepresentation| |principalAncestors| + |enumerate| |lflimitedint| |rightRecip| + |removeRoughlyRedundantFactorsInPols| |e01baf| |apply| |pushuconst| + |isImplies| |cot| |singularitiesOf| |zeroDimensional?| + |OMencodingUnknown| |removeRoughlyRedundantFactorsInContents| |genus| + |unaryFunction| |spherical| |perspective| |moebiusMu| |cycleRagits| + |routines| |sec| |lazyIntegrate| |zero| |multiEuclidean| + |listBranches| |genericRightTrace| |double| |failed?| + |radicalEigenvectors| |solveLinear| |size| |expenseOfEvaluationIF| + |extendedResultant| |csc| |e04ycf| |mindegTerm| |commutative?| |cAcot| + |createLowComplexityTable| |width| |irVar| |script| |chebyshevT| + |rdHack1| |trapezoidalo| |extension| |subHeight| |And| |innerint| + |makeprod| |completeHensel| |coercePreimagesImages| |pquo| + |removeZero| |constDsolve| |setScreenResolution| |readBytes!| + |scanOneDimSubspaces| |Or| |pmComplexintegrate| |internalZeroSetSplit| + |algSplitSimple| |fillPascalTriangle| |pol| |s18adf| |SturmHabicht| + |first| |e02dcf| |commaSeparate| |charpol| |nextLatticePermutation| + |Not| |outputFixed| |s17def| |setPoly| |tex| |prime?| |equation| + |stFuncN| |nativeModuleExtension| |composite| |rest| |nullary?| + |pastel| |palgextint0| |clearTheIFTable| |c02aff| |round| |complex?| + |super| |headAst| |substitute| |log2| |changeThreshhold| |convergents| + |scripted?| |polyred| |resetVariableOrder| |secIfCan| |hash| + |removeDuplicates| |signAround| |f02xef| |comparison| |appendPoint| + |triangulate| |purelyTranscendental?| |outputFloating| |fixedDivisor| + |shellSort| |count| |declare!| |morphism| |nthFractionalTerm| + |rubiksGroup| |associative?| |mr| |setErrorBound| |newSubProgram| + |SturmHabichtSequence| |getCurve| |digit?| |modularFactor| |name| + |optional| |constantCoefficientRicDE| |blankSeparate| |unit?| |just| + |multiple?| |showAllElements| |UP2ifCan| |body| |cardinality| + |crushedSet| |polyPart| |maxdeg| |integerBound| |infLex?| |prinshINFO| + |infiniteProduct| |OMopenFile| |iidsum| |parent| |lazyVariations| + |viewThetaDefault| |cylindrical| |readLineIfCan!| |rk4a| |clipSurface| + |splitConstant| |elaboration| |ODESolve| |wholePart| |retractable?| + |bits| |key?| |makeResult| |debug3D| |setStatus| |null?| |lowerCase!| + |over| |autoReduced?| |printCode| |numberOfPrimitivePoly| + |initiallyReduce| |fortranLiteral| |sub| + |stoseInternalLastSubResultant| |max| |cyclic| |selectOrPolynomials| + |tryFunctionalDecomposition| |extractIfCan| |box| |startStats!| + |segment| |cTanh| |writeByte!| |error| |initTable!| |drawCurves| + SEGMENT |gradient| |cot2tan| |critB| |symmetricTensors| |port| + |generalTwoFactor| |numberOfNormalPoly| |incrementKthElement| |dec| + |xn| |balancedFactorisation| |boundOfCauchy| |assert| + |tubeRadiusDefault| |redmat| |bezoutMatrix| |s18aff| |extractProperty| + |expt| |basisOfCommutingElements| |ReduceOrder| |perfectNthPower?| + |indicialEquation| |createGenericMatrix| |collectQuasiMonic| + |lieAlgebra?| |t| |submod| |karatsuba| |maxPoints3D| |applyRules| + |linSolve| |yellow| |rightTrace| |tower| |monomials| |e02def| + |triangular?| |asechIfCan| |palgintegrate| |loadNativeModule| |f2st| + |makeVariable| |selectPolynomials| |rotatex| |measure2Result| |subst| + |s18aef| |totalGroebner| |predicate| |buildSyntax| |extendedEuclidean| + |d03edf| |monicLeftDivide| |critMTonD1| |aspFilename| |factorFraction| + |cAcoth| |var1StepsDefault| |errorInfo| |integralMatrixAtInfinity| + |OMputEndAtp| |recip| |rightOne| |limitPlus| |cyclotomic| + |mainSquareFreePart| |root?| |leastMonomial| |decomposeFunc| + |palgint0| |viewDeltaXDefault| |prolateSpheroidal| |findConstructor| + |weierstrass| |voidMode| |constantKernel| |decimal| + |generalizedContinuumHypothesisAssumed| |roughBasicSet| + |squareFreeLexTriangular| |addMatch| |complexNumeric| |transpose| + |lookup| |conjugates| |startTableInvSet!| |elliptic?| |epilogue| + |iicosh| |sylvesterSequence| |iteratedInitials| |compound?| |cons| + |stoseInvertibleSetsqfreg| |limit| |mapGen| |asinhIfCan| |permutation| + |getConstant| |reopen!| |integers| |kernels| |asinIfCan| |step| + |satisfy?| |objects| |d02cjf| |antiCommutator| |associates?| + |operator| |OMlistSymbols| |indiceSubResultant| |companionBlocks| + |nullSpace| |points| |base| |expandTrigProducts| |uniform| + |interpretString| |diophantineSystem| |rootProduct| |tracePowMod| + |makeViewport2D| |mkAnswer| |laguerreL| |bezoutDiscriminant| |factor1| + |inconsistent?| |optpair| |clipParametric| |iibinom| |integral?| + |roughSubIdeal?| |univariate| |selectSumOfSquaresRoutines| + |reducedContinuedFraction| |iiacos| |zeroSquareMatrix| |parameters| + |numeric| |setClosed| |coerce| |trace2PowMod| |setleaves!| + |rewriteSetByReducingWithParticularGenerators| |OMconnInDevice| + |deepestInitial| |repeatUntilLoop| |saturate| |radical| |merge!| + |rangePascalTriangle| |construct| |subTriSet?| |factorGroebnerBasis| + |gcdprim| |byteBuffer| |tRange| |source| |explicitEntries?| + |stiffnessAndStabilityFactor| |leftUnits| + |factorSquareFreeByRecursion| |alternative?| |pointData| + |mapBivariate| |exptMod| |factor| |mainVariable| |extractClosed| + |irDef| |setvalue!| |SturmHabichtCoefficients| |space| |sts2stst| |Ci| + |sincos| |sqrt| |thetaCoord| |iisqrt3| |schwerpunkt| + |nextsubResultant2| |digit| |cn| |critMonD1| |pushdterm| |linGenPos| + |besselI| |real| |OMputEndApp| |directory| |reverseLex| + |lazyResidueClass| |monic?| |iitanh| |precision| |d03eef| |integrate| + |imag| |cyclicParents| |eigenMatrix| |polygon| |fortranDoubleComplex| + |OMencodingXML| |OMReadError?| |yCoord| |setLength!| |systemSizeIF| + |directProduct| |diff| |getZechTable| |readInt16!| |target| |bitTruth| + |updateStatus!| |connect| |simpleBounds?| |monomial?| |external?| + |minimumExponent| |complexExpand| |vertConcat| |outputArgs| + |shanksDiscLogAlgorithm| |scalarMatrix| |rootOfIrreduciblePoly| + |groebnerFactorize| |resultantReduitEuclidean| |moreAlgebraic?| + |csch2sinh| |brace| |setPredicates| |ptree| |kind| |previous| |red| + |inverseIntegralMatrixAtInfinity| |integral| |lquo| + |differentialVariables| |lineColorDefault| |nonSingularModel| + |normFactors| |destruct| |vconcat| |swapColumns!| |op| |e02baf| + |cyclicEntries| |singleFactorBound| |makeGraphImage| |interval| + |ip4Address| |basisOfRightNucloid| |pmintegrate| |iicsch| + |OMgetString| |opeval| |minIndex| |unitNormal| |d03faf| + |symmetricGroup| |besselK| |createThreeSpace| |ravel| |leadingTerm| + |euclideanSize| |leftTraceMatrix| |cyclicGroup| |trivialIdeal?| + |reindex| |rowEchelon| |oneDimensionalArray| |radix| |reshape| + |numberOfComputedEntries| |infinityNorm| |factorByRecursion| |edf2fi| + |setelt| |bipolar| |OMgetEndAtp| |operation| |integralCoordinates| + |problemPoints| |euler| |minRowIndex| |linearAssociatedOrder| + |members| |btwFact| |diagonal| |cAtanh| |rewriteSetWithReduction| + |separateFactors| |tanIfCan| |simpson| |isTimes| |areEquivalent?| + |minordet| |randnum| |copy| |exportedOperators| |showTheSymbolTable| + |leader| |palgLODE0| |fixedPoint| UTS2UP |union| |pop!| + |hyperelliptic| |ratpart| |cothIfCan| |pushup| |Si| |isOr| + |integralRepresents| |redpps| |linearPart| |startPolynomial| + |getMatch| |lfunc| |fortranTypeOf| |invertibleElseSplit?| |prologue| + |reduceBasisAtInfinity| |kovacic| |update| |PollardSmallFactor| + |exteriorDifferential| |root| |rootDirectory| |any| |autoCoerce| + |factorOfDegree| |selectFiniteRoutines| |lastSubResultantElseSplit| + |internalIntegrate0| |rCoord| |computeInt| |factorAndSplit| + |cyclicEqual?| |vector| |identityMatrix| |norm| |lazyPseudoDivide| + |sin2csc| |normalizedAssociate| |deriv| |primitive?| |userOrdered?| + |rectangularMatrix| |differentiate| |hasTopPredicate?| |imagJ| + |midpoint| |tab| |permutations| |point?| |f01brf| |variable?| |c06fqf| + |binaryTree| |interpolate| |cCoth| |s17aff| |fullPartialFraction| + |lazyGintegrate| |dimension| |sequence| |setAdaptive| |addPoint2| + |padecf| |moduloP| |mainVariables| |edf2df| |KrullNumber| |position| + |scalarTypeOf| |irreducibleFactors| |prepareSubResAlgo| + |rightExtendedGcd| |powern| |dfRange| |npcoef| |rightQuotient| + |partitions| |match?| |normalize| |critBonD| |maxrow| |pade| + |continuedFraction| |factorials| |crest| |var1Steps| |testModulus| + |optional?| |denomRicDE| |showClipRegion| |before?| |vectorise| + |ef2edf| |OMputEndAttr| |infieldIntegrate| |cCosh| |mathieu12| + |associatorDependence| |principalIdeal| |callForm?| |divisors| |sum| + |ellipticCylindrical| |e01bff| |moduleSum| |realZeros| + |sturmVariationsOf| |f02fjf| |create| |imagK| |cyclic?| |sayLength| + |Lazard| |derivationCoordinates| |s19adf| |fortranCarriageReturn| + |logGamma| |monicRightDivide| |subresultantSequence| |symmetricPower| + |pushucoef| |completeEchelonBasis| |generators| |divideIfCan| |leaves| + |declare| |dimensions| |rightDiscriminant| |lllip| |setchildren!| + |abs| |infieldint| |withPredicates| |reducedForm| |phiCoord| |radPoly| + |lp| |hex| |choosemon| |setPosition| |whatInfinity| |trigs| |is?| + |LowTriBddDenomInv| |cycles| |complexSolve| + |numberOfImproperPartitions| |physicalLength!| |doublyTransitive?| + |cAsin| |printHeader| |colorDef| |setColumn!| |clip| |graphImage| + |arg1| |endOfFile?| |characteristicPolynomial| |conditionP| |aromberg| + |zeroSetSplitIntoTriangularSystems| |close| |hermite| |primeFactor| + |calcRanges| |arg2| |enterInCache| |write!| |orbit| |iisinh| + |squareMatrix| |tValues| |lazyIrreducibleFactors| |nthr| |chiSquare1| + |tubePointsDefault| |radicalOfLeftTraceForm| |untab| |display| F2FG + |bright| |baseRDE| |clikeUniv| |stirling2| |conditions| |length| + |eigenvalues| |initializeGroupForWordProblem| |cTan| |d01gaf| + |superHeight| |genericLeftTrace| |matrixDimensions| |groebner| |match| + |scripts| |weights| |symmetricDifference| |critpOrder| + |pointSizeDefault| |taylorRep| |neglist| |adaptive?| |factorial| + |schema| |contours| |duplicates?| |exists?| |li| |zoom| |e02bbf| + |nthFlag| |cfirst| |selectPDERoutines| |bounds| |pow| |constantIfCan| + |oddintegers| |color| |nthFactor| |numerator| |jordanAdmissible?| + |critT| |input| |swap!| |leftCharacteristicPolynomial| |represents| + |leftDiscriminant| |extractIndex| |htrigs| |domainTemplate| + |currentCategoryFrame| |library| |mainCoefficients| |leftExtendedGcd| + |integralMatrix| |newTypeLists| |clipWithRanges| |ksec| |mapExpon| + |bottom!| |curry| |polCase| |iiexp| |shuffle| |factors| |linear?| + |OMgetType| |getlo| |lprop| RF2UTS |LiePoly| |stronglyReduced?| + |logIfCan| |revert| |maxIndex| |unit| |dominantTerm| + |fortranLinkerArgs| |Nul| |f02aff| |set| |addMatchRestricted| |mulmod| + |ridHack1| |resultantEuclidean| |iisec| |inc| |monicCompleteDecompose| + |optAttributes| |algebraicDecompose| |id| |iidprod| + |semiResultantReduitEuclidean| |eyeDistance| |primes| |build| + |reorder| |addmod| |s17acf| |monicDecomposeIfCan| |SFunction| |ode| + |algebraicOf| |test| |isPower| |setValue!| |cAsec| |OMopenString| + |table| |floor| |homogeneous?| |Vectorise| |rightAlternative?| + |squareFreePrim| |leftAlternative?| |makeUnit| |insert| |new| + |equality| |iitan| |s19acf| |definingInequation| |obj| + |normalizeIfCan| |mightHaveRoots| |iiabs| |rk4f| |gcdcofact| |elRow1!| + |c06frf| |deepExpand| |cache| |s13adf| |unrankImproperPartitions1| + |f07adf| |trapezoidal| |iicos| |curve| |addPoint| |arity| + |clearFortranOutputStack| |OMputBind| |realRoots| |conjug| |lepol| + |delete| |coerceL| |eq| |signature| |structuralConstants| |point| + |normalizeAtInfinity| |prefix| |palgRDE0| |baseRDEsys| + |fortranLiteralLine| |palgLODE| |resetBadValues| |iter| |chebyshevU| + |mapUp!| |leftUnit| |middle| |putProperties| |cschIfCan| |palgextint| + |headReduced?| |hasSolution?| |setfirst!| |f02axf| + |unrankImproperPartitions0| |iiperm| |s17dlf| |showScalarValues| + |leftRank| |lazyPseudoQuotient| |mergeDifference| |alphabetic| + |hexDigit| |minPol| |series| |nextSublist| |primintfldpoly| + |univariatePolynomials| |zeroVector| |toseSquareFreePart| |OMputBVar| + |intersect| |cSinh| |argumentListOf| |fractRadix| |compiledFunction| + |SturmHabichtMultiple| |elRow2!| |badNum| |collectUnder| + |stiffnessAndStabilityOfODEIF| |resetAttributeButtons| |e04fdf| + |nthExponent| |readByte!| |subNode?| |nilFactor| |findCycle| + |getOperands| |flexible?| |qfactor| |OMgetEndBVar| |parabolic| + |setelt!| |multisect| |hypergeometric0F1| |multMonom| |arguments| + |rangeIsFinite| |left| |distdfact| |rationalIfCan| |min| |rational?| + |sinhcosh| |retractIfCan| |squareTop| |fintegrate| |overlap| + |midpoints| |c06gsf| |/\\| |right| |f02akf| |bytes| |slex| + |numberOfDivisors| |halfExtendedResultant1| |shufflein| |iiacsc| + |elements| |bag| |\\/| |checkRur| |atoms| |OMgetEndObject| |numer| + |times!| |pointColorPalette| |FormatRoman| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 13fe3e19..577ad65d 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5378 +1,5378 @@ -(3228508 . 3481463066) -((-1618 (((-112) (-1 (-112) |#2| |#2|) $) 86) (((-112) $) NIL)) (-1676 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3926 ((|#2| $ (-570) |#2|) NIL) ((|#2| $ (-1244 (-570)) |#2|) 44)) (-3309 (($ $) 80)) (-4214 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50) ((|#2| (-1 |#2| |#2| |#2|) $) 49)) (-4021 (((-570) (-1 (-112) |#2|) $) 27) (((-570) |#2| $) NIL) (((-570) |#2| $ (-570)) 96)) (-3647 (((-650 |#2|) $) 13)) (-2549 (($ (-1 (-112) |#2| |#2|) $ $) 64) (($ $ $) NIL)) (-1521 (($ (-1 |#2| |#2|) $) 37)) (-1381 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 60)) (-4295 (($ |#2| $ (-570)) NIL) (($ $ $ (-570)) 67)) (-2466 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 29)) (-3990 (((-112) (-1 (-112) |#2|) $) 23)) (-1926 ((|#2| $ (-570) |#2|) NIL) ((|#2| $ (-570)) NIL) (($ $ (-1244 (-570))) 66)) (-4327 (($ $ (-570)) 76) (($ $ (-1244 (-570))) 75)) (-3589 (((-777) (-1 (-112) |#2|) $) 34) (((-777) |#2| $) NIL)) (-2664 (($ $ $ (-570)) 69)) (-3945 (($ $) 68)) (-3811 (($ (-650 |#2|)) 73)) (-2603 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 87) (($ (-650 $)) 85)) (-3801 (((-868) $) 92)) (-3557 (((-112) (-1 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(|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-174)) ((-102) -2905 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2905 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -2905 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-622 #0=(-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-622 (-570)) -2905 (|has| |#2| (-1058)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-622 |#2|) -2905 (|has| |#2| (-1109)) (|has| |#2| (-174))) ((-619 (-868)) -2905 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-619 (-868))) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-619 (-1277 |#2|)) . T) ((-174) |has| |#2| (-174)) ((-233 |#2|) |has| |#2| (-1058)) ((-235) -12 (|has| |#2| (-235)) (|has| |#2| (-1058))) ((-290 #1=(-570) |#2|) . T) ((-292 #1# |#2|) . T) ((-313 |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-373) |has| |#2| (-373)) ((-382 |#2|) |has| |#2| (-1058)) ((-417 |#2|) |has| |#2| (-1109)) ((-495 |#2|) . T) ((-610 #1# |#2|) . T) ((-520 |#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-652 (-570)) -2905 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -2905 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -2905 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -2905 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -2905 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -2905 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -2905 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -2905 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -2905 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -2905 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -2905 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -2905 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-907 (-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058))) ((-1047 #0#) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-1047 (-570)) -12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) ((-1047 |#2|) |has| |#2| (-1109)) ((-1060 |#2|) -2905 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -2905 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -2905 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -2905 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -2905 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -2905 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1227) . T) ((-1284 |#2|) |has| |#2| (-368))) -((-3639 (((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 21)) (-4214 ((|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 23)) (-1381 (((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)) 18))) -(((-241 |#1| |#2| |#3|) (-10 -7 (-15 -3639 ((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -4214 (|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -1381 ((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)))) (-777) (-1227) (-1227)) (T -241)) -((-1381 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *7 (-1227)) (-5 *2 (-242 *5 *7)) (-5 *1 (-241 *5 *6 *7)))) (-4214 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *2 (-1227)) (-5 *1 (-241 *5 *6 *2)))) (-3639 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-242 *6 *7)) (-14 *6 (-777)) (-4 *7 (-1227)) (-4 *5 (-1227)) (-5 *2 (-242 *6 *5)) (-5 *1 (-241 *6 *7 *5))))) -(-10 -7 (-15 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|%noBranch|) (IF (|has| |t#2| (-132)) (-6 (-132)) |%noBranch|) (IF (|has| |t#2| (-732)) (PROGN (-6 (-732)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-373)) (-6 (-373)) |%noBranch|) (IF (|has| |t#2| (-174)) (PROGN (-6 (-38 |t#2|)) (-6 (-174))) |%noBranch|) (IF (|has| |t#2| (-6 -4449)) (-6 -4449) |%noBranch|) (IF (|has| |t#2| (-854)) (-6 (-854)) |%noBranch|) (IF (|has| |t#2| (-799)) (-6 (-799)) |%noBranch|) (IF (|has| |t#2| (-368)) (-6 (-1284 |t#2|)) |%noBranch|))) +(((-21) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-23) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-25) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-174)) ((-102) -2854 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2854 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-622 #0=(-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-622 (-570)) -2854 (|has| |#2| (-1058)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-622 |#2|) -2854 (|has| |#2| (-1109)) (|has| |#2| (-174))) ((-619 (-868)) -2854 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-619 (-868))) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-619 (-1277 |#2|)) . T) ((-174) |has| |#2| (-174)) ((-233 |#2|) |has| |#2| (-1058)) ((-235) -12 (|has| |#2| (-235)) (|has| |#2| (-1058))) ((-290 #1=(-570) |#2|) . T) ((-292 #1# |#2|) . T) ((-313 |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-373) |has| |#2| (-373)) ((-382 |#2|) |has| |#2| (-1058)) ((-417 |#2|) |has| |#2| (-1109)) ((-495 |#2|) . T) ((-610 #1# |#2|) . T) ((-520 |#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-652 (-570)) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -2854 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -2854 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -2854 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -2854 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -2854 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -2854 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -2854 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -2854 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-907 (-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058))) ((-1047 #0#) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-1047 (-570)) -12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) ((-1047 |#2|) |has| |#2| (-1109)) ((-1060 |#2|) -2854 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -2854 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -2854 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1227) . T) ((-1284 |#2|) |has| |#2| (-368))) +((-2771 (((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 21)) (-1661 ((|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 23)) (-1376 (((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)) 18))) +(((-241 |#1| |#2| |#3|) (-10 -7 (-15 -2771 ((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -1661 (|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -1376 ((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)))) (-777) (-1227) (-1227)) (T -241)) +((-1376 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *7 (-1227)) (-5 *2 (-242 *5 *7)) (-5 *1 (-241 *5 *6 *7)))) (-1661 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *2 (-1227)) (-5 *1 (-241 *5 *6 *2)))) (-2771 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-242 *6 *7)) (-14 *6 (-777)) (-4 *7 (-1227)) (-4 *5 (-1227)) (-5 *2 (-242 *6 *5)) (-5 *1 (-241 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-174) -2905 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-620 (-542)) -12 (|has| |#1| (-620 (-542))) (|has| |#3| (-620 (-542)))) ((-620 (-899 (-384))) -12 (|has| |#1| (-620 (-899 (-384)))) (|has| |#3| (-620 (-899 (-384))))) ((-620 (-899 (-570))) -12 (|has| |#1| (-620 (-899 (-570)))) (|has| |#3| (-620 (-899 (-570))))) ((-233 |#1|) . T) ((-235) |has| |#1| (-235)) ((-294) -2905 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-313 $) . T) ((-330 |#1| |#4|) . T) ((-382 |#1|) . T) ((-417 |#1|) . T) ((-458) -2905 (|has| |#1| (-916)) (|has| |#1| (-458))) ((-520 |#2| |#1|) |has| |#1| (-235)) ((-520 |#2| $) |has| |#1| (-235)) ((-520 |#3| |#1|) . T) ((-520 |#3| $) . T) ((-520 $ $) . T) ((-562) -2905 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-652 #0#) |has| |#1| (-38 (-413 (-570)))) ((-652 (-570)) . T) ((-652 |#1|) . T) ((-652 $) . T) ((-654 #0#) |has| |#1| (-38 (-413 (-570)))) ((-654 |#1|) . T) ((-654 $) . T) ((-646 #0#) |has| |#1| (-38 (-413 (-570)))) ((-646 |#1|) |has| |#1| (-174)) ((-646 $) -2905 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-645 (-570)) |has| |#1| (-645 (-570))) ((-645 |#1|) . T) ((-723 #0#) |has| |#1| (-38 (-413 (-570)))) ((-723 |#1|) |has| |#1| (-174)) ((-723 $) -2905 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-732) . T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-907 |#3|) . T) ((-893 (-384)) -12 (|has| |#1| (-893 (-384))) (|has| |#3| (-893 (-384)))) ((-893 (-570)) -12 (|has| |#1| (-893 (-570))) (|has| |#3| (-893 (-570)))) ((-956 |#1| |#4| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 |#1|) . T) ((-1047 |#2|) . T) ((-1047 |#3|) . T) ((-1060 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1060 |#1|) . T) ((-1060 $) -2905 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1065 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -2905 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1231) |has| |#1| (-916))) -((-2578 (((-112) $ $) 19 (|has| |#1| (-1109)))) (-2455 ((|#1| $) 55)) (-3363 ((|#1| $) 45)) (-2587 (((-112) $ (-777)) 8)) (-2883 (($) 7 T CONST)) (-3353 (($ $) 61)) (-3309 (($ $) 49)) (-2501 ((|#1| |#1| $) 47)) (-1809 ((|#1| $) 46)) (-3647 (((-650 |#1|) $) 31 (|has| $ (-6 -4452)))) (-2591 (((-112) $ (-777)) 9)) (-3501 (((-650 |#1|) $) 30 (|has| $ (-6 -4452)))) (-1397 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4452))))) (-1521 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4453)))) (-1381 (($ (-1 |#1| |#1|) $) 36)) (-1629 (((-112) $ (-777)) 10)) (-1380 (((-777) $) 62)) (-3003 (((-1168) $) 22 (|has| |#1| (-1109)))) (-1855 ((|#1| $) 40)) (-2880 ((|#1| |#1| $) 53)) (-2245 ((|#1| |#1| $) 52)) (-3783 (($ |#1| $) 41)) (-1467 (((-777) $) 56)) (-3579 (((-1129) $) 21 (|has| |#1| (-1109)))) (-2772 ((|#1| $) 63)) (-1518 ((|#1| $) 51)) (-2351 ((|#1| $) 50)) (-1576 ((|#1| $) 42)) (-3990 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4452)))) (-1753 (($ $ (-650 (-298 |#1|))) 27 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ (-298 |#1|)) 26 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ (-650 |#1|) (-650 |#1|)) 24 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))))) (-3573 (((-112) $ $) 14)) (-1935 ((|#1| |#1| $) 59)) (-2783 (((-112) $) 11)) (-3226 (($) 12)) (-4036 ((|#1| $) 60)) (-3619 (($) 58) (($ (-650 |#1|)) 57)) (-2952 (((-777) $) 44)) (-3589 (((-777) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4452))) (((-777) |#1| $) 29 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4452))))) (-3945 (($ $) 13)) (-3801 (((-868) $) 18 (|has| |#1| (-619 (-868))))) (-2319 ((|#1| $) 54)) (-4138 (((-112) $ $) 23 (|has| |#1| (-1109)))) (-4379 (($ (-650 |#1|)) 43)) (-2274 ((|#1| $) 64)) (-3557 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4452)))) (-3034 (((-112) $ $) 20 (|has| |#1| (-1109)))) (-2589 (((-777) $) 6 (|has| $ (-6 -4452))))) +((-3738 (*1 *2 *3) (-12 (-4 *4 (-1058)) (-4 *3 (-856)) (-4 *5 (-269 *3)) (-4 *6 (-799)) (-5 *2 (-1 *1 (-777))) (-4 *1 (-256 *4 *3 *5 *6)))) (-3936 (*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *5 *6)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-650 *4)))) (-3094 (*1 *2 *1 *3) (-12 (-4 *1 (-256 *4 *3 *5 *6)) (-4 *4 (-1058)) (-4 *3 (-856)) (-4 *5 (-269 *3)) (-4 *6 (-799)) (-5 *2 (-777)))) (-3094 (*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *5 *6)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-777)))) (-2672 (*1 *2 *1 *3) (-12 (-4 *1 (-256 *4 *3 *5 *6)) (-4 *4 (-1058)) (-4 *3 (-856)) (-4 *5 (-269 *3)) (-4 *6 (-799)) (-5 *2 (-777)))) (-4202 (*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *5 *6)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-650 (-777))))) (-2290 (*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *5 *6)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-777)))) (-4202 (*1 *2 *1 *3) (-12 (-4 *1 (-256 *4 *3 *5 *6)) (-4 *4 (-1058)) (-4 *3 (-856)) (-4 *5 (-269 *3)) (-4 *6 (-799)) (-5 *2 (-650 (-777))))) (-2290 (*1 *2 *1 *3) (-12 (-4 *1 (-256 *4 *3 *5 *6)) (-4 *4 (-1058)) (-4 *3 (-856)) (-4 *5 (-269 *3)) (-4 *6 (-799)) (-5 *2 (-777)))) (-1377 (*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *5 *6)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-112)))) (-4000 (*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *2 *5)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-799)) (-4 *2 (-269 *4)))) (-1521 (*1 *1 *1) (-12 (-4 *1 (-256 *2 *3 *4 *5)) (-4 *2 (-1058)) (-4 *3 (-856)) (-4 *4 (-269 *3)) (-4 *5 (-799)))) (-2114 (*1 *1 *1) (-12 (-4 *1 (-256 *2 *3 *4 *5)) (-4 *2 (-1058)) (-4 *3 (-856)) (-4 *4 (-269 *3)) (-4 *5 (-799)))) (-3738 (*1 *2 *1) (-12 (-4 *3 (-235)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-1 *1 (-777))) (-4 *1 (-256 *3 *4 *5 *6))))) +(-13 (-956 |t#1| |t#4| |t#3|) (-233 |t#1|) (-1047 |t#2|) (-10 -8 (-15 -3738 ((-1 $ (-777)) |t#2|)) (-15 -3936 ((-650 |t#2|) $)) (-15 -3094 ((-777) $ |t#2|)) (-15 -3094 ((-777) $)) (-15 -2672 ((-777) $ |t#2|)) (-15 -4202 ((-650 (-777)) $)) (-15 -2290 ((-777) $)) (-15 -4202 ((-650 (-777)) $ |t#2|)) (-15 -2290 ((-777) $ |t#2|)) (-15 -1377 ((-112) $)) (-15 -4000 (|t#3| $)) (-15 -1521 ($ $)) (-15 -2114 ($ $)) (IF (|has| |t#1| (-235)) (PROGN (-6 (-520 |t#2| |t#1|)) (-6 (-520 |t#2| $)) (-6 (-313 $)) (-15 -3738 ((-1 $ (-777)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-413 (-570)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-622 #0#) -2854 (|has| |#1| (-1047 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570))))) ((-622 (-570)) . T) ((-622 |#1|) . T) ((-622 |#2|) . T) ((-622 |#3|) . T) ((-622 $) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-619 (-868)) . T) ((-174) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-620 (-542)) -12 (|has| |#1| (-620 (-542))) (|has| |#3| (-620 (-542)))) ((-620 (-899 (-384))) -12 (|has| |#1| (-620 (-899 (-384)))) (|has| |#3| (-620 (-899 (-384))))) ((-620 (-899 (-570))) -12 (|has| |#1| (-620 (-899 (-570)))) (|has| |#3| (-620 (-899 (-570))))) ((-233 |#1|) . T) ((-235) |has| |#1| (-235)) ((-294) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-313 $) . T) ((-330 |#1| |#4|) . T) ((-382 |#1|) . T) ((-417 |#1|) . T) ((-458) -2854 (|has| |#1| (-916)) (|has| |#1| (-458))) ((-520 |#2| |#1|) |has| |#1| (-235)) ((-520 |#2| $) |has| |#1| (-235)) ((-520 |#3| |#1|) . T) ((-520 |#3| $) . T) ((-520 $ $) . T) ((-562) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-652 #0#) |has| |#1| (-38 (-413 (-570)))) ((-652 (-570)) . T) ((-652 |#1|) . T) ((-652 $) . T) ((-654 #0#) |has| |#1| (-38 (-413 (-570)))) ((-654 |#1|) . T) ((-654 $) . T) ((-646 #0#) |has| |#1| (-38 (-413 (-570)))) ((-646 |#1|) |has| |#1| (-174)) ((-646 $) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-645 (-570)) |has| |#1| (-645 (-570))) ((-645 |#1|) . T) ((-723 #0#) |has| |#1| (-38 (-413 (-570)))) ((-723 |#1|) |has| |#1| (-174)) ((-723 $) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-732) . T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-907 |#3|) . T) ((-893 (-384)) -12 (|has| |#1| (-893 (-384))) (|has| |#3| (-893 (-384)))) ((-893 (-570)) -12 (|has| |#1| (-893 (-570))) (|has| |#3| (-893 (-570)))) ((-956 |#1| |#4| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 |#1|) . T) ((-1047 |#2|) . T) ((-1047 |#3|) . T) ((-1060 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1060 |#1|) . T) ((-1060 $) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1065 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1231) |has| |#1| (-916))) +((-2462 (((-112) $ $) 19 (|has| |#1| (-1109)))) (-3222 ((|#1| $) 55)) (-3378 ((|#1| $) 45)) (-2088 (((-112) $ (-777)) 8)) (-2984 (($) 7 T CONST)) (-2013 (($ $) 61)) (-2809 (($ $) 49)) (-2435 ((|#1| |#1| $) 47)) (-4005 ((|#1| $) 46)) (-3225 (((-650 |#1|) $) 31 (|has| $ (-6 -4452)))) (-2108 (((-112) $ (-777)) 9)) (-3985 (((-650 |#1|) $) 30 (|has| $ (-6 -4452)))) (-2455 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4452))))) (-3347 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4453)))) (-1376 (($ (-1 |#1| |#1|) $) 36)) (-2842 (((-112) $ (-777)) 10)) (-4191 (((-777) $) 62)) (-2916 (((-1168) $) 22 (|has| |#1| (-1109)))) (-3177 ((|#1| $) 40)) (-2954 ((|#1| |#1| $) 53)) (-2808 ((|#1| |#1| $) 52)) (-1719 (($ |#1| $) 41)) (-1450 (((-777) $) 56)) (-3611 (((-1129) $) 21 (|has| |#1| (-1109)))) (-3329 ((|#1| $) 63)) (-3015 ((|#1| $) 51)) (-1433 ((|#1| $) 50)) (-2309 ((|#1| $) 42)) (-1961 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4452)))) (-1715 (($ $ (-650 (-298 |#1|))) 27 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ (-298 |#1|)) 26 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ (-650 |#1|) (-650 |#1|)) 24 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))))) (-3403 (((-112) $ $) 14)) (-2668 ((|#1| |#1| $) 59)) (-3451 (((-112) $) 11)) (-3217 (($) 12)) (-2366 ((|#1| $) 60)) (-2522 (($) 58) (($ (-650 |#1|)) 57)) (-1775 (((-777) $) 44)) (-3622 (((-777) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4452))) (((-777) |#1| $) 29 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4452))))) (-3997 (($ $) 13)) (-3838 (((-868) $) 18 (|has| |#1| (-619 (-868))))) (-4246 ((|#1| $) 54)) (-4096 (((-112) $ $) 23 (|has| |#1| (-1109)))) (-4424 (($ (-650 |#1|)) 43)) (-1904 ((|#1| $) 64)) (-3257 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4452)))) (-2992 (((-112) $ $) 20 (|has| |#1| (-1109)))) (-2473 (((-777) $) 6 (|has| $ (-6 -4452))))) (((-257 |#1|) (-141) (-1227)) (T -257)) -((-3619 (*1 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-3619 (*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1227)) (-4 *1 (-257 *3)))) (-1467 (*1 *2 *1) (-12 (-4 *1 (-257 *3)) (-4 *3 (-1227)) (-5 *2 (-777)))) (-2455 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-2319 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-2880 (*1 *2 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-2245 (*1 *2 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-1518 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-2351 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-3309 (*1 *1 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227))))) -(-13 (-1130 |t#1|) (-1004 |t#1|) (-10 -8 (-15 -3619 ($)) (-15 -3619 ($ (-650 |t#1|))) (-15 -1467 ((-777) $)) (-15 -2455 (|t#1| $)) (-15 -2319 (|t#1| $)) (-15 -2880 (|t#1| |t#1| $)) (-15 -2245 (|t#1| |t#1| $)) (-15 -1518 (|t#1| $)) (-15 -2351 (|t#1| $)) (-15 -3309 ($ $)))) -(((-34) . 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"Range not yet evaluated")))))))) 26)) (-2254 (((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1861 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1861 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) 38)) (-1665 (((-650 (-2 (|:| -2046 (-2 (|:| |var| (-1186)) (|:| |fn| 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|upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1861 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1861 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))))) (T -565)) +((-2254 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1861 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| 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($ (-650 (-2 (|:| -2046 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1861 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2254 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1861 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (-15 -1719 ($ (-2 (|:| -2046 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) 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T) ((-23) . T) ((-47 |#1| #0=(-570)) . T) ((-25) . T) ((-38 #1=(-413 (-570))) -2854 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-368)) ((-38 $) -2854 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-35) |has| |#1| (-38 (-413 (-570)))) ((-95) |has| |#1| (-38 (-413 (-570)))) ((-102) . T) ((-111 #1# #1#) -2854 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-368)) ((-111 $ $) -2854 (|has| |#1| (-562)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-132) . T) ((-146) -2854 (-12 (|has| |#1| (-368)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -2854 (-12 (|has| |#1| (-368)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-622 #1#) -2854 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-622 (-570)) . T) ((-622 #2=(-1186)) -12 (|has| |#1| (-368)) (|has| |#2| (-1047 (-1186)))) ((-622 |#1|) |has| |#1| (-174)) ((-622 |#2|) . 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T) ((-646 #1#) -2854 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-646 |#1|) |has| |#1| (-174)) ((-646 |#2|) |has| |#1| (-368)) ((-646 $) -2854 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-645 (-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-645 (-570)))) ((-645 |#2|) |has| |#1| (-368)) ((-723 #1#) -2854 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-723 |#1|) |has| |#1| (-174)) ((-723 |#2|) |has| |#1| (-368)) ((-723 $) -2854 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-732) . 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T) ((-23) . T) ((-47 |#1| #0=(-413 (-570))) . T) ((-25) . T) ((-38 #1=(-413 (-570))) -2905 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2905 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-35) |has| |#1| (-38 (-413 (-570)))) ((-95) |has| |#1| (-38 (-413 (-570)))) ((-102) . T) ((-111 #1# #1#) -2905 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2905 (|has| |#1| (-562)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-622 #1#) -2905 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-622 (-570)) . T) ((-622 |#1|) |has| |#1| (-174)) ((-622 $) -2905 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-619 (-868)) . T) ((-174) -2905 (|has| |#1| (-562)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-235) |has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) ((-245) |has| |#1| (-368)) ((-288) |has| |#1| (-38 (-413 (-570)))) ((-290 #0# |#1|) . 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"TS" 2941649 NIL TS (NIL T) -8 NIL NIL NIL) (-1220 2925266 2929385 2929482 "TSETCAT" 2934751 NIL TSETCAT (NIL T T T T) -9 NIL 2936282 NIL) (-1219 2919998 2921598 2923489 "TSETCAT-" 2923494 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1218 2914637 2915484 2916413 "TRMANIP" 2919134 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1217 2914078 2914141 2914304 "TRIMAT" 2914569 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1216 2911944 2912181 2912538 "TRIGMNIP" 2913827 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1215 2911464 2911577 2911607 "TRIGCAT" 2911820 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1214 2911133 2911212 2911353 "TRIGCAT-" 2911358 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2907978 2909991 2910272 "TREE" 2910887 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2907252 2907780 2907810 "TRANFUN" 2907845 T TRANFUN (NIL) -9 NIL 2907911 NIL) (-1211 2906531 2906722 2907002 "TRANFUN-" 2907007 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2906335 2906367 2906428 "TOPSP" 2906492 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2905683 2905798 2905952 "TOOLSIGN" 2906216 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2904317 2904860 2905099 "TEXTFILE" 2905466 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2902229 2902770 2903199 "TEX" 2903910 T TEX (NIL) -8 NIL NIL NIL) (-1206 2902010 2902041 2902113 "TEX1" 2902192 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2901658 2901721 2901811 "TEMUTL" 2901942 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2899812 2900092 2900417 "TBCMPPK" 2901381 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2891589 2897972 2898028 "TBAGG" 2898428 NIL TBAGG (NIL T T) -9 NIL 2898639 NIL) (-1202 2886659 2888147 2889901 "TBAGG-" 2889906 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2886043 2886150 2886295 "TANEXP" 2886548 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2885554 2885818 2885908 "TALGOP" 2885988 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2878944 2885411 2885504 "TABLE" 2885509 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2878356 2878455 2878593 "TABLEAU" 2878841 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2872964 2874184 2875432 "TABLBUMP" 2877142 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2872186 2872333 2872514 "SYSTEM" 2872805 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2868645 2869344 2870127 "SYSSOLP" 2871437 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2868443 2868600 2868631 "SYSPTR" 2868636 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2867487 2867992 2868111 "SYSNNI" 2868297 NIL SYSNNI (NIL NIL) -8 NIL NIL 2868382) (-1192 2866794 2867253 2867332 "SYSINT" 2867392 NIL SYSINT (NIL NIL) -8 NIL NIL 2867437) (-1191 2863126 2864072 2864782 "SYNTAX" 2866106 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2860284 2860886 2861518 "SYMTAB" 2862516 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2855533 2856435 2857418 "SYMS" 2859323 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2852768 2854991 2855221 "SYMPOLY" 2855338 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2852285 2852360 2852483 "SYMFUNC" 2852680 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2848305 2849597 2850410 "SYMBOL" 2851494 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2841844 2843533 2845253 "SWITCH" 2846607 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2835078 2840665 2840968 "SUTS" 2841599 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827144 2834325 2834598 "SUPXS" 2834863 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2818903 2826762 2826888 "SUP" 2827053 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2818062 2818189 2818406 "SUPFRACF" 2818771 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2817683 2817742 2817855 "SUP2" 2817997 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816131 2816405 2816761 "SUMRF" 2817382 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2815466 2815532 2815724 "SUMFS" 2816052 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2799433 2814643 2814894 "SULS" 2815273 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2799035 2799255 2799325 "SUCHTAST" 2799385 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2798330 2798560 2798700 "SUCH" 2798943 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2792197 2793236 2794195 "SUBSPACE" 2797418 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2791627 2791717 2791881 "SUBRESP" 2792085 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2784995 2786292 2787603 "STTF" 2790363 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2779168 2780288 2781435 "STTFNC" 2783895 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2770481 2772350 2774144 "STTAYLOR" 2777409 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2763611 2770345 2770428 "STRTBL" 2770433 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2758975 2763566 2763597 "STRING" 2763602 T STRING (NIL) -8 NIL NIL NIL) (-1167 2753806 2758318 2758348 "STRICAT" 2758407 T STRICAT (NIL) -9 NIL 2758469 NIL) (-1166 2746559 2751425 2752036 "STREAM" 2753230 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2746069 2746146 2746290 "STREAM3" 2746476 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2745051 2745234 2745469 "STREAM2" 2745882 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2744739 2744791 2744884 "STREAM1" 2744993 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2743755 2743936 2744167 "STINPROD" 2744555 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2743307 2743517 2743547 "STEP" 2743627 T STEP (NIL) -9 NIL 2743705 NIL) (-1160 2742494 2742796 2742944 "STEPAST" 2743181 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2735926 2742393 2742470 "STBL" 2742475 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2731021 2735117 2735160 "STAGG" 2735313 NIL STAGG (NIL T) -9 NIL 2735402 NIL) (-1157 2728723 2729325 2730197 "STAGG-" 2730202 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2726870 2728493 2728585 "STACK" 2728666 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2719565 2725011 2725467 "SREGSET" 2726500 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2711990 2713359 2714872 "SRDCMPK" 2718171 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2704877 2709400 2709430 "SRAGG" 2710733 T SRAGG (NIL) -9 NIL 2711341 NIL) (-1152 2703894 2704149 2704528 "SRAGG-" 2704533 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2698354 2702841 2703262 "SQMATRIX" 2703520 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2692039 2695072 2695799 "SPLTREE" 2697699 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2688002 2688695 2689341 "SPLNODE" 2691465 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2687049 2687282 2687312 "SPFCAT" 2687756 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2685786 2685996 2686260 "SPECOUT" 2686807 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2676896 2678768 2678798 "SPADXPT" 2683474 T SPADXPT (NIL) -9 NIL 2685638 NIL) (-1145 2676657 2676697 2676766 "SPADPRSR" 2676849 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2674706 2676612 2676643 "SPADAST" 2676648 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2666651 2668424 2668467 "SPACEC" 2672840 NIL SPACEC (NIL T) -9 NIL 2674656 NIL) (-1142 2664781 2666583 2666632 "SPACE3" 2666637 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2663533 2663704 2663995 "SORTPAK" 2664586 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2661625 2661928 2662340 "SOLVETRA" 2663197 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2660675 2660897 2661158 "SOLVESER" 2661398 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2655979 2656867 2657862 "SOLVERAD" 2659727 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2651794 2652403 2653132 "SOLVEFOR" 2655346 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2646064 2651143 2651240 "SNTSCAT" 2651245 NIL SNTSCAT (NIL T T T T) -9 NIL 2651315 NIL) (-1135 2640170 2644387 2644778 "SMTS" 2645754 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2634855 2640058 2640135 "SMP" 2640140 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2633014 2633315 2633713 "SMITH" 2634552 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2625727 2629923 2630026 "SMATCAT" 2631377 NIL SMATCAT (NIL NIL T T T) -9 NIL 2631927 NIL) (-1131 2622667 2623490 2624668 "SMATCAT-" 2624673 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2620333 2621903 2621946 "SKAGG" 2622207 NIL SKAGG (NIL T) -9 NIL 2622342 NIL) (-1129 2616659 2619806 2619990 "SINT" 2620142 T SINT (NIL) -8 NIL NIL 2620304) (-1128 2616431 2616469 2616535 "SIMPAN" 2616615 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2615710 2615966 2616106 "SIG" 2616313 T SIG (NIL) -8 NIL NIL NIL) (-1126 2614548 2614769 2615044 "SIGNRF" 2615469 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2613381 2613532 2613816 "SIGNEF" 2614377 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2612687 2612964 2613088 "SIGAST" 2613279 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2610377 2610831 2611337 "SHP" 2612228 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2604229 2610278 2610354 "SHDP" 2610359 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2603802 2603994 2604024 "SGROUP" 2604117 T SGROUP (NIL) -9 NIL 2604179 NIL) (-1120 2603660 2603686 2603759 "SGROUP-" 2603764 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2600451 2601149 2601872 "SGCF" 2602959 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2594819 2599898 2599995 "SFRTCAT" 2600000 NIL SFRTCAT (NIL T T T T) -9 NIL 2600039 NIL) (-1117 2588240 2589258 2590394 "SFRGCD" 2593802 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2581366 2582439 2583625 "SFQCMPK" 2587173 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2580986 2581075 2581186 "SFORT" 2581307 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2580104 2580826 2580947 "SEXOF" 2580952 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2579211 2579985 2580053 "SEX" 2580058 T SEX (NIL) -8 NIL NIL NIL) (-1112 2574992 2575707 2575802 "SEXCAT" 2578424 NIL SEXCAT (NIL T T T T T) -9 NIL 2578984 NIL) (-1111 2572145 2574926 2574974 "SET" 2574979 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2570369 2570858 2571163 "SETMN" 2571886 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2569865 2570017 2570047 "SETCAT" 2570223 T SETCAT (NIL) -9 NIL 2570333 NIL) (-1108 2569557 2569635 2569765 "SETCAT-" 2569770 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2565918 2568018 2568061 "SETAGG" 2568931 NIL SETAGG (NIL T) -9 NIL 2569271 NIL) (-1106 2565376 2565492 2565729 "SETAGG-" 2565734 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2564819 2565072 2565173 "SEQAST" 2565297 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2564018 2564312 2564373 "SEGXCAT" 2564659 NIL SEGXCAT (NIL T T) -9 NIL 2564779 NIL) (-1103 2563024 2563684 2563866 "SEG" 2563871 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2562003 2562217 2562260 "SEGCAT" 2562782 NIL SEGCAT (NIL T) -9 NIL 2563003 NIL) (-1101 2560935 2561366 2561574 "SEGBIND" 2561830 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2560556 2560615 2560728 "SEGBIND2" 2560870 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560129 2560357 2560434 "SEGAST" 2560501 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2559348 2559474 2559678 "SEG2" 2559973 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2558758 2559283 2559330 "SDVAR" 2559335 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2551285 2558528 2558658 "SDPOL" 2558663 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2549878 2550144 2550463 "SCPKG" 2551000 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2549042 2549214 2549406 "SCOPE" 2549708 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548262 2548396 2548575 "SCACHE" 2548897 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2547908 2548094 2548124 "SASTCAT" 2548129 T SASTCAT (NIL) -9 NIL 2548142 NIL) (-1091 2547395 2547743 2547819 "SAOS" 2547854 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2546960 2546995 2547168 "SAERFFC" 2547354 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2540899 2546857 2546937 "SAE" 2546942 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2540492 2540527 2540686 "SAEFACT" 2540858 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2538813 2539127 2539528 "RURPK" 2540158 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2537450 2537756 2538061 "RULESET" 2538647 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2534673 2535203 2535661 "RULE" 2537131 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2534285 2534467 2534550 "RULECOLD" 2534625 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2534075 2534103 2534174 "RTVALUE" 2534236 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2533546 2533792 2533886 "RSTRCAST" 2534003 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2528394 2529189 2530109 "RSETGCD" 2532745 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2517624 2522703 2522800 "RSETCAT" 2526919 NIL RSETCAT (NIL T T T T) -9 NIL 2528016 NIL) (-1079 2515551 2516090 2516914 "RSETCAT-" 2516919 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2507937 2509313 2510833 "RSDCMPK" 2514150 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2505916 2506383 2506457 "RRCC" 2507543 NIL RRCC (NIL T T) -9 NIL 2507887 NIL) (-1076 2505267 2505441 2505720 "RRCC-" 2505725 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2504710 2504963 2505064 "RPTAST" 2505188 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2478556 2487915 2487982 "RPOLCAT" 2498648 NIL RPOLCAT (NIL T T T) -9 NIL 2501808 NIL) (-1073 2470054 2472394 2475516 "RPOLCAT-" 2475521 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2460985 2468265 2468747 "ROUTINE" 2469594 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2457783 2460611 2460751 "ROMAN" 2460867 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2456027 2456643 2456903 "ROIRC" 2457588 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452259 2454543 2454573 "RNS" 2454877 T RNS (NIL) -9 NIL 2455151 NIL) (-1068 2450768 2451151 2451685 "RNS-" 2451760 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450171 2450579 2450609 "RNG" 2450614 T RNG (NIL) -9 NIL 2450635 NIL) (-1066 2449174 2449536 2449738 "RNGBIND" 2450022 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2448573 2448961 2449004 "RMODULE" 2449009 NIL RMODULE (NIL T) -9 NIL 2449036 NIL) (-1064 2447409 2447503 2447839 "RMCAT2" 2448474 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444259 2446755 2447052 "RMATRIX" 2447171 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2437086 2439346 2439461 "RMATCAT" 2442820 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2443802 NIL) (-1061 2436461 2436608 2436915 "RMATCAT-" 2436920 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2435862 2436083 2436126 "RLINSET" 2436320 NIL RLINSET (NIL T) -9 NIL 2436411 NIL) (-1059 2435429 2435504 2435632 "RINTERP" 2435781 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2434487 2435041 2435071 "RING" 2435127 T RING (NIL) -9 NIL 2435219 NIL) (-1057 2434279 2434323 2434420 "RING-" 2434425 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2433120 2433357 2433615 "RIDIST" 2434043 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2424409 2432588 2432794 "RGCHAIN" 2432968 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2423759 2424165 2424206 "RGBCSPC" 2424264 NIL RGBCSPC (NIL T) -9 NIL 2424316 NIL) (-1053 2422917 2423298 2423339 "RGBCMDL" 2423571 NIL RGBCMDL (NIL T) -9 NIL 2423685 NIL) (-1052 2419911 2420525 2421195 "RF" 2422281 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2419557 2419620 2419723 "RFFACTOR" 2419842 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419282 2419317 2419414 "RFFACT" 2419516 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2417399 2417763 2418145 "RFDIST" 2418922 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2416852 2416944 2417107 "RETSOL" 2417301 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2416488 2416568 2416611 "RETRACT" 2416744 NIL RETRACT (NIL T) -9 NIL 2416831 NIL) (-1046 2416337 2416362 2416449 "RETRACT-" 2416454 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2415939 2416159 2416229 "RETAST" 2416289 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2408677 2415592 2415719 "RESULT" 2415834 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407268 2407946 2408145 "RESRING" 2408580 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2406904 2406953 2407051 "RESLATC" 2407205 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2406609 2406644 2406751 "REPSQ" 2406863 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2404031 2404611 2405213 "REP" 2406029 T REP (NIL) -7 NIL NIL NIL) (-1039 2403728 2403763 2403874 "REPDB" 2403990 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2397628 2399017 2400240 "REP2" 2402540 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2394005 2394686 2395494 "REP1" 2396855 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2386701 2392146 2392602 "REGSET" 2393635 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2385466 2385849 2386099 "REF" 2386486 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2384843 2384946 2385113 "REDORDER" 2385350 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2380811 2384056 2384283 "RECLOS" 2384671 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2379863 2380044 2380259 "REALSOLV" 2380618 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2379709 2379750 2379780 "REAL" 2379785 T REAL (NIL) -9 NIL 2379820 NIL) (-1030 2376192 2376994 2377878 "REAL0Q" 2378874 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2371793 2372781 2373842 "REAL0" 2375173 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371264 2371510 2371604 "RDUCEAST" 2371721 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2370669 2370741 2370948 "RDIV" 2371186 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2369737 2369911 2370124 "RDIST" 2370491 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2368334 2368621 2368993 "RDETRS" 2369445 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366146 2366600 2367138 "RDETR" 2367876 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2364771 2365049 2365446 "RDEEFS" 2365862 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363280 2363586 2364011 "RDEEF" 2364459 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2357341 2360261 2360291 "RCFIELD" 2361586 T RCFIELD (NIL) -9 NIL 2362317 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QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-996 2289639 2290087 2290515 "QALGSET" 2291745 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-995 2288884 2289058 2289290 "QALGSET2" 2289459 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-994 2287574 2287798 2288115 "PWFFINTB" 2288657 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-993 2285756 2285924 2286278 "PUSHVAR" 2287388 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-992 2281674 2282728 2282769 "PTRANFN" 2284653 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-991 2280076 2280367 2280689 "PTPACK" 2281385 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-990 2279708 2279765 2279874 "PTFUNC2" 2280013 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-989 2274153 2278550 2278591 "PTCAT" 2278887 NIL PTCAT (NIL T) -9 NIL 2279040 NIL) (-988 2273811 2273846 2273970 "PSQFR" 2274112 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-987 2272406 2272704 2273038 "PSEUDLIN" 2273509 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-986 2259169 2261540 2263864 "PSETPK" 2270166 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) 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NIL NIL NIL) (-866 2000818 2000983 2001011 "OUTBCON" 2001329 T OUTBCON (NIL) -9 NIL 2001495 NIL) (-865 2000419 2000531 2000688 "OUTBCON-" 2000693 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-864 1999799 2000148 2000237 "OSI" 2000350 T OSI (NIL) -8 NIL NIL NIL) (-863 1999329 1999667 1999695 "OSGROUP" 1999700 T OSGROUP (NIL) -9 NIL 1999722 NIL) (-862 1998074 1998301 1998586 "ORTHPOL" 1999076 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-861 1995625 1997909 1998030 "OREUP" 1998035 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-860 1993028 1995316 1995443 "ORESUP" 1995567 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990556 1991056 1991617 "OREPCTO" 1992517 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984242 1986443 1986484 "OREPCAT" 1988832 NIL OREPCAT (NIL T) -9 NIL 1989936 NIL) (-857 1981389 1982171 1983229 "OREPCAT-" 1983234 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980540 1980838 1980866 "ORDSET" 1981175 T ORDSET (NIL) -9 NIL 1981339 NIL) (-855 1979971 1980119 1980343 "ORDSET-" 1980348 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978536 1979327 1979355 "ORDRING" 1979557 T ORDRING (NIL) -9 NIL 1979682 NIL) (-853 1978181 1978275 1978419 "ORDRING-" 1978424 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977561 1978024 1978052 "ORDMON" 1978057 T ORDMON (NIL) -9 NIL 1978078 NIL) (-851 1976723 1976870 1977065 "ORDFUNS" 1977410 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976061 1976480 1976508 "ORDFIN" 1976573 T ORDFIN (NIL) -9 NIL 1976647 NIL) (-849 1972620 1974647 1975056 "ORDCOMP" 1975685 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1971886 1972013 1972199 "ORDCOMP2" 1972480 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968467 1969377 1970191 "OPTPROB" 1971092 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965269 1965908 1966612 "OPTPACK" 1967783 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1962956 1963722 1963750 "OPTCAT" 1964569 T OPTCAT (NIL) -9 NIL 1965219 NIL) (-844 1962340 1962633 1962738 "OPSIG" 1962871 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962108 1962147 1962213 "OPQUERY" 1962294 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959239 1960419 1960923 "OP" 1961637 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958613 1958839 1958880 "OPERCAT" 1959092 NIL OPERCAT (NIL T) -9 NIL 1959189 NIL) (-840 1958368 1958424 1958541 "OPERCAT-" 1958546 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955181 1957165 1957534 "ONECOMP" 1958032 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954486 1954601 1954775 "ONECOMP2" 1955053 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1953905 1954011 1954141 "OMSERVER" 1954376 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1950767 1953345 1953385 "OMSAGG" 1953446 NIL OMSAGG (NIL T) -9 NIL 1953510 NIL) (-835 1949390 1949653 1949935 "OMPKG" 1950505 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1948820 1948923 1948951 "OM" 1949250 T OM (NIL) -9 NIL NIL NIL) (-833 1947367 1948369 1948538 "OMLO" 1948701 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946327 1946474 1946694 "OMEXPR" 1947193 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945618 1945873 1946009 "OMERR" 1946211 T OMERR (NIL) -8 NIL NIL NIL) (-830 1944769 1945039 1945199 "OMERRK" 1945478 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944220 1944446 1944554 "OMENC" 1944681 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938115 1939300 1940471 "OMDEV" 1943069 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937184 1937355 1937549 "OMCONN" 1937941 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1935705 1936681 1936709 "OINTDOM" 1936714 T OINTDOM (NIL) -9 NIL 1936735 NIL) (-825 1933043 1934393 1934730 "OFMONOID" 1935400 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932454 1932980 1933025 "ODVAR" 1933030 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1929877 1932199 1932354 "ODR" 1932359 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922458 1929653 1929779 "ODPOL" 1929784 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916280 1922330 1922435 "ODP" 1922440 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915046 1915261 1915536 "ODETOOLS" 1916054 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912013 1912671 1913387 "ODESYS" 1914379 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1906895 1907803 1908828 "ODERTRIC" 1911088 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906321 1906403 1906597 "ODERED" 1906807 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903209 1903757 1904434 "ODERAT" 1905744 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900168 1900633 1901230 "ODEPRRIC" 1902738 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898111 1898707 1899193 "ODEPROB" 1899702 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894631 1895116 1895763 "ODEPRIM" 1897590 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1893880 1893982 1894242 "ODEPAL" 1894523 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890042 1890833 1891697 "ODEPACK" 1893036 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889103 1889210 1889432 "ODEINT" 1889931 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883204 1884629 1886076 "ODEIFTBL" 1887676 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878602 1879388 1880340 "ODEEF" 1882363 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1877951 1878040 1878263 "ODECONST" 1878507 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876076 1876737 1876765 "ODECAT" 1877370 T ODECAT (NIL) -9 NIL 1877901 NIL) (-805 1872931 1875781 1875903 "OCT" 1875986 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872569 1872612 1872739 "OCTCT2" 1872882 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867180 1869615 1869655 "OC" 1870752 NIL OC (NIL T) -9 NIL 1871610 NIL) (-802 1864407 1865155 1866145 "OC-" 1866239 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1863759 1864227 1864255 "OCAMON" 1864260 T OCAMON (NIL) -9 NIL 1864281 NIL) (-800 1863290 1863631 1863659 "OASGP" 1863664 T OASGP (NIL) -9 NIL 1863684 NIL) (-799 1862551 1863040 1863068 "OAMONS" 1863108 T OAMONS (NIL) -9 NIL 1863151 NIL) (-798 1861965 1862398 1862426 "OAMON" 1862431 T OAMON (NIL) -9 NIL 1862451 NIL) (-797 1861223 1861741 1861769 "OAGROUP" 1861774 T OAGROUP (NIL) -9 NIL 1861794 NIL) (-796 1860913 1860963 1861051 "NUMTUBE" 1861167 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854486 1856004 1857540 "NUMQUAD" 1859397 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850242 1851230 1852255 "NUMODE" 1853481 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847597 1848477 1848505 "NUMINT" 1849428 T NUMINT (NIL) -9 NIL 1850192 NIL) (-792 1846545 1846742 1846960 "NUMFMT" 1847399 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1832904 1835849 1838381 "NUMERIC" 1844052 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827274 1832353 1832448 "NTSCAT" 1832453 NIL NTSCAT (NIL T T T T) -9 NIL 1832492 NIL) (-789 1826468 1826633 1826826 "NTPOLFN" 1827113 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814545 1823293 1824105 "NSUP" 1825689 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814177 1814234 1814343 "NSUP2" 1814482 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804403 1813951 1814084 "NSMP" 1814089 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1802835 1803136 1803493 "NREP" 1804091 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801426 1801678 1802036 "NPCOEF" 1802578 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800492 1800607 1800823 "NORMRETR" 1801307 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798533 1798823 1799232 "NORMPK" 1800200 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798218 1798246 1798370 "NORMMA" 1798499 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798018 1798175 1798204 "NONE" 1798209 T NONE (NIL) -8 NIL NIL NIL) (-779 1797807 1797836 1797905 "NONE1" 1797982 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797304 1797366 1797545 "NODE1" 1797739 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795589 1796440 1796695 "NNI" 1797042 T NNI (NIL) -8 NIL NIL 1797277) (-776 1794009 1794322 1794686 "NLINSOL" 1795257 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790250 1791245 1792144 "NIPROB" 1793130 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789007 1789241 1789543 "NFINTBAS" 1790012 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788181 1788657 1788698 "NETCLT" 1788870 NIL NETCLT (NIL T) -9 NIL 1788952 NIL) (-772 1786889 1787120 1787401 "NCODIV" 1787949 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1786651 1786688 1786763 "NCNTFRAC" 1786846 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1784831 1785195 1785615 "NCEP" 1786276 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1783682 1784455 1784483 "NASRING" 1784593 T NASRING (NIL) -9 NIL 1784673 NIL) (-768 1783477 1783521 1783615 "NASRING-" 1783620 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782584 1783109 1783137 "NARNG" 1783254 T NARNG (NIL) -9 NIL 1783345 NIL) (-766 1782276 1782343 1782477 "NARNG-" 1782482 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781155 1781362 1781597 "NAGSP" 1782061 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772427 1774111 1775784 "NAGS" 1779502 T NAGS (NIL) -7 NIL NIL NIL) (-763 1770975 1771283 1771614 "NAGF07" 1772116 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765513 1766804 1768111 "NAGF04" 1769688 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758481 1760095 1761728 "NAGF02" 1763900 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1753705 1754805 1755922 "NAGF01" 1757384 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747333 1748899 1750484 "NAGE04" 1752140 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738502 1740623 1742753 "NAGE02" 1745223 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734455 1735402 1736366 "NAGE01" 1737558 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732250 1732784 1733342 "NAGD03" 1733917 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724000 1725928 1727882 "NAGD02" 1730316 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1717811 1719236 1720676 "NAGD01" 1722580 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714020 1714842 1715679 "NAGC06" 1716994 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712485 1712817 1713173 "NAGC05" 1713684 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1711861 1711980 1712124 "NAGC02" 1712361 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1710820 1711403 1711443 "NAALG" 1711522 NIL NAALG (NIL T) -9 NIL 1711583 NIL) (-749 1710655 1710684 1710774 "NAALG-" 1710779 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704605 1705713 1706900 "MULTSQFR" 1709551 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1703924 1703999 1704183 "MULTFACT" 1704517 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1696648 1700561 1700614 "MTSCAT" 1701684 NIL MTSCAT (NIL T T) -9 NIL 1702199 NIL) (-745 1696360 1696414 1696506 "MTHING" 1696588 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696152 1696185 1696245 "MSYSCMD" 1696320 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692234 1694907 1695227 "MSET" 1695865 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689303 1691795 1691836 "MSETAGG" 1691841 NIL MSETAGG (NIL T) -9 NIL 1691875 NIL) (-741 1685145 1686682 1687427 "MRING" 1688603 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1684711 1684778 1684909 "MRF2" 1685072 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684329 1684364 1684508 "MRATFAC" 1684670 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1681941 1682236 1682667 "MPRFF" 1684034 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676238 1681795 1681892 "MPOLY" 1681897 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1675728 1675763 1675971 "MPCPF" 1676197 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675242 1675285 1675469 "MPC3" 1675679 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674437 1674518 1674739 "MPC2" 1675157 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1672738 1673075 1673465 "MONOTOOL" 1674097 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1671963 1672280 1672308 "MONOID" 1672527 T MONOID (NIL) -9 NIL 1672674 NIL) (-731 1671509 1671628 1671809 "MONOID-" 1671814 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1661984 1667935 1667994 "MONOGEN" 1668668 NIL MONOGEN (NIL T T) -9 NIL 1669124 NIL) (-729 1659202 1659937 1660937 "MONOGEN-" 1661056 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658035 1658481 1658509 "MONADWU" 1658901 T MONADWU (NIL) -9 NIL 1659139 NIL) (-727 1657407 1657566 1657814 "MONADWU-" 1657819 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1656766 1657010 1657038 "MONAD" 1657245 T MONAD (NIL) -9 NIL 1657357 NIL) (-725 1656451 1656529 1656661 "MONAD-" 1656666 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1654740 1655364 1655643 "MOEBIUS" 1656204 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654018 1654422 1654462 "MODULE" 1654467 NIL MODULE (NIL T) -9 NIL 1654506 NIL) (-722 1653586 1653682 1653872 "MODULE-" 1653877 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651266 1651950 1652277 "MODRING" 1653410 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648210 1649371 1649892 "MODOP" 1650795 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1646798 1647277 1647554 "MODMONOM" 1648073 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1636842 1645089 1645503 "MODMON" 1646435 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1633998 1635686 1635962 "MODFIELD" 1636717 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1632975 1633279 1633469 "MMLFORM" 1633828 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632501 1632544 1632723 "MMAP" 1632926 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630580 1631347 1631388 "MLO" 1631811 NIL MLO (NIL T) -9 NIL 1632053 NIL) (-713 1627946 1628462 1629064 "MLIFT" 1630061 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627337 1627421 1627575 "MKUCFUNC" 1627857 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1626936 1627006 1627129 "MKRECORD" 1627260 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1625983 1626145 1626373 "MKFUNC" 1626747 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625371 1625475 1625631 "MKFLCFN" 1625866 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1624648 1624750 1624935 "MKBCFUNC" 1625264 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621355 1624202 1624338 "MINT" 1624532 T MINT (NIL) -8 NIL NIL NIL) (-706 1620167 1620410 1620687 "MHROWRED" 1621110 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615547 1618702 1619107 "MFLOAT" 1619782 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1614904 1614980 1615151 "MFINFACT" 1615459 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611219 1612067 1612951 "MESH" 1614040 T MESH (NIL) -7 NIL NIL NIL) (-702 1609609 1609921 1610274 "MDDFACT" 1610906 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606404 1608768 1608809 "MDAGG" 1609064 NIL MDAGG (NIL T) -9 NIL 1609207 NIL) (-700 1596144 1605697 1605904 "MCMPLX" 1606217 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595281 1595427 1595628 "MCDEN" 1595993 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593171 1593441 1593821 "MCALCFN" 1595011 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592096 1592336 1592569 "MAYBE" 1592977 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1589708 1590231 1590793 "MATSTOR" 1591567 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1585665 1589080 1589328 "MATRIX" 1589493 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581431 1582138 1582874 "MATLIN" 1585022 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571537 1574723 1574800 "MATCAT" 1579680 NIL MATCAT (NIL T T T) -9 NIL 1581097 NIL) (-692 1567893 1568914 1570270 "MATCAT-" 1570275 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566487 1566640 1566973 "MATCAT2" 1567728 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564599 1564923 1565307 "MAPPKG3" 1566162 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563580 1563753 1563975 "MAPPKG2" 1564423 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562079 1562363 1562690 "MAPPKG1" 1563286 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561158 1561485 1561662 "MAPPAST" 1561922 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1560769 1560827 1560950 "MAPHACK3" 1561094 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560361 1560422 1560536 "MAPHACK2" 1560701 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1559799 1559902 1560044 "MAPHACK1" 1560252 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1557878 1558499 1558803 "MAGMA" 1559527 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557357 1557602 1557693 "MACROAST" 1557807 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1553775 1555596 1556057 "M3D" 1556929 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1547850 1552114 1552155 "LZSTAGG" 1552937 NIL LZSTAGG (NIL T) -9 NIL 1553232 NIL) (-679 1543808 1544981 1546438 "LZSTAGG-" 1546443 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1540895 1541699 1542186 "LWORD" 1543353 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540471 1540699 1540774 "LSTAST" 1540840 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1533637 1540242 1540376 "LSQM" 1540381 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1532861 1533000 1533228 "LSPP" 1533492 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1530673 1530974 1531430 "LSMP" 1532550 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527452 1528126 1528856 "LSMP1" 1529975 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521298 1526589 1526630 "LSAGG" 1526692 NIL LSAGG (NIL T) -9 NIL 1526770 NIL) (-671 1517993 1518917 1520130 "LSAGG-" 1520135 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1515592 1517137 1517386 "LPOLY" 1517788 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515174 1515259 1515382 "LPEFRAC" 1515501 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513495 1514268 1514521 "LO" 1515006 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513147 1513259 1513287 "LOGIC" 1513398 T LOGIC (NIL) -9 NIL 1513479 NIL) (-666 1513009 1513032 1513103 "LOGIC-" 1513108 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512202 1512342 1512535 "LODOOPS" 1512865 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1509625 1512118 1512184 "LODO" 1512189 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508163 1508398 1508751 "LODOF" 1509372 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504367 1506798 1506839 "LODOCAT" 1507277 NIL LODOCAT (NIL T) -9 NIL 1507488 NIL) (-661 1504100 1504158 1504285 "LODOCAT-" 1504290 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501420 1503941 1504059 "LODO2" 1504064 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1498855 1501357 1501402 "LODO1" 1501407 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1497736 1497901 1498206 "LODEEF" 1498678 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493039 1495930 1495971 "LNAGG" 1496833 NIL LNAGG (NIL T) -9 NIL 1497268 NIL) (-656 1492186 1492400 1492742 "LNAGG-" 1492747 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488322 1489111 1489750 "LMOPS" 1491601 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1487725 1488113 1488154 "LMODULE" 1488159 NIL LMODULE (NIL T) -9 NIL 1488185 NIL) (-653 1484923 1487370 1487493 "LMDICT" 1487635 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484329 1484550 1484591 "LLINSET" 1484782 NIL LLINSET (NIL T) -9 NIL 1484873 NIL) (-651 1484028 1484237 1484297 "LITERAL" 1484302 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477191 1482962 1483266 "LIST" 1483757 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1476716 1476790 1476929 "LIST3" 1477111 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1475723 1475901 1476129 "LIST2" 1476534 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1473857 1474169 1474568 "LIST2MAP" 1475370 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473453 1473690 1473731 "LINSET" 1473736 NIL LINSET (NIL T) -9 NIL 1473770 NIL) (-645 1472114 1472784 1472825 "LINEXP" 1473080 NIL LINEXP (NIL T) -9 NIL 1473229 NIL) (-644 1470761 1471021 1471318 "LINDEP" 1471866 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467528 1468247 1469024 "LIMITRF" 1470016 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1465831 1466127 1466536 "LIMITPS" 1467223 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460259 1465342 1465570 "LIE" 1465652 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459207 1459676 1459716 "LIECAT" 1459856 NIL LIECAT (NIL T) -9 NIL 1460007 NIL) (-639 1459048 1459075 1459163 "LIECAT-" 1459168 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451635 1458588 1458744 "LIB" 1458912 T LIB (NIL) -8 NIL NIL NIL) (-637 1447270 1448153 1449088 "LGROBP" 1450752 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445268 1445542 1445892 "LF" 1446991 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444108 1444800 1444828 "LFCAT" 1445035 T LFCAT (NIL) -9 NIL 1445174 NIL) (-634 1441010 1441640 1442328 "LEXTRIPK" 1443472 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1437754 1438580 1439083 "LEXP" 1440590 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437230 1437475 1437567 "LETAST" 1437682 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435628 1435941 1436342 "LEADCDET" 1436912 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1434818 1434892 1435121 "LAZM3PK" 1435549 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1429735 1432895 1433433 "LAUPOL" 1434330 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429314 1429358 1429519 "LAPLACE" 1429685 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427253 1428415 1428666 "LA" 1429147 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426247 1426831 1426872 "LALG" 1426934 NIL LALG (NIL T) -9 NIL 1426993 NIL) (-625 1425961 1426020 1426156 "LALG-" 1426161 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1425796 1425820 1425861 "KVTFROM" 1425923 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1424719 1425163 1425348 "KTVLOGIC" 1425631 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424554 1424578 1424619 "KRCFROM" 1424681 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423458 1423645 1423944 "KOVACIC" 1424354 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423293 1423317 1423358 "KONVERT" 1423420 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423128 1423152 1423193 "KOERCE" 1423255 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1420958 1421721 1422098 "KERNEL" 1422784 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420454 1420535 1420667 "KERNEL2" 1420872 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414224 1418993 1419047 "KDAGG" 1419424 NIL KDAGG (NIL T T) -9 NIL 1419630 NIL) (-615 1413753 1413877 1414082 "KDAGG-" 1414087 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1406901 1413414 1413569 "KAFILE" 1413631 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401329 1406412 1406640 "JORDAN" 1406722 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400708 1400978 1401099 "JOINAST" 1401228 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400554 1400613 1400668 "JAVACODE" 1400673 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1396806 1398759 1398813 "IXAGG" 1399742 NIL IXAGG (NIL T T) -9 NIL 1400201 NIL) (-609 1395725 1396031 1396450 "IXAGG-" 1396455 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391255 1395647 1395706 "IVECTOR" 1395711 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390021 1390258 1390524 "ITUPLE" 1391022 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388523 1388700 1388995 "ITRIGMNP" 1389843 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387268 1387472 1387755 "ITFUN3" 1388299 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1386900 1386957 1387066 "ITFUN2" 1387205 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386059 1386380 1386554 "ITFORM" 1386746 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384020 1385079 1385357 "ITAYLOR" 1385814 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1372965 1378157 1379320 "ISUPS" 1382890 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372069 1372209 1372445 "ISUMP" 1372812 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367444 1372014 1372055 "ISTRING" 1372060 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1366920 1367165 1367257 "ISAST" 1367372 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366129 1366211 1366427 "IRURPK" 1366834 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365065 1365266 1365506 "IRSN" 1365909 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363136 1363491 1363920 "IRRF2F" 1364703 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1362883 1362921 1362997 "IRREDFFX" 1363092 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361498 1361757 1362056 "IROOT" 1362616 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358102 1359182 1359874 "IR" 1360838 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357307 1357595 1357746 "IRFORM" 1357971 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1354920 1355415 1355981 "IR2" 1356785 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354020 1354133 1354347 "IR2F" 1354803 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1353811 1353845 1353905 "IPRNTPK" 1353980 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350392 1353700 1353769 "IPF" 1353774 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1348719 1350317 1350374 "IPADIC" 1350379 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348031 1348279 1348409 "IP4ADDR" 1348609 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347405 1347660 1347792 "IOMODE" 1347919 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346478 1347002 1347129 "IOBFILE" 1347298 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1345966 1346382 1346410 "IOBCON" 1346415 T IOBCON (NIL) -9 NIL 1346436 NIL) (-581 1345477 1345535 1345718 "INVLAPLA" 1345902 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335125 1337479 1339865 "INTTR" 1343141 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331460 1332202 1333067 "INTTOOLS" 1334310 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331046 1331137 1331254 "INTSLPE" 1331363 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1328999 1330969 1331028 "INTRVL" 1331033 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326601 1327113 1327688 "INTRF" 1328484 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326012 1326109 1326251 "INTRET" 1326499 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324009 1324398 1324868 "INTRAT" 1325620 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321272 1321855 1322474 "INTPM" 1323494 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318017 1318616 1319354 "INTPAF" 1320658 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313196 1314158 1315209 "INTPACK" 1316986 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310144 1312993 1313102 "INT" 1313107 T INT (NIL) -8 NIL NIL NIL) (-569 1309396 1309548 1309756 "INTHERTR" 1309986 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1308835 1308915 1309103 "INTHERAL" 1309310 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306681 1307124 1307581 "INTHEORY" 1308398 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298087 1299708 1301480 "INTG0" 1305033 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278660 1283450 1288260 "INTFTBL" 1293297 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1277909 1278047 1278220 "INTFACT" 1278519 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275336 1275782 1276339 "INTEF" 1277463 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273703 1274442 1274470 "INTDOM" 1274771 T INTDOM (NIL) -9 NIL 1274978 NIL) (-561 1273072 1273246 1273488 "INTDOM-" 1273493 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269460 1271388 1271442 "INTCAT" 1272241 NIL INTCAT (NIL T) -9 NIL 1272562 NIL) (-559 1268932 1269035 1269163 "INTBIT" 1269352 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267631 1267785 1268092 "INTALG" 1268777 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267114 1267204 1267361 "INTAF" 1267535 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260457 1266924 1267064 "INTABL" 1267069 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1259798 1260264 1260329 "INT8" 1260363 T INT8 (NIL) -8 NIL NIL 1260408) (-554 1259138 1259604 1259669 "INT64" 1259703 T INT64 (NIL) -8 NIL NIL 1259748) (-553 1258478 1258944 1259009 "INT32" 1259043 T INT32 (NIL) -8 NIL NIL 1259088) (-552 1257818 1258284 1258349 "INT16" 1258383 T INT16 (NIL) -8 NIL NIL 1258428) (-551 1252728 1255441 1255469 "INS" 1256403 T INS (NIL) -9 NIL 1257068 NIL) (-550 1249968 1250739 1251713 "INS-" 1251786 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1248743 1248970 1249268 "INPSIGN" 1249721 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1247861 1247978 1248175 "INPRODPF" 1248623 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1246755 1246872 1247109 "INPRODFF" 1247741 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1245755 1245907 1246167 "INNMFACT" 1246591 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1244952 1245049 1245237 "INMODGCD" 1245654 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243460 1243705 1244029 "INFSP" 1244697 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242644 1242761 1242944 "INFPROD0" 1243340 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239499 1240709 1241224 "INFORM" 1242137 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239109 1239169 1239267 "INFORM1" 1239434 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238632 1238721 1238835 "INFINITY" 1239015 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1237808 1238352 1238453 "INETCLTS" 1238551 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236424 1236674 1236995 "INEP" 1237556 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235673 1236321 1236386 "INDE" 1236391 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235237 1235305 1235422 "INCRMAPS" 1235600 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234055 1234506 1234712 "INBFILE" 1235051 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229354 1230291 1231235 "INBFF" 1233143 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228262 1228531 1228559 "INBCON" 1229072 T INBCON (NIL) -9 NIL 1229338 NIL) (-532 1227514 1227737 1228013 "INBCON-" 1228018 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1226993 1227238 1227329 "INAST" 1227443 T INAST (NIL) -8 NIL NIL NIL) (-530 1226420 1226672 1226778 "IMPTAST" 1226907 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1222866 1226264 1226368 "IMATRIX" 1226373 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221574 1221697 1222013 "IMATQF" 1222722 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1219794 1220021 1220358 "IMATLIN" 1221330 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214372 1219718 1219776 "ILIST" 1219781 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212277 1214232 1214345 "IIARRAY2" 1214350 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207675 1212188 1212252 "IFF" 1212257 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207022 1207292 1207408 "IFAST" 1207579 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202017 1206314 1206502 "IFARRAY" 1206879 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201197 1201921 1201994 "IFAMON" 1201999 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1200781 1200846 1200900 "IEVALAB" 1201107 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200456 1200524 1200684 "IEVALAB-" 1200689 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200087 1200370 1200433 "IDPO" 1200438 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199337 1199976 1200051 "IDPOAMS" 1200056 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198644 1199226 1199301 "IDPOAM" 1199306 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197703 1197979 1198032 "IDPC" 1198445 NIL IDPC (NIL T T) -9 NIL 1198594 NIL) (-514 1197172 1197595 1197668 "IDPAM" 1197673 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196548 1197064 1197137 "IDPAG" 1197142 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196193 1196384 1196459 "IDENT" 1196493 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192448 1193296 1194191 "IDECOMP" 1195350 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185286 1186371 1187418 "IDEAL" 1191484 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184446 1184558 1184758 "ICDEN" 1185170 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183517 1183926 1184073 "ICARD" 1184319 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181577 1181890 1182295 "IBPTOOLS" 1183194 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177184 1181197 1181310 "IBITS" 1181496 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1173907 1174483 1175178 "IBATOOL" 1176601 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171686 1172148 1172681 "IBACHIN" 1173442 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169515 1171532 1171635 "IARRAY2" 1171640 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165621 1169441 1169498 "IARRAY1" 1169503 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1159730 1164033 1164514 "IAN" 1165160 T IAN (NIL) -8 NIL NIL NIL) (-500 1159241 1159298 1159471 "IALGFACT" 1159667 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1158769 1158882 1158910 "HYPCAT" 1159117 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158307 1158424 1158610 "HYPCAT-" 1158615 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1157902 1158102 1158185 "HOSTNAME" 1158244 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1157747 1157784 1157825 "HOMOTOP" 1157830 NIL HOMOTOP (NIL T) -9 NIL 1157863 NIL) (-495 1154379 1155757 1155798 "HOAGG" 1156779 NIL HOAGG (NIL T) -9 NIL 1157458 NIL) (-494 1152973 1153372 1153898 "HOAGG-" 1153903 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1146975 1152566 1152716 "HEXADEC" 1152843 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1145723 1145945 1146208 "HEUGCD" 1146752 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1144799 1145560 1145690 "HELLFDIV" 1145695 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1142978 1144576 1144664 "HEAP" 1144743 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142241 1142530 1142664 "HEADAST" 1142864 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136107 1142156 1142218 "HDP" 1142223 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130095 1135742 1135894 "HDMP" 1136008 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129419 1129559 1129723 "HB" 1129951 T HB (NIL) -7 NIL NIL NIL) (-485 1122805 1129265 1129369 "HASHTBL" 1129374 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122281 1122526 1122618 "HASAST" 1122733 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120059 1121903 1122085 "HACKPI" 1122119 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1115727 1119912 1120025 "GTSET" 1120030 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109142 1115605 1115703 "GSTBL" 1115708 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101420 1108173 1108438 "GSERIES" 1108933 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100561 1100978 1101006 "GROUP" 1101209 T GROUP (NIL) -9 NIL 1101343 NIL) (-478 1099927 1100086 1100337 "GROUP-" 1100342 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098294 1098615 1099002 "GROEBSOL" 1099604 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097208 1097496 1097547 "GRMOD" 1098076 NIL GRMOD (NIL T T) -9 NIL 1098244 NIL) (-475 1096976 1097012 1097140 "GRMOD-" 1097145 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092266 1093330 1094330 "GRIMAGE" 1095996 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1090732 1090993 1091317 "GRDEF" 1091962 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090176 1090292 1090433 "GRAY" 1090611 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089363 1089769 1089820 "GRALG" 1089973 NIL GRALG (NIL T T) -9 NIL 1090066 NIL) (-470 1089024 1089097 1089260 "GRALG-" 1089265 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1085801 1088609 1088787 "GPOLSET" 1088931 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085155 1085212 1085470 "GOSPER" 1085738 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1080887 1081593 1082119 "GMODPOL" 1084854 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1079892 1080076 1080314 "GHENSEL" 1080699 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074048 1074891 1075911 "GENUPS" 1078976 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1073745 1073796 1073885 "GENUFACT" 1073991 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073157 1073234 1073399 "GENPGCD" 1073663 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072631 1072666 1072879 "GENMFACT" 1073116 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071197 1071454 1071761 "GENEEZ" 1072374 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065345 1070808 1070970 "GDMP" 1071120 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054688 1059116 1060222 "GCNAALG" 1064328 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053015 1053877 1053905 "GCDDOM" 1054160 T GCDDOM (NIL) -9 NIL 1054317 NIL) (-457 1052485 1052612 1052827 "GCDDOM-" 1052832 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051157 1051342 1051646 "GB" 1052264 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1039773 1042103 1044495 "GBINTERN" 1048848 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037610 1037902 1038323 "GBF" 1039448 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036391 1036556 1036823 "GBEUCLID" 1037426 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1035740 1035865 1036014 "GAUSSFAC" 1036262 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034107 1034409 1034723 "GALUTIL" 1035459 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032415 1032689 1033013 "GALPOLYU" 1033834 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1029780 1030070 1030477 "GALFACTU" 1032112 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021586 1023085 1024693 "GALFACT" 1028212 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1018974 1019632 1019660 "FVFUN" 1020816 T FVFUN (NIL) -9 NIL 1021536 NIL) (-446 1018240 1018422 1018450 "FVC" 1018741 T FVC (NIL) -9 NIL 1018924 NIL) (-445 1017883 1018065 1018133 "FUNDESC" 1018192 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017498 1017680 1017761 "FUNCTION" 1017835 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015242 1015820 1016286 "FT" 1017052 T FT (NIL) -8 NIL NIL NIL) (-442 1014033 1014543 1014746 "FTEM" 1015059 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012324 1012613 1013010 "FSUPFACT" 1013724 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1010721 1011010 1011342 "FST" 1012012 T FST (NIL) -8 NIL NIL NIL) (-439 1009920 1010026 1010214 "FSRED" 1010603 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008619 1008875 1009222 "FSPRMELT" 1009635 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1005925 1006363 1006849 "FSPECF" 1008182 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987563 995894 995935 "FS" 999819 NIL FS (NIL T) -9 NIL 1002108 NIL) (-435 976206 979199 983256 "FS-" 983556 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 975734 975788 975958 "FSINT" 976147 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974026 974727 975030 "FSERIES" 975513 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973068 973184 973408 "FSCINT" 973906 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969276 972012 972053 "FSAGG" 972423 NIL FSAGG (NIL T) -9 NIL 972682 NIL) (-430 967038 967639 968435 "FSAGG-" 968530 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966080 966223 966450 "FSAGG2" 966891 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 963762 964042 964589 "FS2UPS" 965798 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963396 963439 963568 "FS2" 963713 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962274 962445 962747 "FS2EXPXP" 963221 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961700 961815 961967 "FRUTIL" 962154 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953113 957195 958553 "FR" 960374 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948127 950802 950842 "FRNAALG" 952162 NIL FRNAALG (NIL T) -9 NIL 952760 NIL) (-422 943800 944876 946151 "FRNAALG-" 946901 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943438 943481 943608 "FRNAAF2" 943751 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 941813 942287 942583 "FRMOD" 943250 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939556 940188 940506 "FRIDEAL" 941604 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938747 938834 939125 "FRIDEAL2" 939463 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 937880 938294 938335 "FRETRCT" 938340 NIL FRETRCT (NIL T) -9 NIL 938516 NIL) (-416 936992 937223 937574 "FRETRCT-" 937579 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934080 935290 935349 "FRAMALG" 936231 NIL FRAMALG (NIL T T) -9 NIL 936523 NIL) (-414 932214 932669 933299 "FRAMALG-" 933522 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926133 931687 931964 "FRAC" 931969 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 925769 925826 925933 "FRAC2" 926070 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925405 925462 925569 "FR2" 925706 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 919918 922811 922839 "FPS" 923958 T FPS (NIL) -9 NIL 924515 NIL) (-409 919367 919476 919640 "FPS-" 919786 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916669 918338 918366 "FPC" 918591 T FPC (NIL) -9 NIL 918733 NIL) (-407 916462 916502 916599 "FPC-" 916604 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915252 915950 915991 "FPATMAB" 915996 NIL FPATMAB (NIL T) -9 NIL 916148 NIL) (-405 912925 913428 913854 "FPARFRAC" 914889 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908319 908817 909499 "FORTRAN" 912357 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906035 906535 907074 "FORT" 907800 T FORT (NIL) -7 NIL NIL NIL) (-402 903711 904273 904301 "FORTFN" 905361 T FORTFN (NIL) -9 NIL 905985 NIL) (-401 903475 903525 903553 "FORTCAT" 903612 T FORTCAT (NIL) -9 NIL 903674 NIL) (-400 901581 902091 902481 "FORMULA" 903105 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901369 901399 901468 "FORMULA1" 901545 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 900892 900944 901117 "FORDER" 901311 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 899988 900152 900345 "FOP" 900719 T FOP (NIL) -7 NIL NIL NIL) (-396 898569 899268 899442 "FNLA" 899870 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897298 897713 897741 "FNCAT" 898201 T FNCAT (NIL) -9 NIL 898461 NIL) (-394 896837 897257 897285 "FNAME" 897290 T FNAME (NIL) -8 NIL NIL NIL) (-393 895400 896363 896391 "FMTC" 896396 T FMTC (NIL) -9 NIL 896432 NIL) (-392 894146 895336 895382 "FMONOID" 895387 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 890974 892142 892183 "FMONCAT" 893400 NIL FMONCAT (NIL T) -9 NIL 894005 NIL) (-390 890166 890716 890865 "FM" 890870 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887590 888236 888264 "FMFUN" 889408 T FMFUN (NIL) -9 NIL 890116 NIL) (-388 886859 887040 887068 "FMC" 887358 T FMC (NIL) -9 NIL 887540 NIL) (-387 883938 884798 884852 "FMCAT" 886047 NIL FMCAT (NIL T T) -9 NIL 886542 NIL) (-386 882804 883704 883804 "FM1" 883883 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880578 880994 881488 "FLOATRP" 882355 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874156 878307 878928 "FLOAT" 879977 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871594 872094 872672 "FLOATCP" 873623 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870334 871172 871213 "FLINEXP" 871218 NIL FLINEXP (NIL T) -9 NIL 871311 NIL) (-381 869488 869723 870051 "FLINEXP-" 870056 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868564 868708 868932 "FLASORT" 869340 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865680 866548 866600 "FLALG" 867827 NIL FLALG (NIL T T) -9 NIL 868294 NIL) (-378 859386 863136 863177 "FLAGG" 864439 NIL FLAGG (NIL T) -9 NIL 865091 NIL) (-377 858112 858451 858941 "FLAGG-" 858946 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857154 857297 857524 "FLAGG2" 857965 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854005 855013 855072 "FINRALG" 856200 NIL FINRALG (NIL T T) -9 NIL 856708 NIL) (-374 853165 853394 853733 "FINRALG-" 853738 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852545 852784 852812 "FINITE" 853008 T FINITE (NIL) -9 NIL 853115 NIL) (-372 844902 847089 847129 "FINAALG" 850796 NIL FINAALG (NIL T) -9 NIL 852249 NIL) (-371 840234 841284 842428 "FINAALG-" 843807 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839602 839989 840092 "FILE" 840164 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838260 838598 838652 "FILECAT" 839336 NIL FILECAT (NIL T T) -9 NIL 839552 NIL) (-368 835976 837504 837532 "FIELD" 837572 T FIELD (NIL) -9 NIL 837652 NIL) (-367 834596 834981 835492 "FIELD-" 835497 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832446 833231 833578 "FGROUP" 834282 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831536 831700 831920 "FGLMICPK" 832278 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827368 831461 831518 "FFX" 831523 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 826969 827030 827165 "FFSLPE" 827301 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 822959 823741 824537 "FFPOLY" 826205 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822463 822499 822708 "FFPOLY2" 822917 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818309 822382 822445 "FFP" 822450 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813707 818220 818284 "FF" 818289 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 808833 813050 813240 "FFNBX" 813561 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 803761 807968 808226 "FFNBP" 808687 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798394 803045 803256 "FFNB" 803594 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797226 797424 797739 "FFINTBAS" 798191 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793295 795515 795543 "FFIELDC" 796163 T FFIELDC (NIL) -9 NIL 796539 NIL) (-353 791957 792328 792825 "FFIELDC-" 792830 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791526 791572 791696 "FFHOM" 791899 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789221 789708 790225 "FFF" 791041 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 784839 788963 789064 "FFCGX" 789164 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780461 784571 784678 "FFCGP" 784782 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775644 780188 780296 "FFCG" 780397 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757040 766121 766207 "FFCAT" 771372 NIL FFCAT (NIL T T T) -9 NIL 772823 NIL) (-346 752237 753285 754599 "FFCAT-" 755829 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751648 751691 751926 "FFCAT2" 752188 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 740971 744620 745840 "FEXPR" 750500 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 739933 740368 740409 "FEVALAB" 740493 NIL FEVALAB (NIL T) -9 NIL 740754 NIL) (-342 739092 739302 739640 "FEVALAB-" 739645 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737658 738475 738678 "FDIV" 738991 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734678 735419 735534 "FDIVCAT" 737102 NIL FDIVCAT (NIL T T T T) -9 NIL 737539 NIL) (-339 734440 734467 734637 "FDIVCAT-" 734642 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733660 733747 734024 "FDIV2" 734347 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732634 732955 733157 "FCTRDATA" 733478 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731320 731579 731868 "FCPAK1" 732365 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730419 730820 730961 "FCOMP" 731211 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714124 717569 721107 "FC" 726901 T FC (NIL) -8 NIL NIL NIL) (-333 706487 710515 710555 "FAXF" 712357 NIL FAXF (NIL T) -9 NIL 713049 NIL) (-332 703764 704421 705246 "FAXF-" 705711 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 698816 703140 703316 "FARRAY" 703621 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 693710 695777 695830 "FAMR" 696853 NIL FAMR (NIL T T) -9 NIL 697313 NIL) (-329 692600 692902 693337 "FAMR-" 693342 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 691769 692522 692575 "FAMONOID" 692580 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689555 690265 690318 "FAMONC" 691259 NIL FAMONC (NIL T T) -9 NIL 691645 NIL) (-326 688219 689309 689446 "FAGROUP" 689451 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686014 686333 686736 "FACUTIL" 687900 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685113 685298 685520 "FACTFUNC" 685824 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677535 684416 684615 "EXPUPXS" 684969 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675018 675558 676144 "EXPRTUBE" 676969 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671289 671881 672611 "EXPRODE" 674357 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 656774 669938 670367 "EXPR" 670893 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651328 651915 652721 "EXPR2UPS" 656072 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 650960 651017 651126 "EXPR2" 651265 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642348 650111 650402 "EXPEXPAN" 650796 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642148 642305 642334 "EXIT" 642339 T EXIT (NIL) -8 NIL NIL NIL) (-315 641628 641872 641963 "EXITAST" 642077 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641255 641317 641430 "EVALCYC" 641560 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 640796 640914 640955 "EVALAB" 641125 NIL EVALAB (NIL T) -9 NIL 641229 NIL) (-312 640277 640399 640620 "EVALAB-" 640625 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637645 638947 638975 "EUCDOM" 639530 T EUCDOM (NIL) -9 NIL 639880 NIL) (-310 636050 636492 637082 "EUCDOM-" 637087 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623589 626348 629098 "ESTOOLS" 633320 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623221 623278 623387 "ESTOOLS2" 623526 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 622972 623014 623094 "ESTOOLS1" 623173 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617009 618617 618645 "ES" 621413 T ES (NIL) -9 NIL 622823 NIL) (-305 611956 613243 615060 "ES-" 615224 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608330 609091 609871 "ESCONT" 611196 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608075 608107 608189 "ESCONT1" 608292 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 607750 607800 607900 "ES2" 608019 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607380 607438 607547 "ES1" 607686 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606596 606725 606901 "ERROR" 607224 T ERROR (NIL) -7 NIL NIL NIL) (-299 599988 606455 606546 "EQTBL" 606551 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592491 595302 596751 "EQ" 598572 NIL -2210 (NIL T) -8 NIL NIL NIL) (-297 592123 592180 592289 "EQ2" 592428 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587414 588461 589554 "EP" 591062 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586014 586305 586611 "ENV" 587128 T ENV (NIL) -8 NIL NIL NIL) (-294 585108 585662 585690 "ENTIRER" 585695 T ENTIRER (NIL) -9 NIL 585741 NIL) (-293 581802 583290 583651 "EMR" 584916 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 580932 581117 581171 "ELTAGG" 581551 NIL ELTAGG (NIL T T) -9 NIL 581762 NIL) (-291 580651 580713 580854 "ELTAGG-" 580859 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580415 580444 580498 "ELTAB" 580582 NIL ELTAB (NIL T T) -9 NIL 580634 NIL) (-289 579541 579687 579886 "ELFUTS" 580266 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579283 579339 579367 "ELEMFUN" 579472 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579153 579174 579242 "ELEMFUN-" 579247 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 573967 577223 577264 "ELAGG" 578204 NIL ELAGG (NIL T) -9 NIL 578667 NIL) (-285 572252 572686 573349 "ELAGG-" 573354 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571564 571701 571857 "ELABOR" 572116 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570225 570504 570798 "ELABEXPR" 571290 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563089 564892 565719 "EFUPXS" 569501 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556539 558340 559150 "EFULS" 562365 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554024 554382 554854 "EFSTRUC" 556171 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543815 545381 546929 "EF" 552539 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 542889 543300 543449 "EAB" 543686 T EAB (NIL) -8 NIL NIL NIL) (-277 542071 542848 542876 "E04UCFA" 542881 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541253 542030 542058 "E04NAFA" 542063 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540435 541212 541240 "E04MBFA" 541245 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539617 540394 540422 "E04JAFA" 540427 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538801 539576 539604 "E04GCFA" 539609 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 537985 538760 538788 "E04FDFA" 538793 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537167 537944 537972 "E04DGFA" 537977 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531340 532692 534056 "E04AGNT" 535823 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530020 530526 530566 "DVARCAT" 531041 NIL DVARCAT (NIL T) -9 NIL 531240 NIL) (-268 529224 529436 529750 "DVARCAT-" 529755 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522361 529023 529152 "DSMP" 529157 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517142 518306 519374 "DROPT" 521313 T DROPT (NIL) -8 NIL NIL NIL) (-265 516807 516866 516964 "DROPT1" 517077 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 511922 513048 514185 "DROPT0" 515690 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510267 510592 510978 "DRAWPT" 511556 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504854 505777 506856 "DRAW" 509241 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504487 504540 504658 "DRAWHACK" 504795 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503218 503487 503778 "DRAWCX" 504216 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502733 502802 502953 "DRAWCURV" 503144 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493201 495163 497278 "DRAWCFUN" 500638 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 489965 491894 491935 "DQAGG" 492564 NIL DQAGG (NIL T) -9 NIL 492838 NIL) (-256 478089 484558 484641 "DPOLCAT" 486493 NIL DPOLCAT (NIL T T T T) -9 NIL 487038 NIL) (-255 472926 474274 476232 "DPOLCAT-" 476237 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466048 472787 472885 "DPMO" 472890 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459073 465828 465995 "DPMM" 466000 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458643 458857 458946 "DOMTMPLT" 459004 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458076 458445 458525 "DOMCTOR" 458583 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457288 457556 457707 "DOMAIN" 457945 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451276 456923 457075 "DMP" 457189 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450876 450932 451076 "DLP" 451214 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444698 450203 450393 "DLIST" 450718 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441495 443551 443592 "DLAGG" 444142 NIL DLAGG (NIL T) -9 NIL 444372 NIL) (-245 440171 440835 440863 "DIVRING" 440955 T DIVRING (NIL) -9 NIL 441038 NIL) (-244 439408 439598 439898 "DIVRING-" 439903 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437510 437867 438273 "DISPLAY" 439022 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431398 437424 437487 "DIRPROD" 437492 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430246 430449 430714 "DIRPROD2" 431191 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419021 425027 425080 "DIRPCAT" 425490 NIL DIRPCAT (NIL NIL T) -9 NIL 426330 NIL) (-239 416347 416989 417870 "DIRPCAT-" 418207 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415634 415794 415980 "DIOSP" 416181 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412289 414546 414587 "DIOPS" 415021 NIL DIOPS (NIL T) -9 NIL 415250 NIL) (-236 411838 411952 412143 "DIOPS-" 412148 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410661 411289 411317 "DIFRING" 411504 T DIFRING (NIL) -9 NIL 411614 NIL) (-234 410307 410384 410536 "DIFRING-" 410541 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408043 409315 409356 "DIFEXT" 409719 NIL DIFEXT (NIL T) -9 NIL 410013 NIL) (-232 406328 406756 407422 "DIFEXT-" 407427 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403603 405860 405901 "DIAGG" 405906 NIL DIAGG (NIL T) -9 NIL 405926 NIL) (-230 402987 403144 403396 "DIAGG-" 403401 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398404 401946 402223 "DHMATRIX" 402756 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394016 394925 395935 "DFSFUN" 397414 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389095 392947 393259 "DFLOAT" 393724 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387358 387639 388028 "DFINTTLS" 388803 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384387 385379 385779 "DERHAM" 387024 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382188 384162 384251 "DEQUEUE" 384331 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381442 381575 381758 "DEGRED" 382050 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377872 378617 379463 "DEFINTRF" 380670 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375427 375896 376488 "DEFINTEF" 377391 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374777 375047 375162 "DEFAST" 375332 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368779 374370 374520 "DECIMAL" 374647 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366291 366749 367255 "DDFACT" 368323 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365887 365930 366081 "DBLRESP" 366242 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363759 364120 364480 "DBASE" 365654 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363001 363239 363385 "DATAARY" 363658 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362107 362960 362988 "D03FAFA" 362993 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361214 362066 362094 "D03EEFA" 362099 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359164 359630 360119 "D03AGNT" 360745 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358453 359123 359151 "D02EJFA" 359156 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357742 358412 358440 "D02CJFA" 358445 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357031 357701 357729 "D02BHFA" 357734 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356320 356990 357018 "D02BBFA" 357023 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349517 351106 352712 "D02AGNT" 354734 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347285 347808 348354 "D01WGTS" 348991 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346352 347244 347272 "D01TRNS" 347277 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345420 346311 346339 "D01GBFA" 346344 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344488 345379 345407 "D01FCFA" 345412 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343556 344447 344475 "D01ASFA" 344480 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342624 343515 343543 "D01AQFA" 343548 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341692 342583 342611 "D01APFA" 342616 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340760 341651 341679 "D01ANFA" 341684 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339828 340719 340747 "D01AMFA" 340752 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338896 339787 339815 "D01ALFA" 339820 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 337964 338855 338883 "D01AKFA" 338888 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337032 337923 337951 "D01AJFA" 337956 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330327 331880 333441 "D01AGNT" 335491 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329664 329792 329944 "CYCLOTOM" 330195 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326397 327112 327839 "CYCLES" 328957 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325709 325843 326014 "CVMP" 326258 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323550 323808 324177 "CTRIGMNP" 325437 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 322986 323344 323417 "CTOR" 323497 T CTOR (NIL) -8 NIL NIL NIL) (-188 322495 322717 322818 "CTORKIND" 322905 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321786 322102 322130 "CTORCAT" 322312 T CTORCAT (NIL) -9 NIL 322425 NIL) (-186 321384 321495 321654 "CTORCAT-" 321659 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320846 321058 321166 "CTORCALL" 321308 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320220 320319 320472 "CSTTOOLS" 320743 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316019 316676 317434 "CRFP" 319532 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315494 315740 315832 "CRCEAST" 315947 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314541 314726 314954 "CRAPACK" 315298 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313925 314026 314230 "CPMATCH" 314417 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313650 313678 313784 "CPIMA" 313891 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 309998 310670 311389 "COORDSYS" 312985 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309410 309531 309673 "CONTOUR" 309876 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305301 307413 307905 "CONTFRAC" 308950 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305181 305202 305230 "CONDUIT" 305267 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304269 304823 304851 "COMRING" 304856 T COMRING (NIL) -9 NIL 304908 NIL) (-173 303323 303627 303811 "COMPPROP" 304105 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 302984 303019 303147 "COMPLPAT" 303282 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293275 302793 302902 "COMPLEX" 302907 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292911 292968 293075 "COMPLEX2" 293212 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292250 292371 292531 "COMPILER" 292771 T COMPILER (NIL) -8 NIL NIL NIL) (-168 291968 292003 292101 "COMPFACT" 292209 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276048 286042 286082 "COMPCAT" 287086 NIL COMPCAT (NIL T) -9 NIL 288434 NIL) (-166 265560 268487 272114 "COMPCAT-" 272470 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265289 265317 265420 "COMMUPC" 265526 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265083 265117 265176 "COMMONOP" 265250 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264639 264834 264921 "COMM" 265016 T COMM (NIL) -8 NIL NIL NIL) (-162 264215 264443 264518 "COMMAAST" 264584 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263464 263658 263686 "COMBOPC" 264024 T COMBOPC (NIL) -9 NIL 264199 NIL) (-160 262360 262570 262812 "COMBINAT" 263254 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258817 259391 260018 "COMBF" 261782 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257575 257933 258168 "COLOR" 258602 T COLOR (NIL) -8 NIL NIL NIL) (-157 257051 257296 257388 "COLONAST" 257503 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256691 256738 256863 "CMPLXRT" 256998 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256139 256391 256490 "CLLCTAST" 256612 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251641 252669 253749 "CLIP" 255079 T CLIP (NIL) -7 NIL NIL NIL) (-153 249982 250742 250982 "CLIF" 251468 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246157 248128 248169 "CLAGG" 249098 NIL CLAGG (NIL T) -9 NIL 249634 NIL) (-151 244579 245036 245619 "CLAGG-" 245624 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244123 244208 244348 "CINTSLPE" 244488 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241624 242095 242643 "CHVAR" 243651 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240798 241352 241380 "CHARZ" 241385 T CHARZ (NIL) -9 NIL 241400 NIL) (-147 240552 240592 240670 "CHARPOL" 240752 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239610 240197 240225 "CHARNZ" 240272 T CHARNZ (NIL) -9 NIL 240328 NIL) (-145 237516 238264 238617 "CHAR" 239277 T CHAR (NIL) -8 NIL NIL NIL) (-144 237242 237303 237331 "CFCAT" 237442 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236483 236594 236777 "CDEN" 237126 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232448 235636 235916 "CCLASS" 236223 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231699 231856 232033 "CATEGORY" 232291 T -10 (NIL) -8 NIL NIL NIL) (-140 231272 231618 231666 "CATCTOR" 231671 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230723 230975 231073 "CATAST" 231194 T CATAST (NIL) -8 NIL NIL NIL) (-138 230199 230444 230536 "CASEAST" 230651 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225337 226356 227100 "CARTEN" 229511 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224445 224593 224814 "CARTEN2" 225184 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222761 223595 223852 "CARD" 224208 T CARD (NIL) -8 NIL NIL NIL) (-134 222337 222565 222640 "CAPSLAST" 222706 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221841 222049 222077 "CACHSET" 222209 T CACHSET (NIL) -9 NIL 222287 NIL) (-132 221311 221633 221661 "CABMON" 221711 T CABMON (NIL) -9 NIL 221767 NIL) (-131 220784 221015 221125 "BYTEORD" 221221 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219766 220318 220460 "BYTE" 220623 T BYTE (NIL) -8 NIL NIL 220745) (-129 215116 219271 219443 "BYTEBUF" 219614 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212625 214808 214915 "BTREE" 215042 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 210074 212273 212395 "BTOURN" 212535 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207444 209544 209585 "BTCAT" 209653 NIL BTCAT (NIL T) -9 NIL 209730 NIL) (-125 207111 207191 207340 "BTCAT-" 207345 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202490 206370 206398 "BTAGG" 206512 T BTAGG (NIL) -9 NIL 206622 NIL) (-123 201980 202105 202311 "BTAGG-" 202316 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198975 201258 201473 "BSTREE" 201797 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198113 198239 198423 "BRILL" 198831 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194765 196839 196880 "BRAGG" 197529 NIL BRAGG (NIL T) -9 NIL 197787 NIL) (-119 193294 193700 194255 "BRAGG-" 194260 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186521 192638 192823 "BPADICRT" 193141 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184836 186458 186503 "BPADIC" 186508 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184534 184564 184678 "BOUNDZRO" 184800 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179762 180960 181872 "BOP" 183642 T BOP (NIL) -8 NIL NIL NIL) (-114 177543 177947 178422 "BOP1" 179320 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177244 177305 177333 "BOOLE" 177444 T BOOLE (NIL) -9 NIL 177526 NIL) (-112 176069 176818 176967 "BOOLEAN" 177115 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175348 175752 175806 "BMODULE" 175811 NIL BMODULE (NIL T T) -9 NIL 175876 NIL) (-110 171149 175146 175219 "BITS" 175295 T BITS (NIL) -8 NIL NIL NIL) (-109 170570 170689 170829 "BINDING" 171029 T BINDING (NIL) -8 NIL NIL NIL) (-108 164575 170165 170314 "BINARY" 170441 T BINARY (NIL) -8 NIL NIL NIL) (-107 162355 163830 163871 "BGAGG" 164131 NIL BGAGG (NIL T) -9 NIL 164268 NIL) (-106 162186 162218 162309 "BGAGG-" 162314 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161257 161570 161775 "BFUNCT" 162001 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159947 160125 160413 "BEZOUT" 161081 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156416 158799 159129 "BBTREE" 159650 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156150 156203 156231 "BASTYPE" 156350 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156002 156031 156104 "BASTYPE-" 156109 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155436 155512 155664 "BALFACT" 155913 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154292 154851 155037 "AUTOMOR" 155281 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154018 154023 154049 "ATTREG" 154054 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152270 152715 153067 "ATTRBUT" 153684 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151878 152098 152164 "ATTRAST" 152222 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151414 151527 151553 "ATRIG" 151754 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151223 151264 151351 "ATRIG-" 151356 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150868 151054 151080 "ASTCAT" 151085 T ASTCAT (NIL) -9 NIL 151115 NIL) (-92 150595 150654 150773 "ASTCAT-" 150778 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148744 150371 150459 "ASTACK" 150538 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147249 147546 147911 "ASSOCEQ" 148426 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146281 146908 147032 "ASP9" 147156 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146044 146229 146268 "ASP8" 146273 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144912 145649 145791 "ASP80" 145933 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143810 144547 144679 "ASP7" 144811 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142764 143487 143605 "ASP78" 143723 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141733 142444 142561 "ASP77" 142678 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140645 141371 141502 "ASP74" 141633 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139545 140280 140412 "ASP73" 140544 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138649 139371 139471 "ASP6" 139476 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137596 138326 138444 "ASP55" 138562 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136545 137270 137389 "ASP50" 137508 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135633 136246 136356 "ASP4" 136466 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134721 135334 135444 "ASP49" 135554 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133505 134260 134428 "ASP42" 134610 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132282 133038 133208 "ASP41" 133392 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131232 131959 132077 "ASP35" 132195 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130997 131180 131219 "ASP34" 131224 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130734 130801 130877 "ASP33" 130952 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129628 130369 130501 "ASP31" 130633 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129393 129576 129615 "ASP30" 129620 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129128 129197 129273 "ASP29" 129348 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128893 129076 129115 "ASP28" 129120 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128658 128841 128880 "ASP27" 128885 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127742 128356 128467 "ASP24" 128578 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126819 127544 127656 "ASP20" 127661 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125907 126520 126630 "ASP1" 126740 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124850 125581 125700 "ASP19" 125819 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124587 124654 124730 "ASP12" 124805 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123439 124186 124330 "ASP10" 124474 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121290 123283 123374 "ARRAY2" 123379 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117055 120938 121052 "ARRAY1" 121207 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116087 116260 116481 "ARRAY12" 116878 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110399 112317 112392 "ARR2CAT" 115022 NIL ARR2CAT (NIL T T T) -9 NIL 115780 NIL) (-56 107833 108577 109531 "ARR2CAT-" 109536 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107150 107460 107585 "ARITY" 107726 T ARITY (NIL) -8 NIL NIL NIL) (-54 105926 106078 106377 "APPRULE" 106986 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105577 105625 105744 "APPLYORE" 105872 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104931 105170 105290 "ANY" 105475 T ANY (NIL) -8 NIL NIL NIL) (-51 104209 104332 104489 "ANY1" 104805 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101739 102646 102973 "ANTISYM" 103933 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101231 101446 101542 "ANON" 101661 T ANON (NIL) -8 NIL NIL NIL) (-48 95480 99770 100224 "AN" 100795 T AN (NIL) -8 NIL NIL NIL) (-47 91378 92766 92817 "AMR" 93565 NIL AMR (NIL T T) -9 NIL 94165 NIL) (-46 90490 90711 91074 "AMR-" 91079 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74929 90407 90468 "ALIST" 90473 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71734 74523 74692 "ALGSC" 74847 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68290 68844 69451 "ALGPKG" 71174 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67567 67668 67852 "ALGMFACT" 68176 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63602 64181 64775 "ALGMANIP" 67151 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54972 63228 63378 "ALGFF" 63535 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54168 54299 54478 "ALGFACT" 54830 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53109 53709 53747 "ALGEBRA" 53752 NIL ALGEBRA (NIL T) -9 NIL 53793 NIL) (-37 52827 52886 53018 "ALGEBRA-" 53023 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34890 50799 50851 "ALAGG" 50987 NIL ALAGG (NIL T T) -9 NIL 51148 NIL) (-35 34426 34539 34565 "AHYP" 34766 T AHYP (NIL) -9 NIL NIL NIL) (-34 33357 33605 33631 "AGG" 34130 T AGG (NIL) -9 NIL 34409 NIL) (-33 32791 32953 33167 "AGG-" 33172 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30597 31020 31425 "AF" 32433 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30077 30322 30412 "ADDAST" 30525 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29345 29604 29760 "ACPLOT" 29939 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18668 26472 26510 "ACFS" 27117 NIL ACFS (NIL T) -9 NIL 27356 NIL) (-28 16695 17185 17947 "ACFS-" 17952 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12813 14742 14768 "ACF" 15647 T ACF (NIL) -9 NIL 16060 NIL) (-26 11517 11851 12344 "ACF-" 12349 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11089 11284 11310 "ABELSG" 11402 T ABELSG (NIL) -9 NIL 11467 NIL) (-24 10956 10981 11047 "ABELSG-" 11052 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10299 10586 10612 "ABELMON" 10782 T ABELMON (NIL) -9 NIL 10894 NIL) (-22 9963 10047 10185 "ABELMON-" 10190 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9311 9683 9709 "ABELGRP" 9781 T ABELGRP (NIL) -9 NIL 9856 NIL) (-20 8774 8903 9119 "ABELGRP-" 9124 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3228501 3228506 3228511 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3228486 3228491 3228496 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3228471 3228476 3228481 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3228456 3228461 3228466 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1306 3227599 3228331 3228408 "ZMOD" 3228413 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1305 3226709 3226873 3227082 "ZLINDEP" 3227431 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1304 3216009 3217777 3219749 "ZDSOLVE" 3224839 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1303 3215255 3215396 3215585 "YSTREAM" 3215855 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1302 3214683 3214929 3215042 "YDIAGRAM" 3215164 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1301 3212457 3213984 3214188 "XRPOLY" 3214526 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3209010 3210328 3210903 "XPR" 3211929 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1299 3206731 3208341 3208545 "XPOLY" 3208841 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1298 3204384 3205752 3205807 "XPOLYC" 3206095 NIL XPOLYC (NIL T T) -9 NIL 3206208 NIL) (-1297 3200760 3202901 3203289 "XPBWPOLY" 3204042 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3196455 3198750 3198792 "XF" 3199413 NIL XF (NIL T) -9 NIL 3199813 NIL) (-1295 3196076 3196164 3196333 "XF-" 3196338 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1294 3191272 3192561 3192616 "XFALG" 3194788 NIL XFALG (NIL T T) -9 NIL 3195577 NIL) (-1293 3190405 3190509 3190714 "XEXPPKG" 3191164 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1292 3188514 3190255 3190351 "XDPOLY" 3190356 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1291 3187321 3187921 3187964 "XALG" 3187969 NIL XALG (NIL T) -9 NIL 3188080 NIL) (-1290 3180763 3185298 3185792 "WUTSET" 3186913 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1289 3179019 3179815 3180138 "WP" 3180574 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1288 3178621 3178841 3178911 "WHILEAST" 3178971 T WHILEAST (NIL) -8 NIL NIL NIL) (-1287 3178093 3178338 3178432 "WHEREAST" 3178549 T WHEREAST (NIL) -8 NIL NIL NIL) (-1286 3176979 3177177 3177472 "WFFINTBS" 3177890 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1285 3174883 3175310 3175772 "WEIER" 3176551 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1284 3173929 3174379 3174421 "VSPACE" 3174557 NIL VSPACE (NIL T) -9 NIL 3174631 NIL) (-1283 3173767 3173794 3173885 "VSPACE-" 3173890 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1282 3173576 3173618 3173686 "VOID" 3173721 T VOID (NIL) -8 NIL NIL NIL) (-1281 3171712 3172071 3172477 "VIEW" 3173192 T VIEW (NIL) -7 NIL NIL NIL) (-1280 3168136 3168775 3169512 "VIEWDEF" 3170997 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1279 3157440 3159684 3161857 "VIEW3D" 3165985 T VIEW3D (NIL) -8 NIL NIL NIL) (-1278 3149691 3151351 3152930 "VIEW2D" 3155883 T VIEW2D (NIL) -8 NIL NIL NIL) (-1277 3145044 3149461 3149553 "VECTOR" 3149634 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1276 3143621 3143880 3144198 "VECTOR2" 3144774 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1275 3137063 3141372 3141415 "VECTCAT" 3142410 NIL VECTCAT (NIL T) -9 NIL 3142997 NIL) (-1274 3136077 3136331 3136721 "VECTCAT-" 3136726 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1273 3135531 3135728 3135848 "VARIABLE" 3135992 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1272 3135464 3135469 3135499 "UTYPE" 3135504 T UTYPE (NIL) -9 NIL NIL NIL) (-1271 3134294 3134448 3134710 "UTSODETL" 3135290 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1270 3131734 3132194 3132718 "UTSODE" 3133835 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1269 3123572 3129360 3129849 "UTS" 3131303 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1268 3114409 3119777 3119820 "UTSCAT" 3120932 NIL UTSCAT (NIL T) -9 NIL 3121690 NIL) (-1267 3111757 3112479 3113468 "UTSCAT-" 3113473 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1266 3111384 3111427 3111560 "UTS2" 3111708 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1265 3105610 3108222 3108265 "URAGG" 3110335 NIL URAGG (NIL T) -9 NIL 3111058 NIL) (-1264 3102549 3103412 3104535 "URAGG-" 3104540 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1263 3098258 3101184 3101649 "UPXSSING" 3102213 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1262 3090324 3097505 3097778 "UPXS" 3098043 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3083397 3090228 3090300 "UPXSCONS" 3090305 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3073105 3079899 3079961 "UPXSCCA" 3080535 NIL UPXSCCA (NIL T T) -9 NIL 3080768 NIL) (-1259 3072743 3072828 3073002 "UPXSCCA-" 3073007 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1258 3062303 3068870 3068913 "UPXSCAT" 3069561 NIL UPXSCAT (NIL T) -9 NIL 3070170 NIL) (-1257 3061733 3061812 3061991 "UPXS2" 3062218 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3060387 3060640 3060991 "UPSQFREE" 3061476 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1255 3053860 3056918 3056973 "UPSCAT" 3058053 NIL UPSCAT (NIL T T) -9 NIL 3058818 NIL) (-1254 3053064 3053271 3053598 "UPSCAT-" 3053603 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1253 3038705 3046473 3046516 "UPOLYC" 3048617 NIL UPOLYC (NIL T) -9 NIL 3049838 NIL) (-1252 3030033 3032459 3035606 "UPOLYC-" 3035611 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1251 3029660 3029703 3029836 "UPOLYC2" 3029984 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1250 3021471 3029343 3029472 "UP" 3029579 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1249 3020810 3020917 3021081 "UPMP" 3021360 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1248 3020363 3020444 3020583 "UPDIVP" 3020723 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1247 3018931 3019180 3019496 "UPDECOMP" 3020112 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1246 3018162 3018274 3018460 "UPCDEN" 3018815 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1245 3017681 3017750 3017899 "UP2" 3018087 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1244 3016148 3016885 3017162 "UNISEG" 3017439 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1243 3015363 3015490 3015695 "UNISEG2" 3015991 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1242 3014423 3014603 3014829 "UNIFACT" 3015179 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1241 2998355 3013600 3013851 "ULS" 3014230 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1240 2986353 2998259 2998331 "ULSCONS" 2998336 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1239 2968361 2980347 2980409 "ULSCCAT" 2981047 NIL ULSCCAT (NIL T T) -9 NIL 2981336 NIL) (-1238 2967411 2967656 2968044 "ULSCCAT-" 2968049 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1237 2956748 2963229 2963272 "ULSCAT" 2964135 NIL ULSCAT (NIL T) -9 NIL 2964866 NIL) (-1236 2956178 2956257 2956436 "ULS2" 2956663 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1235 2955305 2955815 2955922 "UINT8" 2956033 T UINT8 (NIL) -8 NIL NIL 2956118) (-1234 2954431 2954941 2955048 "UINT64" 2955159 T UINT64 (NIL) -8 NIL NIL 2955244) (-1233 2953557 2954067 2954174 "UINT32" 2954285 T UINT32 (NIL) -8 NIL NIL 2954370) (-1232 2952683 2953193 2953300 "UINT16" 2953411 T UINT16 (NIL) -8 NIL NIL 2953496) (-1231 2950986 2951943 2951973 "UFD" 2952185 T UFD (NIL) -9 NIL 2952299 NIL) (-1230 2950780 2950826 2950921 "UFD-" 2950926 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1229 2949862 2950045 2950261 "UDVO" 2950586 T UDVO (NIL) -7 NIL NIL NIL) (-1228 2947678 2948087 2948558 "UDPO" 2949426 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1227 2947611 2947616 2947646 "TYPE" 2947651 T TYPE (NIL) -9 NIL NIL NIL) (-1226 2947371 2947566 2947597 "TYPEAST" 2947602 T TYPEAST (NIL) -8 NIL NIL NIL) (-1225 2946342 2946544 2946784 "TWOFACT" 2947165 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1224 2945365 2945751 2945986 "TUPLE" 2946142 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1223 2943056 2943575 2944114 "TUBETOOL" 2944848 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1222 2941905 2942110 2942351 "TUBE" 2942849 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1221 2936634 2940877 2941160 "TS" 2941657 NIL TS (NIL T) -8 NIL NIL NIL) (-1220 2925274 2929393 2929490 "TSETCAT" 2934759 NIL TSETCAT (NIL T T T T) -9 NIL 2936290 NIL) (-1219 2920006 2921606 2923497 "TSETCAT-" 2923502 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1218 2914645 2915492 2916421 "TRMANIP" 2919142 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1217 2914086 2914149 2914312 "TRIMAT" 2914577 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1216 2911952 2912189 2912546 "TRIGMNIP" 2913835 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1215 2911472 2911585 2911615 "TRIGCAT" 2911828 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1214 2911141 2911220 2911361 "TRIGCAT-" 2911366 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2907986 2909999 2910280 "TREE" 2910895 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2907260 2907788 2907818 "TRANFUN" 2907853 T TRANFUN (NIL) -9 NIL 2907919 NIL) (-1211 2906539 2906730 2907010 "TRANFUN-" 2907015 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2906343 2906375 2906436 "TOPSP" 2906500 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2905691 2905806 2905960 "TOOLSIGN" 2906224 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2904325 2904868 2905107 "TEXTFILE" 2905474 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2902237 2902778 2903207 "TEX" 2903918 T TEX (NIL) -8 NIL NIL NIL) (-1206 2902018 2902049 2902121 "TEX1" 2902200 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2901666 2901729 2901819 "TEMUTL" 2901950 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2899820 2900100 2900425 "TBCMPPK" 2901389 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2891597 2897980 2898036 "TBAGG" 2898436 NIL TBAGG (NIL T T) -9 NIL 2898647 NIL) (-1202 2886667 2888155 2889909 "TBAGG-" 2889914 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2886051 2886158 2886303 "TANEXP" 2886556 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2885562 2885826 2885916 "TALGOP" 2885996 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2878952 2885419 2885512 "TABLE" 2885517 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2878364 2878463 2878601 "TABLEAU" 2878849 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2872972 2874192 2875440 "TABLBUMP" 2877150 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2872194 2872341 2872522 "SYSTEM" 2872813 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2868653 2869352 2870135 "SYSSOLP" 2871445 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2868451 2868608 2868639 "SYSPTR" 2868644 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2867495 2868000 2868119 "SYSNNI" 2868305 NIL SYSNNI (NIL NIL) -8 NIL NIL 2868390) (-1192 2866802 2867261 2867340 "SYSINT" 2867400 NIL SYSINT (NIL NIL) -8 NIL NIL 2867445) (-1191 2863134 2864080 2864790 "SYNTAX" 2866114 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2860292 2860894 2861526 "SYMTAB" 2862524 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2855541 2856443 2857426 "SYMS" 2859331 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2852776 2854999 2855229 "SYMPOLY" 2855346 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2852293 2852368 2852491 "SYMFUNC" 2852688 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2848313 2849605 2850418 "SYMBOL" 2851502 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2841852 2843541 2845261 "SWITCH" 2846615 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2835086 2840673 2840976 "SUTS" 2841607 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827152 2834333 2834606 "SUPXS" 2834871 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2818911 2826770 2826896 "SUP" 2827061 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2818070 2818197 2818414 "SUPFRACF" 2818779 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2817691 2817750 2817863 "SUP2" 2818005 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816139 2816413 2816769 "SUMRF" 2817390 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2815474 2815540 2815732 "SUMFS" 2816060 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2799441 2814651 2814902 "SULS" 2815281 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2799043 2799263 2799333 "SUCHTAST" 2799393 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2798338 2798568 2798708 "SUCH" 2798951 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2792205 2793244 2794203 "SUBSPACE" 2797426 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2791635 2791725 2791889 "SUBRESP" 2792093 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2785003 2786300 2787611 "STTF" 2790371 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2779176 2780296 2781443 "STTFNC" 2783903 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2770489 2772358 2774152 "STTAYLOR" 2777417 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2763619 2770353 2770436 "STRTBL" 2770441 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2758983 2763574 2763605 "STRING" 2763610 T STRING (NIL) -8 NIL NIL NIL) (-1167 2753812 2758326 2758356 "STRICAT" 2758415 T STRICAT (NIL) -9 NIL 2758477 NIL) (-1166 2746565 2751431 2752042 "STREAM" 2753236 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2746075 2746152 2746296 "STREAM3" 2746482 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2745057 2745240 2745475 "STREAM2" 2745888 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2744745 2744797 2744890 "STREAM1" 2744999 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2743761 2743942 2744173 "STINPROD" 2744561 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2743313 2743523 2743553 "STEP" 2743633 T STEP (NIL) -9 NIL 2743711 NIL) (-1160 2742500 2742802 2742950 "STEPAST" 2743187 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2735932 2742399 2742476 "STBL" 2742481 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2731027 2735123 2735166 "STAGG" 2735319 NIL STAGG (NIL T) -9 NIL 2735408 NIL) (-1157 2728729 2729331 2730203 "STAGG-" 2730208 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2726876 2728499 2728591 "STACK" 2728672 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2719571 2725017 2725473 "SREGSET" 2726506 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2711996 2713365 2714878 "SRDCMPK" 2718177 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2704881 2709406 2709436 "SRAGG" 2710739 T SRAGG (NIL) -9 NIL 2711347 NIL) (-1152 2703898 2704153 2704532 "SRAGG-" 2704537 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2698358 2702845 2703266 "SQMATRIX" 2703524 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2692043 2695076 2695803 "SPLTREE" 2697703 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2688006 2688699 2689345 "SPLNODE" 2691469 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2687053 2687286 2687316 "SPFCAT" 2687760 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2685790 2686000 2686264 "SPECOUT" 2686811 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2676900 2678772 2678802 "SPADXPT" 2683478 T SPADXPT (NIL) -9 NIL 2685642 NIL) (-1145 2676661 2676701 2676770 "SPADPRSR" 2676853 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2674710 2676616 2676647 "SPADAST" 2676652 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2666655 2668428 2668471 "SPACEC" 2672844 NIL SPACEC (NIL T) -9 NIL 2674660 NIL) (-1142 2664785 2666587 2666636 "SPACE3" 2666641 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2663537 2663708 2663999 "SORTPAK" 2664590 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2661629 2661932 2662344 "SOLVETRA" 2663201 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2660679 2660901 2661162 "SOLVESER" 2661402 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2655983 2656871 2657866 "SOLVERAD" 2659731 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2651798 2652407 2653136 "SOLVEFOR" 2655350 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2646068 2651147 2651244 "SNTSCAT" 2651249 NIL SNTSCAT (NIL T T T T) -9 NIL 2651319 NIL) (-1135 2640174 2644391 2644782 "SMTS" 2645758 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2634859 2640062 2640139 "SMP" 2640144 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2633018 2633319 2633717 "SMITH" 2634556 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2625731 2629927 2630030 "SMATCAT" 2631381 NIL SMATCAT (NIL NIL T T T) -9 NIL 2631931 NIL) (-1131 2622671 2623494 2624672 "SMATCAT-" 2624677 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2620337 2621907 2621950 "SKAGG" 2622211 NIL SKAGG (NIL T) -9 NIL 2622346 NIL) (-1129 2616663 2619810 2619994 "SINT" 2620146 T SINT (NIL) -8 NIL NIL 2620308) (-1128 2616435 2616473 2616539 "SIMPAN" 2616619 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2615714 2615970 2616110 "SIG" 2616317 T SIG (NIL) -8 NIL NIL NIL) (-1126 2614552 2614773 2615048 "SIGNRF" 2615473 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2613385 2613536 2613820 "SIGNEF" 2614381 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2612691 2612968 2613092 "SIGAST" 2613283 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2610381 2610835 2611341 "SHP" 2612232 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2604233 2610282 2610358 "SHDP" 2610363 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2603806 2603998 2604028 "SGROUP" 2604121 T SGROUP (NIL) -9 NIL 2604183 NIL) (-1120 2603664 2603690 2603763 "SGROUP-" 2603768 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2600455 2601153 2601876 "SGCF" 2602963 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2594823 2599902 2599999 "SFRTCAT" 2600004 NIL SFRTCAT (NIL T T T T) -9 NIL 2600043 NIL) (-1117 2588244 2589262 2590398 "SFRGCD" 2593806 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2581370 2582443 2583629 "SFQCMPK" 2587177 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2580990 2581079 2581190 "SFORT" 2581311 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2580108 2580830 2580951 "SEXOF" 2580956 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2579215 2579989 2580057 "SEX" 2580062 T SEX (NIL) -8 NIL NIL NIL) (-1112 2574996 2575711 2575806 "SEXCAT" 2578428 NIL SEXCAT (NIL T T T T T) -9 NIL 2578988 NIL) (-1111 2572149 2574930 2574978 "SET" 2574983 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2570373 2570862 2571167 "SETMN" 2571890 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2569869 2570021 2570051 "SETCAT" 2570227 T SETCAT (NIL) -9 NIL 2570337 NIL) (-1108 2569561 2569639 2569769 "SETCAT-" 2569774 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2565922 2568022 2568065 "SETAGG" 2568935 NIL SETAGG (NIL T) -9 NIL 2569275 NIL) (-1106 2565380 2565496 2565733 "SETAGG-" 2565738 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2564823 2565076 2565177 "SEQAST" 2565301 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2564022 2564316 2564377 "SEGXCAT" 2564663 NIL SEGXCAT (NIL T T) -9 NIL 2564783 NIL) (-1103 2563028 2563688 2563870 "SEG" 2563875 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2562007 2562221 2562264 "SEGCAT" 2562786 NIL SEGCAT (NIL T) -9 NIL 2563007 NIL) (-1101 2560939 2561370 2561578 "SEGBIND" 2561834 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2560560 2560619 2560732 "SEGBIND2" 2560874 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560133 2560361 2560438 "SEGAST" 2560505 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2559352 2559478 2559682 "SEG2" 2559977 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2558762 2559287 2559334 "SDVAR" 2559339 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2551289 2558532 2558662 "SDPOL" 2558667 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2549882 2550148 2550467 "SCPKG" 2551004 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2549046 2549218 2549410 "SCOPE" 2549712 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548266 2548400 2548579 "SCACHE" 2548901 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2547912 2548098 2548128 "SASTCAT" 2548133 T SASTCAT (NIL) -9 NIL 2548146 NIL) (-1091 2547399 2547747 2547823 "SAOS" 2547858 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2546964 2546999 2547172 "SAERFFC" 2547358 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2540903 2546861 2546941 "SAE" 2546946 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2540496 2540531 2540690 "SAEFACT" 2540862 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2538817 2539131 2539532 "RURPK" 2540162 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2537454 2537760 2538065 "RULESET" 2538651 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2534677 2535207 2535665 "RULE" 2537135 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2534289 2534471 2534554 "RULECOLD" 2534629 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2534079 2534107 2534178 "RTVALUE" 2534240 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2533550 2533796 2533890 "RSTRCAST" 2534007 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2528398 2529193 2530113 "RSETGCD" 2532749 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2517628 2522707 2522804 "RSETCAT" 2526923 NIL RSETCAT (NIL T T T T) -9 NIL 2528020 NIL) (-1079 2515555 2516094 2516918 "RSETCAT-" 2516923 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2507941 2509317 2510837 "RSDCMPK" 2514154 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2505920 2506387 2506461 "RRCC" 2507547 NIL RRCC (NIL T T) -9 NIL 2507891 NIL) (-1076 2505271 2505445 2505724 "RRCC-" 2505729 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2504714 2504967 2505068 "RPTAST" 2505192 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2478560 2487919 2487986 "RPOLCAT" 2498652 NIL RPOLCAT (NIL T T T) -9 NIL 2501812 NIL) (-1073 2470058 2472398 2475520 "RPOLCAT-" 2475525 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2460989 2468269 2468751 "ROUTINE" 2469598 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2457787 2460615 2460755 "ROMAN" 2460871 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2456031 2456647 2456907 "ROIRC" 2457592 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452263 2454547 2454577 "RNS" 2454881 T RNS (NIL) -9 NIL 2455155 NIL) (-1068 2450772 2451155 2451689 "RNS-" 2451764 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450175 2450583 2450613 "RNG" 2450618 T RNG (NIL) -9 NIL 2450639 NIL) (-1066 2449178 2449540 2449742 "RNGBIND" 2450026 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2448577 2448965 2449008 "RMODULE" 2449013 NIL RMODULE (NIL T) -9 NIL 2449040 NIL) (-1064 2447413 2447507 2447843 "RMCAT2" 2448478 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444263 2446759 2447056 "RMATRIX" 2447175 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2437090 2439350 2439465 "RMATCAT" 2442824 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2443806 NIL) (-1061 2436465 2436612 2436919 "RMATCAT-" 2436924 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2435866 2436087 2436130 "RLINSET" 2436324 NIL RLINSET (NIL T) -9 NIL 2436415 NIL) (-1059 2435433 2435508 2435636 "RINTERP" 2435785 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2434491 2435045 2435075 "RING" 2435131 T RING (NIL) -9 NIL 2435223 NIL) (-1057 2434283 2434327 2434424 "RING-" 2434429 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2433124 2433361 2433619 "RIDIST" 2434047 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2424413 2432592 2432798 "RGCHAIN" 2432972 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2423763 2424169 2424210 "RGBCSPC" 2424268 NIL RGBCSPC (NIL T) -9 NIL 2424320 NIL) (-1053 2422921 2423302 2423343 "RGBCMDL" 2423575 NIL RGBCMDL (NIL T) -9 NIL 2423689 NIL) (-1052 2419915 2420529 2421199 "RF" 2422285 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2419561 2419624 2419727 "RFFACTOR" 2419846 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419286 2419321 2419418 "RFFACT" 2419520 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2417403 2417767 2418149 "RFDIST" 2418926 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2416856 2416948 2417111 "RETSOL" 2417305 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2416492 2416572 2416615 "RETRACT" 2416748 NIL RETRACT (NIL T) -9 NIL 2416835 NIL) (-1046 2416341 2416366 2416453 "RETRACT-" 2416458 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2415943 2416163 2416233 "RETAST" 2416293 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2408681 2415596 2415723 "RESULT" 2415838 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407272 2407950 2408149 "RESRING" 2408584 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2406908 2406957 2407055 "RESLATC" 2407209 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2406613 2406648 2406755 "REPSQ" 2406867 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2404035 2404615 2405217 "REP" 2406033 T REP (NIL) -7 NIL NIL NIL) (-1039 2403732 2403767 2403878 "REPDB" 2403994 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2397632 2399021 2400244 "REP2" 2402544 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2394009 2394690 2395498 "REP1" 2396859 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2386705 2392150 2392606 "REGSET" 2393639 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2385470 2385853 2386103 "REF" 2386490 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2384847 2384950 2385117 "REDORDER" 2385354 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2380815 2384060 2384287 "RECLOS" 2384675 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2379867 2380048 2380263 "REALSOLV" 2380622 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2379713 2379754 2379784 "REAL" 2379789 T REAL (NIL) -9 NIL 2379824 NIL) (-1030 2376196 2376998 2377882 "REAL0Q" 2378878 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2371797 2372785 2373846 "REAL0" 2375177 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371268 2371514 2371608 "RDUCEAST" 2371725 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2370673 2370745 2370952 "RDIV" 2371190 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2369741 2369915 2370128 "RDIST" 2370495 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2368338 2368625 2368997 "RDETRS" 2369449 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366150 2366604 2367142 "RDETR" 2367880 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2364775 2365053 2365450 "RDEEFS" 2365866 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363284 2363590 2364015 "RDEEF" 2364463 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2357345 2360265 2360295 "RCFIELD" 2361590 T RCFIELD (NIL) -9 NIL 2362321 NIL) (-1020 2355409 2355913 2356609 "RCFIELD-" 2356684 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1019 2351678 2353510 2353553 "RCAGG" 2354637 NIL RCAGG (NIL T) -9 NIL 2355102 NIL) (-1018 2351306 2351400 2351563 "RCAGG-" 2351568 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1017 2350641 2350753 2350918 "RATRET" 2351190 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1016 2350194 2350261 2350382 "RATFACT" 2350569 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1015 2349502 2349622 2349774 "RANDSRC" 2350064 T RANDSRC (NIL) -7 NIL NIL NIL) (-1014 2349236 2349280 2349353 "RADUTIL" 2349451 T RADUTIL (NIL) -7 NIL NIL NIL) (-1013 2342350 2348067 2348378 "RADIX" 2348959 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1012 2333969 2342192 2342322 "RADFF" 2342327 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1011 2333616 2333691 2333721 "RADCAT" 2333881 T RADCAT (NIL) -9 NIL NIL NIL) (-1010 2333398 2333446 2333546 "RADCAT-" 2333551 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1009 2331496 2333168 2333260 "QUEUE" 2333341 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1008 2328033 2331429 2331477 "QUAT" 2331482 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1007 2327664 2327707 2327838 "QUATCT2" 2327984 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2321075 2324420 2324462 "QUATCAT" 2325253 NIL QUATCAT (NIL T) -9 NIL 2326019 NIL) (-1005 2317214 2318251 2319641 "QUATCAT-" 2319737 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1004 2314679 2316290 2316333 "QUAGG" 2316714 NIL QUAGG (NIL T) -9 NIL 2316889 NIL) (-1003 2314281 2314501 2314571 "QQUTAST" 2314631 T QQUTAST (NIL) -8 NIL NIL NIL) (-1002 2313294 2313794 2313959 "QFORM" 2314162 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1001 2304287 2309526 2309568 "QFCAT" 2310236 NIL QFCAT (NIL T) -9 NIL 2311237 NIL) (-1000 2299854 2301055 2302649 "QFCAT-" 2302745 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-999 2299488 2299531 2299660 "QFCAT2" 2299805 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-998 2298948 2299058 2299188 "QEQUAT" 2299378 T QEQUAT (NIL) -8 NIL NIL NIL) (-997 2292094 2293167 2294351 "QCMPACK" 2297881 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-996 2289643 2290091 2290519 "QALGSET" 2291749 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-995 2288888 2289062 2289294 "QALGSET2" 2289463 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-994 2287578 2287802 2288119 "PWFFINTB" 2288661 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-993 2285760 2285928 2286282 "PUSHVAR" 2287392 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-992 2281678 2282732 2282773 "PTRANFN" 2284657 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-991 2280080 2280371 2280693 "PTPACK" 2281389 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-990 2279712 2279769 2279878 "PTFUNC2" 2280017 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-989 2274157 2278554 2278595 "PTCAT" 2278891 NIL PTCAT (NIL T) -9 NIL 2279044 NIL) (-988 2273815 2273850 2273974 "PSQFR" 2274116 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-987 2272410 2272708 2273042 "PSEUDLIN" 2273513 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-986 2259173 2261544 2263868 "PSETPK" 2270170 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-985 2252191 2254931 2255027 "PSETCAT" 2258048 NIL PSETCAT (NIL T T T T) -9 NIL 2258862 NIL) (-984 2250027 2250661 2251482 "PSETCAT-" 2251487 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-983 2249376 2249541 2249569 "PSCURVE" 2249837 T PSCURVE (NIL) -9 NIL 2250004 NIL) (-982 2245374 2246890 2246955 "PSCAT" 2247799 NIL PSCAT (NIL T T T) -9 NIL 2248039 NIL) (-981 2244437 2244653 2245053 "PSCAT-" 2245058 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-980 2242796 2243506 2243769 "PRTITION" 2244194 T PRTITION (NIL) -8 NIL NIL NIL) (-979 2242271 2242517 2242609 "PRTDAST" 2242724 T PRTDAST (NIL) -8 NIL NIL NIL) (-978 2231361 2233575 2235763 "PRS" 2240133 NIL PRS (NIL T T) -7 NIL NIL NIL) (-977 2229172 2230711 2230751 "PRQAGG" 2230934 NIL PRQAGG (NIL T) -9 NIL 2231036 NIL) (-976 2228508 2228813 2228841 "PROPLOG" 2228980 T PROPLOG (NIL) -9 NIL 2229095 NIL) (-975 2228112 2228169 2228292 "PROPFUN2" 2228431 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-974 2227427 2227548 2227720 "PROPFUN1" 2227973 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-973 2225608 2226174 2226471 "PROPFRML" 2227163 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-972 2225077 2225184 2225312 "PROPERTY" 2225500 T PROPERTY (NIL) -8 NIL NIL NIL) (-971 2219135 2223243 2224063 "PRODUCT" 2224303 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-970 2216413 2218593 2218827 "PR" 2218946 NIL PR (NIL T T) -8 NIL NIL NIL) (-969 2216209 2216241 2216300 "PRINT" 2216374 T PRINT (NIL) -7 NIL NIL NIL) (-968 2215549 2215666 2215818 "PRIMES" 2216089 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-967 2213614 2214015 2214481 "PRIMELT" 2215128 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-966 2213343 2213392 2213420 "PRIMCAT" 2213544 T PRIMCAT (NIL) -9 NIL NIL NIL) (-965 2209458 2213281 2213326 "PRIMARR" 2213331 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-964 2208465 2208643 2208871 "PRIMARR2" 2209276 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-963 2208108 2208164 2208275 "PREASSOC" 2208403 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-962 2207583 2207716 2207744 "PPCURVE" 2207949 T PPCURVE (NIL) -9 NIL 2208085 NIL) (-961 2207178 2207378 2207461 "PORTNUM" 2207520 T PORTNUM (NIL) -8 NIL NIL NIL) (-960 2204537 2204936 2205528 "POLYROOT" 2206759 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-959 2198719 2204141 2204301 "POLY" 2204410 NIL POLY (NIL T) -8 NIL NIL NIL) (-958 2198102 2198160 2198394 "POLYLIFT" 2198655 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-957 2194377 2194826 2195455 "POLYCATQ" 2197647 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-956 2181089 2186217 2186282 "POLYCAT" 2189796 NIL POLYCAT (NIL T T T) -9 NIL 2191674 NIL) (-955 2174538 2176400 2178784 "POLYCAT-" 2178789 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-954 2174125 2174193 2174313 "POLY2UP" 2174464 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-953 2173757 2173814 2173923 "POLY2" 2174062 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-952 2172442 2172681 2172957 "POLUTIL" 2173531 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-951 2170797 2171074 2171405 "POLTOPOL" 2172164 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-950 2166262 2170733 2170779 "POINT" 2170784 NIL POINT (NIL T) -8 NIL NIL NIL) (-949 2164449 2164806 2165181 "PNTHEORY" 2165907 T PNTHEORY (NIL) -7 NIL NIL NIL) (-948 2162907 2163204 2163603 "PMTOOLS" 2164147 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-947 2162500 2162578 2162695 "PMSYM" 2162823 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-946 2162008 2162077 2162252 "PMQFCAT" 2162425 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-945 2161363 2161473 2161629 "PMPRED" 2161885 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-944 2160756 2160842 2161004 "PMPREDFS" 2161264 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-943 2159420 2159628 2160006 "PMPLCAT" 2160518 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-942 2158952 2159031 2159183 "PMLSAGG" 2159335 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-941 2158425 2158501 2158683 "PMKERNEL" 2158870 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-940 2158042 2158117 2158230 "PMINS" 2158344 NIL PMINS (NIL T) -7 NIL NIL NIL) (-939 2157484 2157553 2157762 "PMFS" 2157967 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-938 2156712 2156830 2157035 "PMDOWN" 2157361 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-937 2155879 2156037 2156218 "PMASS" 2156551 T PMASS (NIL) -7 NIL NIL NIL) (-936 2155152 2155262 2155425 "PMASSFS" 2155766 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-935 2154807 2154875 2154969 "PLOTTOOL" 2155078 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-934 2149414 2150618 2151766 "PLOT" 2153679 T PLOT (NIL) -8 NIL NIL NIL) (-933 2145218 2146262 2147183 "PLOT3D" 2148513 T PLOT3D (NIL) -8 NIL NIL NIL) (-932 2144130 2144307 2144542 "PLOT1" 2145022 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-931 2119521 2124196 2129047 "PLEQN" 2139396 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-930 2118839 2118961 2119141 "PINTERP" 2119386 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-929 2118532 2118579 2118682 "PINTERPA" 2118786 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-928 2117753 2118301 2118388 "PI" 2118428 T PI (NIL) -8 NIL NIL 2118495) (-927 2116050 2117025 2117053 "PID" 2117235 T PID (NIL) -9 NIL 2117369 NIL) (-926 2115801 2115838 2115913 "PICOERCE" 2116007 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-925 2115121 2115260 2115436 "PGROEB" 2115657 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-924 2110708 2111522 2112427 "PGE" 2114236 T PGE (NIL) -7 NIL NIL NIL) (-923 2108831 2109078 2109444 "PGCD" 2110425 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-922 2108169 2108272 2108433 "PFRPAC" 2108715 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-921 2104809 2106717 2107070 "PFR" 2107848 NIL PFR (NIL T) -8 NIL NIL NIL) (-920 2103198 2103442 2103767 "PFOTOOLS" 2104556 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-919 2101731 2101970 2102321 "PFOQ" 2102955 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-918 2100232 2100444 2100800 "PFO" 2101515 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-917 2096785 2100121 2100190 "PF" 2100195 NIL PF (NIL NIL) -8 NIL NIL NIL) (-916 2094119 2095390 2095418 "PFECAT" 2096003 T PFECAT (NIL) -9 NIL 2096387 NIL) (-915 2093564 2093718 2093932 "PFECAT-" 2093937 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-914 2092167 2092419 2092720 "PFBRU" 2093313 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-913 2090033 2090385 2090817 "PFBR" 2091818 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-912 2085915 2087409 2088085 "PERM" 2089390 NIL PERM (NIL T) -8 NIL NIL NIL) (-911 2081149 2082122 2082992 "PERMGRP" 2085078 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-910 2079255 2080212 2080253 "PERMCAT" 2080699 NIL PERMCAT (NIL T) -9 NIL 2081004 NIL) (-909 2078908 2078949 2079073 "PERMAN" 2079208 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-908 2076396 2078573 2078695 "PENDTREE" 2078819 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-907 2074420 2075188 2075229 "PDRING" 2075886 NIL PDRING (NIL T) -9 NIL 2076172 NIL) (-906 2073523 2073741 2074103 "PDRING-" 2074108 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-905 2070738 2071516 2072184 "PDEPROB" 2072875 T PDEPROB (NIL) -8 NIL NIL NIL) (-904 2068283 2068787 2069342 "PDEPACK" 2070203 T PDEPACK (NIL) -7 NIL NIL NIL) (-903 2067195 2067385 2067636 "PDECOMP" 2068082 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-902 2064774 2065617 2065645 "PDECAT" 2066432 T PDECAT (NIL) -9 NIL 2067145 NIL) (-901 2064525 2064558 2064648 "PCOMP" 2064735 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-900 2062703 2063326 2063623 "PBWLB" 2064254 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-899 2055176 2056776 2058114 "PATTERN" 2061386 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-898 2054808 2054865 2054974 "PATTERN2" 2055113 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-897 2052565 2052953 2053410 "PATTERN1" 2054397 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-896 2049933 2050514 2050995 "PATRES" 2052130 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-895 2049497 2049564 2049696 "PATRES2" 2049860 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-894 2047380 2047785 2048192 "PATMATCH" 2049164 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-893 2046890 2047099 2047140 "PATMAB" 2047247 NIL PATMAB (NIL T) -9 NIL 2047330 NIL) (-892 2045408 2045744 2046002 "PATLRES" 2046695 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-891 2044954 2045077 2045118 "PATAB" 2045123 NIL PATAB (NIL T) -9 NIL 2045295 NIL) (-890 2043136 2043531 2043954 "PARTPERM" 2044551 T PARTPERM (NIL) -7 NIL NIL NIL) (-889 2042757 2042820 2042922 "PARSURF" 2043067 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-888 2042389 2042446 2042555 "PARSU2" 2042694 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-887 2042153 2042193 2042260 "PARSER" 2042342 T PARSER (NIL) -7 NIL NIL NIL) (-886 2041774 2041837 2041939 "PARSCURV" 2042084 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-885 2041406 2041463 2041572 "PARSC2" 2041711 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-884 2041045 2041103 2041200 "PARPCURV" 2041342 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-883 2040677 2040734 2040843 "PARPC2" 2040982 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-882 2039738 2040050 2040232 "PARAMAST" 2040515 T PARAMAST (NIL) -8 NIL NIL NIL) (-881 2039258 2039344 2039463 "PAN2EXPR" 2039639 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-880 2038035 2038379 2038607 "PALETTE" 2039050 T PALETTE (NIL) -8 NIL NIL NIL) (-879 2036428 2037040 2037400 "PAIR" 2037721 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-878 2030296 2035685 2035880 "PADICRC" 2036282 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-877 2023523 2029640 2029825 "PADICRAT" 2030143 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-876 2021838 2023460 2023505 "PADIC" 2023510 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-875 2018948 2020512 2020552 "PADICCT" 2021133 NIL PADICCT (NIL NIL) -9 NIL 2021415 NIL) (-874 2017905 2018105 2018373 "PADEPAC" 2018735 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-873 2017117 2017250 2017456 "PADE" 2017767 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-872 2015504 2016325 2016605 "OWP" 2016921 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-871 2014997 2015210 2015307 "OVERSET" 2015427 T OVERSET (NIL) -8 NIL NIL NIL) (-870 2014043 2014602 2014774 "OVAR" 2014865 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-869 2013307 2013428 2013589 "OUT" 2013902 T OUT (NIL) -7 NIL NIL NIL) (-868 2002179 2004416 2006616 "OUTFORM" 2011127 T OUTFORM (NIL) -8 NIL NIL NIL) (-867 2001515 2001776 2001903 "OUTBFILE" 2002072 T OUTBFILE (NIL) -8 NIL NIL NIL) (-866 2000822 2000987 2001015 "OUTBCON" 2001333 T OUTBCON (NIL) -9 NIL 2001499 NIL) (-865 2000423 2000535 2000692 "OUTBCON-" 2000697 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-864 1999803 2000152 2000241 "OSI" 2000354 T OSI (NIL) -8 NIL NIL NIL) (-863 1999333 1999671 1999699 "OSGROUP" 1999704 T OSGROUP (NIL) -9 NIL 1999726 NIL) (-862 1998078 1998305 1998590 "ORTHPOL" 1999080 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-861 1995629 1997913 1998034 "OREUP" 1998039 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-860 1993032 1995320 1995447 "ORESUP" 1995571 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990560 1991060 1991621 "OREPCTO" 1992521 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984246 1986447 1986488 "OREPCAT" 1988836 NIL OREPCAT (NIL T) -9 NIL 1989940 NIL) (-857 1981393 1982175 1983233 "OREPCAT-" 1983238 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980544 1980842 1980870 "ORDSET" 1981179 T ORDSET (NIL) -9 NIL 1981343 NIL) (-855 1979975 1980123 1980347 "ORDSET-" 1980352 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978540 1979331 1979359 "ORDRING" 1979561 T ORDRING (NIL) -9 NIL 1979686 NIL) (-853 1978185 1978279 1978423 "ORDRING-" 1978428 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977565 1978028 1978056 "ORDMON" 1978061 T ORDMON (NIL) -9 NIL 1978082 NIL) (-851 1976727 1976874 1977069 "ORDFUNS" 1977414 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976065 1976484 1976512 "ORDFIN" 1976577 T ORDFIN (NIL) -9 NIL 1976651 NIL) (-849 1972624 1974651 1975060 "ORDCOMP" 1975689 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1971890 1972017 1972203 "ORDCOMP2" 1972484 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968471 1969381 1970195 "OPTPROB" 1971096 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965273 1965912 1966616 "OPTPACK" 1967787 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1962960 1963726 1963754 "OPTCAT" 1964573 T OPTCAT (NIL) -9 NIL 1965223 NIL) (-844 1962344 1962637 1962742 "OPSIG" 1962875 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962112 1962151 1962217 "OPQUERY" 1962298 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959243 1960423 1960927 "OP" 1961641 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958617 1958843 1958884 "OPERCAT" 1959096 NIL OPERCAT (NIL T) -9 NIL 1959193 NIL) (-840 1958372 1958428 1958545 "OPERCAT-" 1958550 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955185 1957169 1957538 "ONECOMP" 1958036 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954490 1954605 1954779 "ONECOMP2" 1955057 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1953909 1954015 1954145 "OMSERVER" 1954380 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1950771 1953349 1953389 "OMSAGG" 1953450 NIL OMSAGG (NIL T) -9 NIL 1953514 NIL) (-835 1949394 1949657 1949939 "OMPKG" 1950509 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1948824 1948927 1948955 "OM" 1949254 T OM (NIL) -9 NIL NIL NIL) (-833 1947371 1948373 1948542 "OMLO" 1948705 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946331 1946478 1946698 "OMEXPR" 1947197 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945622 1945877 1946013 "OMERR" 1946215 T OMERR (NIL) -8 NIL NIL NIL) (-830 1944773 1945043 1945203 "OMERRK" 1945482 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944224 1944450 1944558 "OMENC" 1944685 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938119 1939304 1940475 "OMDEV" 1943073 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937188 1937359 1937553 "OMCONN" 1937945 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1935709 1936685 1936713 "OINTDOM" 1936718 T OINTDOM (NIL) -9 NIL 1936739 NIL) (-825 1933047 1934397 1934734 "OFMONOID" 1935404 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932458 1932984 1933029 "ODVAR" 1933034 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1929881 1932203 1932358 "ODR" 1932363 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922462 1929657 1929783 "ODPOL" 1929788 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916284 1922334 1922439 "ODP" 1922444 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915050 1915265 1915540 "ODETOOLS" 1916058 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912017 1912675 1913391 "ODESYS" 1914383 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1906899 1907807 1908832 "ODERTRIC" 1911092 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906325 1906407 1906601 "ODERED" 1906811 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903213 1903761 1904438 "ODERAT" 1905748 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900172 1900637 1901234 "ODEPRRIC" 1902742 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898115 1898711 1899197 "ODEPROB" 1899706 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894635 1895120 1895767 "ODEPRIM" 1897594 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1893884 1893986 1894246 "ODEPAL" 1894527 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890046 1890837 1891701 "ODEPACK" 1893040 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889107 1889214 1889436 "ODEINT" 1889935 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883208 1884633 1886080 "ODEIFTBL" 1887680 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878606 1879392 1880344 "ODEEF" 1882367 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1877955 1878044 1878267 "ODECONST" 1878511 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876080 1876741 1876769 "ODECAT" 1877374 T ODECAT (NIL) -9 NIL 1877905 NIL) (-805 1872935 1875785 1875907 "OCT" 1875990 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872573 1872616 1872743 "OCTCT2" 1872886 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867184 1869619 1869659 "OC" 1870756 NIL OC (NIL T) -9 NIL 1871614 NIL) (-802 1864411 1865159 1866149 "OC-" 1866243 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1863763 1864231 1864259 "OCAMON" 1864264 T OCAMON (NIL) -9 NIL 1864285 NIL) (-800 1863294 1863635 1863663 "OASGP" 1863668 T OASGP (NIL) -9 NIL 1863688 NIL) (-799 1862555 1863044 1863072 "OAMONS" 1863112 T OAMONS (NIL) -9 NIL 1863155 NIL) (-798 1861969 1862402 1862430 "OAMON" 1862435 T OAMON (NIL) -9 NIL 1862455 NIL) (-797 1861227 1861745 1861773 "OAGROUP" 1861778 T OAGROUP (NIL) -9 NIL 1861798 NIL) (-796 1860917 1860967 1861055 "NUMTUBE" 1861171 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854490 1856008 1857544 "NUMQUAD" 1859401 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850246 1851234 1852259 "NUMODE" 1853485 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847601 1848481 1848509 "NUMINT" 1849432 T NUMINT (NIL) -9 NIL 1850196 NIL) (-792 1846549 1846746 1846964 "NUMFMT" 1847403 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1832908 1835853 1838385 "NUMERIC" 1844056 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827278 1832357 1832452 "NTSCAT" 1832457 NIL NTSCAT (NIL T T T T) -9 NIL 1832496 NIL) (-789 1826472 1826637 1826830 "NTPOLFN" 1827117 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814549 1823297 1824109 "NSUP" 1825693 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814181 1814238 1814347 "NSUP2" 1814486 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804407 1813955 1814088 "NSMP" 1814093 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1802839 1803140 1803497 "NREP" 1804095 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801430 1801682 1802040 "NPCOEF" 1802582 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800496 1800611 1800827 "NORMRETR" 1801311 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798537 1798827 1799236 "NORMPK" 1800204 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798222 1798250 1798374 "NORMMA" 1798503 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798022 1798179 1798208 "NONE" 1798213 T NONE (NIL) -8 NIL NIL NIL) (-779 1797811 1797840 1797909 "NONE1" 1797986 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797308 1797370 1797549 "NODE1" 1797743 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795593 1796444 1796699 "NNI" 1797046 T NNI (NIL) -8 NIL NIL 1797281) (-776 1794013 1794326 1794690 "NLINSOL" 1795261 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790254 1791249 1792148 "NIPROB" 1793134 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789011 1789245 1789547 "NFINTBAS" 1790016 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788185 1788661 1788702 "NETCLT" 1788874 NIL NETCLT (NIL T) -9 NIL 1788956 NIL) (-772 1786893 1787124 1787405 "NCODIV" 1787953 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1786655 1786692 1786767 "NCNTFRAC" 1786850 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1784835 1785199 1785619 "NCEP" 1786280 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1783686 1784459 1784487 "NASRING" 1784597 T NASRING (NIL) -9 NIL 1784677 NIL) (-768 1783481 1783525 1783619 "NASRING-" 1783624 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782588 1783113 1783141 "NARNG" 1783258 T NARNG (NIL) -9 NIL 1783349 NIL) (-766 1782280 1782347 1782481 "NARNG-" 1782486 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781159 1781366 1781601 "NAGSP" 1782065 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772431 1774115 1775788 "NAGS" 1779506 T NAGS (NIL) -7 NIL NIL NIL) (-763 1770979 1771287 1771618 "NAGF07" 1772120 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765517 1766808 1768115 "NAGF04" 1769692 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758485 1760099 1761732 "NAGF02" 1763904 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1753709 1754809 1755926 "NAGF01" 1757388 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747337 1748903 1750488 "NAGE04" 1752144 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738506 1740627 1742757 "NAGE02" 1745227 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734459 1735406 1736370 "NAGE01" 1737562 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732254 1732788 1733346 "NAGD03" 1733921 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724004 1725932 1727886 "NAGD02" 1730320 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1717815 1719240 1720680 "NAGD01" 1722584 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714024 1714846 1715683 "NAGC06" 1716998 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712489 1712821 1713177 "NAGC05" 1713688 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1711865 1711984 1712128 "NAGC02" 1712365 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1710824 1711407 1711447 "NAALG" 1711526 NIL NAALG (NIL T) -9 NIL 1711587 NIL) (-749 1710659 1710688 1710778 "NAALG-" 1710783 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704609 1705717 1706904 "MULTSQFR" 1709555 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1703928 1704003 1704187 "MULTFACT" 1704521 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1696652 1700565 1700618 "MTSCAT" 1701688 NIL MTSCAT (NIL T T) -9 NIL 1702203 NIL) (-745 1696364 1696418 1696510 "MTHING" 1696592 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696156 1696189 1696249 "MSYSCMD" 1696324 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692238 1694911 1695231 "MSET" 1695869 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689307 1691799 1691840 "MSETAGG" 1691845 NIL MSETAGG (NIL T) -9 NIL 1691879 NIL) (-741 1685149 1686686 1687431 "MRING" 1688607 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1684715 1684782 1684913 "MRF2" 1685076 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684333 1684368 1684512 "MRATFAC" 1684674 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1681945 1682240 1682671 "MPRFF" 1684038 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676242 1681799 1681896 "MPOLY" 1681901 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1675732 1675767 1675975 "MPCPF" 1676201 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675246 1675289 1675473 "MPC3" 1675683 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674441 1674522 1674743 "MPC2" 1675161 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1672742 1673079 1673469 "MONOTOOL" 1674101 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1671967 1672284 1672312 "MONOID" 1672531 T MONOID (NIL) -9 NIL 1672678 NIL) (-731 1671513 1671632 1671813 "MONOID-" 1671818 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1661988 1667939 1667998 "MONOGEN" 1668672 NIL MONOGEN (NIL T T) -9 NIL 1669128 NIL) (-729 1659206 1659941 1660941 "MONOGEN-" 1661060 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658039 1658485 1658513 "MONADWU" 1658905 T MONADWU (NIL) -9 NIL 1659143 NIL) (-727 1657411 1657570 1657818 "MONADWU-" 1657823 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1656770 1657014 1657042 "MONAD" 1657249 T MONAD (NIL) -9 NIL 1657361 NIL) (-725 1656455 1656533 1656665 "MONAD-" 1656670 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1654744 1655368 1655647 "MOEBIUS" 1656208 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654022 1654426 1654466 "MODULE" 1654471 NIL MODULE (NIL T) -9 NIL 1654510 NIL) (-722 1653590 1653686 1653876 "MODULE-" 1653881 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651270 1651954 1652281 "MODRING" 1653414 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648214 1649375 1649896 "MODOP" 1650799 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1646802 1647281 1647558 "MODMONOM" 1648077 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1636846 1645093 1645507 "MODMON" 1646439 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634002 1635690 1635966 "MODFIELD" 1636721 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1632979 1633283 1633473 "MMLFORM" 1633832 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632505 1632548 1632727 "MMAP" 1632930 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630584 1631351 1631392 "MLO" 1631815 NIL MLO (NIL T) -9 NIL 1632057 NIL) (-713 1627950 1628466 1629068 "MLIFT" 1630065 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627341 1627425 1627579 "MKUCFUNC" 1627861 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1626940 1627010 1627133 "MKRECORD" 1627264 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1625987 1626149 1626377 "MKFUNC" 1626751 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625375 1625479 1625635 "MKFLCFN" 1625870 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1624652 1624754 1624939 "MKBCFUNC" 1625268 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621359 1624206 1624342 "MINT" 1624536 T MINT (NIL) -8 NIL NIL NIL) (-706 1620171 1620414 1620691 "MHROWRED" 1621114 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615551 1618706 1619111 "MFLOAT" 1619786 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1614908 1614984 1615155 "MFINFACT" 1615463 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611223 1612071 1612955 "MESH" 1614044 T MESH (NIL) -7 NIL NIL NIL) (-702 1609613 1609925 1610278 "MDDFACT" 1610910 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606408 1608772 1608813 "MDAGG" 1609068 NIL MDAGG (NIL T) -9 NIL 1609211 NIL) (-700 1596148 1605701 1605908 "MCMPLX" 1606221 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595285 1595431 1595632 "MCDEN" 1595997 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593175 1593445 1593825 "MCALCFN" 1595015 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592100 1592340 1592573 "MAYBE" 1592981 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1589712 1590235 1590797 "MATSTOR" 1591571 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1585669 1589084 1589332 "MATRIX" 1589497 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581435 1582142 1582878 "MATLIN" 1585026 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571541 1574727 1574804 "MATCAT" 1579684 NIL MATCAT (NIL T T T) -9 NIL 1581101 NIL) (-692 1567897 1568918 1570274 "MATCAT-" 1570279 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566491 1566644 1566977 "MATCAT2" 1567732 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564603 1564927 1565311 "MAPPKG3" 1566166 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563584 1563757 1563979 "MAPPKG2" 1564427 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562083 1562367 1562694 "MAPPKG1" 1563290 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561162 1561489 1561666 "MAPPAST" 1561926 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1560773 1560831 1560954 "MAPHACK3" 1561098 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560365 1560426 1560540 "MAPHACK2" 1560705 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1559803 1559906 1560048 "MAPHACK1" 1560256 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1557882 1558503 1558807 "MAGMA" 1559531 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557361 1557606 1557697 "MACROAST" 1557811 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1553779 1555600 1556061 "M3D" 1556933 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1547854 1552118 1552159 "LZSTAGG" 1552941 NIL LZSTAGG (NIL T) -9 NIL 1553236 NIL) (-679 1543812 1544985 1546442 "LZSTAGG-" 1546447 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1540899 1541703 1542190 "LWORD" 1543357 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540475 1540703 1540778 "LSTAST" 1540844 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1533641 1540246 1540380 "LSQM" 1540385 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1532865 1533004 1533232 "LSPP" 1533496 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1530677 1530978 1531434 "LSMP" 1532554 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527456 1528130 1528860 "LSMP1" 1529979 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521302 1526593 1526634 "LSAGG" 1526696 NIL LSAGG (NIL T) -9 NIL 1526774 NIL) (-671 1517997 1518921 1520134 "LSAGG-" 1520139 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1515596 1517141 1517390 "LPOLY" 1517792 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515178 1515263 1515386 "LPEFRAC" 1515505 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513499 1514272 1514525 "LO" 1515010 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513151 1513263 1513291 "LOGIC" 1513402 T LOGIC (NIL) -9 NIL 1513483 NIL) (-666 1513013 1513036 1513107 "LOGIC-" 1513112 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512206 1512346 1512539 "LODOOPS" 1512869 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1509629 1512122 1512188 "LODO" 1512193 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508167 1508402 1508755 "LODOF" 1509376 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504371 1506802 1506843 "LODOCAT" 1507281 NIL LODOCAT (NIL T) -9 NIL 1507492 NIL) (-661 1504104 1504162 1504289 "LODOCAT-" 1504294 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501424 1503945 1504063 "LODO2" 1504068 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1498859 1501361 1501406 "LODO1" 1501411 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1497740 1497905 1498210 "LODEEF" 1498682 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493043 1495934 1495975 "LNAGG" 1496837 NIL LNAGG (NIL T) -9 NIL 1497272 NIL) (-656 1492190 1492404 1492746 "LNAGG-" 1492751 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488326 1489115 1489754 "LMOPS" 1491605 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1487729 1488117 1488158 "LMODULE" 1488163 NIL LMODULE (NIL T) -9 NIL 1488189 NIL) (-653 1484927 1487374 1487497 "LMDICT" 1487639 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484333 1484554 1484595 "LLINSET" 1484786 NIL LLINSET (NIL T) -9 NIL 1484877 NIL) (-651 1484032 1484241 1484301 "LITERAL" 1484306 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477195 1482966 1483270 "LIST" 1483761 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1476720 1476794 1476933 "LIST3" 1477115 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1475727 1475905 1476133 "LIST2" 1476538 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1473861 1474173 1474572 "LIST2MAP" 1475374 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473457 1473694 1473735 "LINSET" 1473740 NIL LINSET (NIL T) -9 NIL 1473774 NIL) (-645 1472118 1472788 1472829 "LINEXP" 1473084 NIL LINEXP (NIL T) -9 NIL 1473233 NIL) (-644 1470765 1471025 1471322 "LINDEP" 1471870 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467532 1468251 1469028 "LIMITRF" 1470020 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1465835 1466131 1466540 "LIMITPS" 1467227 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460263 1465346 1465574 "LIE" 1465656 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459211 1459680 1459720 "LIECAT" 1459860 NIL LIECAT (NIL T) -9 NIL 1460011 NIL) (-639 1459052 1459079 1459167 "LIECAT-" 1459172 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451639 1458592 1458748 "LIB" 1458916 T LIB (NIL) -8 NIL NIL NIL) (-637 1447274 1448157 1449092 "LGROBP" 1450756 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445272 1445546 1445896 "LF" 1446995 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444112 1444804 1444832 "LFCAT" 1445039 T LFCAT (NIL) -9 NIL 1445178 NIL) (-634 1441014 1441644 1442332 "LEXTRIPK" 1443476 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1437758 1438584 1439087 "LEXP" 1440594 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437234 1437479 1437571 "LETAST" 1437686 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435632 1435945 1436346 "LEADCDET" 1436916 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1434822 1434896 1435125 "LAZM3PK" 1435553 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1429739 1432899 1433437 "LAUPOL" 1434334 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429318 1429362 1429523 "LAPLACE" 1429689 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427257 1428419 1428670 "LA" 1429151 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426251 1426835 1426876 "LALG" 1426938 NIL LALG (NIL T) -9 NIL 1426997 NIL) (-625 1425965 1426024 1426160 "LALG-" 1426165 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1425800 1425824 1425865 "KVTFROM" 1425927 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1424723 1425167 1425352 "KTVLOGIC" 1425635 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424558 1424582 1424623 "KRCFROM" 1424685 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423462 1423649 1423948 "KOVACIC" 1424358 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423297 1423321 1423362 "KONVERT" 1423424 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423132 1423156 1423197 "KOERCE" 1423259 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1420962 1421725 1422102 "KERNEL" 1422788 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420458 1420539 1420671 "KERNEL2" 1420876 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414228 1418997 1419051 "KDAGG" 1419428 NIL KDAGG (NIL T T) -9 NIL 1419634 NIL) (-615 1413757 1413881 1414086 "KDAGG-" 1414091 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1406905 1413418 1413573 "KAFILE" 1413635 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401333 1406416 1406644 "JORDAN" 1406726 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400712 1400982 1401103 "JOINAST" 1401232 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400558 1400617 1400672 "JAVACODE" 1400677 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1396810 1398763 1398817 "IXAGG" 1399746 NIL IXAGG (NIL T T) -9 NIL 1400205 NIL) (-609 1395729 1396035 1396454 "IXAGG-" 1396459 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391259 1395651 1395710 "IVECTOR" 1395715 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390025 1390262 1390528 "ITUPLE" 1391026 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388527 1388704 1388999 "ITRIGMNP" 1389847 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387272 1387476 1387759 "ITFUN3" 1388303 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1386904 1386961 1387070 "ITFUN2" 1387209 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386063 1386384 1386558 "ITFORM" 1386750 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384024 1385083 1385361 "ITAYLOR" 1385818 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1372969 1378161 1379324 "ISUPS" 1382894 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372073 1372213 1372449 "ISUMP" 1372816 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367448 1372018 1372059 "ISTRING" 1372064 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1366924 1367169 1367261 "ISAST" 1367376 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366133 1366215 1366431 "IRURPK" 1366838 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365069 1365270 1365510 "IRSN" 1365913 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363140 1363495 1363924 "IRRF2F" 1364707 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1362887 1362925 1363001 "IRREDFFX" 1363096 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361502 1361761 1362060 "IROOT" 1362620 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358106 1359186 1359878 "IR" 1360842 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357311 1357599 1357750 "IRFORM" 1357975 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1354924 1355419 1355985 "IR2" 1356789 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354024 1354137 1354351 "IR2F" 1354807 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1353815 1353849 1353909 "IPRNTPK" 1353984 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350396 1353704 1353773 "IPF" 1353778 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1348723 1350321 1350378 "IPADIC" 1350383 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348035 1348283 1348413 "IP4ADDR" 1348613 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347409 1347664 1347796 "IOMODE" 1347923 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346482 1347006 1347133 "IOBFILE" 1347302 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1345970 1346386 1346414 "IOBCON" 1346419 T IOBCON (NIL) -9 NIL 1346440 NIL) (-581 1345481 1345539 1345722 "INVLAPLA" 1345906 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335129 1337483 1339869 "INTTR" 1343145 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331464 1332206 1333071 "INTTOOLS" 1334314 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331050 1331141 1331258 "INTSLPE" 1331367 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329003 1330973 1331032 "INTRVL" 1331037 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326605 1327117 1327692 "INTRF" 1328488 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326016 1326113 1326255 "INTRET" 1326503 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324013 1324402 1324872 "INTRAT" 1325624 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321276 1321859 1322478 "INTPM" 1323498 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318021 1318620 1319358 "INTPAF" 1320662 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313200 1314162 1315213 "INTPACK" 1316990 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310148 1312997 1313106 "INT" 1313111 T INT (NIL) -8 NIL NIL NIL) (-569 1309400 1309552 1309760 "INTHERTR" 1309990 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1308839 1308919 1309107 "INTHERAL" 1309314 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306685 1307128 1307585 "INTHEORY" 1308402 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298091 1299712 1301484 "INTG0" 1305037 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278664 1283454 1288264 "INTFTBL" 1293301 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1277913 1278051 1278224 "INTFACT" 1278523 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275340 1275786 1276343 "INTEF" 1277467 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273707 1274446 1274474 "INTDOM" 1274775 T INTDOM (NIL) -9 NIL 1274982 NIL) (-561 1273076 1273250 1273492 "INTDOM-" 1273497 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269464 1271392 1271446 "INTCAT" 1272245 NIL INTCAT (NIL T) -9 NIL 1272566 NIL) (-559 1268936 1269039 1269167 "INTBIT" 1269356 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267635 1267789 1268096 "INTALG" 1268781 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267118 1267208 1267365 "INTAF" 1267539 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260461 1266928 1267068 "INTABL" 1267073 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1259802 1260268 1260333 "INT8" 1260367 T INT8 (NIL) -8 NIL NIL 1260412) (-554 1259142 1259608 1259673 "INT64" 1259707 T INT64 (NIL) -8 NIL NIL 1259752) (-553 1258482 1258948 1259013 "INT32" 1259047 T INT32 (NIL) -8 NIL NIL 1259092) (-552 1257822 1258288 1258353 "INT16" 1258387 T INT16 (NIL) -8 NIL NIL 1258432) (-551 1252732 1255445 1255473 "INS" 1256407 T INS (NIL) -9 NIL 1257072 NIL) (-550 1249972 1250743 1251717 "INS-" 1251790 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1248747 1248974 1249272 "INPSIGN" 1249725 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1247865 1247982 1248179 "INPRODPF" 1248627 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1246759 1246876 1247113 "INPRODFF" 1247745 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1245759 1245911 1246171 "INNMFACT" 1246595 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1244956 1245053 1245241 "INMODGCD" 1245658 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243464 1243709 1244033 "INFSP" 1244701 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242648 1242765 1242948 "INFPROD0" 1243344 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239503 1240713 1241228 "INFORM" 1242141 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239113 1239173 1239271 "INFORM1" 1239438 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238636 1238725 1238839 "INFINITY" 1239019 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1237812 1238356 1238457 "INETCLTS" 1238555 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236428 1236678 1236999 "INEP" 1237560 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235677 1236325 1236390 "INDE" 1236395 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235241 1235309 1235426 "INCRMAPS" 1235604 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234059 1234510 1234716 "INBFILE" 1235055 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229358 1230295 1231239 "INBFF" 1233147 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228266 1228535 1228563 "INBCON" 1229076 T INBCON (NIL) -9 NIL 1229342 NIL) (-532 1227518 1227741 1228017 "INBCON-" 1228022 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1226997 1227242 1227333 "INAST" 1227447 T INAST (NIL) -8 NIL NIL NIL) (-530 1226424 1226676 1226782 "IMPTAST" 1226911 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1222870 1226268 1226372 "IMATRIX" 1226377 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221578 1221701 1222017 "IMATQF" 1222726 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1219798 1220025 1220362 "IMATLIN" 1221334 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214376 1219722 1219780 "ILIST" 1219785 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212281 1214236 1214349 "IIARRAY2" 1214354 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207679 1212192 1212256 "IFF" 1212261 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207026 1207296 1207412 "IFAST" 1207583 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202021 1206318 1206506 "IFARRAY" 1206883 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201201 1201925 1201998 "IFAMON" 1202003 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1200785 1200850 1200904 "IEVALAB" 1201111 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200460 1200528 1200688 "IEVALAB-" 1200693 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200091 1200374 1200437 "IDPO" 1200442 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199341 1199980 1200055 "IDPOAMS" 1200060 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198648 1199230 1199305 "IDPOAM" 1199310 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197707 1197983 1198036 "IDPC" 1198449 NIL IDPC (NIL T T) -9 NIL 1198598 NIL) (-514 1197176 1197599 1197672 "IDPAM" 1197677 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196552 1197068 1197141 "IDPAG" 1197146 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196197 1196388 1196463 "IDENT" 1196497 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192452 1193300 1194195 "IDECOMP" 1195354 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185290 1186375 1187422 "IDEAL" 1191488 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184450 1184562 1184762 "ICDEN" 1185174 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183521 1183930 1184077 "ICARD" 1184323 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181581 1181894 1182299 "IBPTOOLS" 1183198 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177188 1181201 1181314 "IBITS" 1181500 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1173911 1174487 1175182 "IBATOOL" 1176605 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171690 1172152 1172685 "IBACHIN" 1173446 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169519 1171536 1171639 "IARRAY2" 1171644 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165625 1169445 1169502 "IARRAY1" 1169507 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1159734 1164037 1164518 "IAN" 1165164 T IAN (NIL) -8 NIL NIL NIL) (-500 1159245 1159302 1159475 "IALGFACT" 1159671 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1158773 1158886 1158914 "HYPCAT" 1159121 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158311 1158428 1158614 "HYPCAT-" 1158619 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1157906 1158106 1158189 "HOSTNAME" 1158248 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1157751 1157788 1157829 "HOMOTOP" 1157834 NIL HOMOTOP (NIL T) -9 NIL 1157867 NIL) (-495 1154383 1155761 1155802 "HOAGG" 1156783 NIL HOAGG (NIL T) -9 NIL 1157462 NIL) (-494 1152977 1153376 1153902 "HOAGG-" 1153907 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1146979 1152570 1152720 "HEXADEC" 1152847 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1145727 1145949 1146212 "HEUGCD" 1146756 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1144803 1145564 1145694 "HELLFDIV" 1145699 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1142982 1144580 1144668 "HEAP" 1144747 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142245 1142534 1142668 "HEADAST" 1142868 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136111 1142160 1142222 "HDP" 1142227 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130099 1135746 1135898 "HDMP" 1136012 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129423 1129563 1129727 "HB" 1129955 T HB (NIL) -7 NIL NIL NIL) (-485 1122809 1129269 1129373 "HASHTBL" 1129378 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122285 1122530 1122622 "HASAST" 1122737 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120063 1121907 1122089 "HACKPI" 1122123 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1115731 1119916 1120029 "GTSET" 1120034 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109146 1115609 1115707 "GSTBL" 1115712 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101424 1108177 1108442 "GSERIES" 1108937 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100565 1100982 1101010 "GROUP" 1101213 T GROUP (NIL) -9 NIL 1101347 NIL) (-478 1099931 1100090 1100341 "GROUP-" 1100346 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098298 1098619 1099006 "GROEBSOL" 1099608 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097212 1097500 1097551 "GRMOD" 1098080 NIL GRMOD (NIL T T) -9 NIL 1098248 NIL) (-475 1096980 1097016 1097144 "GRMOD-" 1097149 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092270 1093334 1094334 "GRIMAGE" 1096000 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1090736 1090997 1091321 "GRDEF" 1091966 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090180 1090296 1090437 "GRAY" 1090615 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089367 1089773 1089824 "GRALG" 1089977 NIL GRALG (NIL T T) -9 NIL 1090070 NIL) (-470 1089028 1089101 1089264 "GRALG-" 1089269 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1085805 1088613 1088791 "GPOLSET" 1088935 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085159 1085216 1085474 "GOSPER" 1085742 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1080891 1081597 1082123 "GMODPOL" 1084858 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1079896 1080080 1080318 "GHENSEL" 1080703 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074052 1074895 1075915 "GENUPS" 1078980 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1073749 1073800 1073889 "GENUFACT" 1073995 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073161 1073238 1073403 "GENPGCD" 1073667 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072635 1072670 1072883 "GENMFACT" 1073120 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071201 1071458 1071765 "GENEEZ" 1072378 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065349 1070812 1070974 "GDMP" 1071124 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054692 1059120 1060226 "GCNAALG" 1064332 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053019 1053881 1053909 "GCDDOM" 1054164 T GCDDOM (NIL) -9 NIL 1054321 NIL) (-457 1052489 1052616 1052831 "GCDDOM-" 1052836 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051161 1051346 1051650 "GB" 1052268 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1039777 1042107 1044499 "GBINTERN" 1048852 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037614 1037906 1038327 "GBF" 1039452 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036395 1036560 1036827 "GBEUCLID" 1037430 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1035744 1035869 1036018 "GAUSSFAC" 1036266 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034111 1034413 1034727 "GALUTIL" 1035463 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032419 1032693 1033017 "GALPOLYU" 1033838 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1029784 1030074 1030481 "GALFACTU" 1032116 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021590 1023089 1024697 "GALFACT" 1028216 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1018978 1019636 1019664 "FVFUN" 1020820 T FVFUN (NIL) -9 NIL 1021540 NIL) (-446 1018244 1018426 1018454 "FVC" 1018745 T FVC (NIL) -9 NIL 1018928 NIL) (-445 1017887 1018069 1018137 "FUNDESC" 1018196 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017502 1017684 1017765 "FUNCTION" 1017839 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015246 1015824 1016290 "FT" 1017056 T FT (NIL) -8 NIL NIL NIL) (-442 1014037 1014547 1014750 "FTEM" 1015063 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012328 1012617 1013014 "FSUPFACT" 1013728 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1010725 1011014 1011346 "FST" 1012016 T FST (NIL) -8 NIL NIL NIL) (-439 1009924 1010030 1010218 "FSRED" 1010607 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008623 1008879 1009226 "FSPRMELT" 1009639 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1005929 1006367 1006853 "FSPECF" 1008186 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987567 995898 995939 "FS" 999823 NIL FS (NIL T) -9 NIL 1002112 NIL) (-435 976210 979203 983260 "FS-" 983560 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 975738 975792 975962 "FSINT" 976151 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974030 974731 975034 "FSERIES" 975517 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973072 973188 973412 "FSCINT" 973910 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969280 972016 972057 "FSAGG" 972427 NIL FSAGG (NIL T) -9 NIL 972686 NIL) (-430 967042 967643 968439 "FSAGG-" 968534 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966084 966227 966454 "FSAGG2" 966895 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 963766 964046 964593 "FS2UPS" 965802 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963400 963443 963572 "FS2" 963717 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962278 962449 962751 "FS2EXPXP" 963225 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961704 961819 961971 "FRUTIL" 962158 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953117 957199 958557 "FR" 960378 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948131 950806 950846 "FRNAALG" 952166 NIL FRNAALG (NIL T) -9 NIL 952764 NIL) (-422 943804 944880 946155 "FRNAALG-" 946905 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943442 943485 943612 "FRNAAF2" 943755 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 941817 942291 942587 "FRMOD" 943254 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939560 940192 940510 "FRIDEAL" 941608 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938751 938838 939129 "FRIDEAL2" 939467 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 937884 938298 938339 "FRETRCT" 938344 NIL FRETRCT (NIL T) -9 NIL 938520 NIL) (-416 936996 937227 937578 "FRETRCT-" 937583 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934084 935294 935353 "FRAMALG" 936235 NIL FRAMALG (NIL T T) -9 NIL 936527 NIL) (-414 932218 932673 933303 "FRAMALG-" 933526 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926137 931691 931968 "FRAC" 931973 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 925773 925830 925937 "FRAC2" 926074 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925409 925466 925573 "FR2" 925710 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 919922 922815 922843 "FPS" 923962 T FPS (NIL) -9 NIL 924519 NIL) (-409 919371 919480 919644 "FPS-" 919790 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916673 918342 918370 "FPC" 918595 T FPC (NIL) -9 NIL 918737 NIL) (-407 916466 916506 916603 "FPC-" 916608 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915256 915954 915995 "FPATMAB" 916000 NIL FPATMAB (NIL T) -9 NIL 916152 NIL) (-405 912929 913432 913858 "FPARFRAC" 914893 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908323 908821 909503 "FORTRAN" 912361 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906039 906539 907078 "FORT" 907804 T FORT (NIL) -7 NIL NIL NIL) (-402 903715 904277 904305 "FORTFN" 905365 T FORTFN (NIL) -9 NIL 905989 NIL) (-401 903479 903529 903557 "FORTCAT" 903616 T FORTCAT (NIL) -9 NIL 903678 NIL) (-400 901585 902095 902485 "FORMULA" 903109 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901373 901403 901472 "FORMULA1" 901549 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 900896 900948 901121 "FORDER" 901315 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 899992 900156 900349 "FOP" 900723 T FOP (NIL) -7 NIL NIL NIL) (-396 898573 899272 899446 "FNLA" 899874 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897302 897717 897745 "FNCAT" 898205 T FNCAT (NIL) -9 NIL 898465 NIL) (-394 896841 897261 897289 "FNAME" 897294 T FNAME (NIL) -8 NIL NIL NIL) (-393 895404 896367 896395 "FMTC" 896400 T FMTC (NIL) -9 NIL 896436 NIL) (-392 894150 895340 895386 "FMONOID" 895391 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 890978 892146 892187 "FMONCAT" 893404 NIL FMONCAT (NIL T) -9 NIL 894009 NIL) (-390 890170 890720 890869 "FM" 890874 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887594 888240 888268 "FMFUN" 889412 T FMFUN (NIL) -9 NIL 890120 NIL) (-388 886863 887044 887072 "FMC" 887362 T FMC (NIL) -9 NIL 887544 NIL) (-387 883942 884802 884856 "FMCAT" 886051 NIL FMCAT (NIL T T) -9 NIL 886546 NIL) (-386 882808 883708 883808 "FM1" 883887 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880582 880998 881492 "FLOATRP" 882359 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874160 878311 878932 "FLOAT" 879981 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871598 872098 872676 "FLOATCP" 873627 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870338 871176 871217 "FLINEXP" 871222 NIL FLINEXP (NIL T) -9 NIL 871315 NIL) (-381 869492 869727 870055 "FLINEXP-" 870060 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868568 868712 868936 "FLASORT" 869344 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865684 866552 866604 "FLALG" 867831 NIL FLALG (NIL T T) -9 NIL 868298 NIL) (-378 859388 863140 863181 "FLAGG" 864443 NIL FLAGG (NIL T) -9 NIL 865095 NIL) (-377 858114 858453 858943 "FLAGG-" 858948 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857156 857299 857526 "FLAGG2" 857967 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854007 855015 855074 "FINRALG" 856202 NIL FINRALG (NIL T T) -9 NIL 856710 NIL) (-374 853167 853396 853735 "FINRALG-" 853740 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852547 852786 852814 "FINITE" 853010 T FINITE (NIL) -9 NIL 853117 NIL) (-372 844904 847091 847131 "FINAALG" 850798 NIL FINAALG (NIL T) -9 NIL 852251 NIL) (-371 840236 841286 842430 "FINAALG-" 843809 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839604 839991 840094 "FILE" 840166 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838262 838600 838654 "FILECAT" 839338 NIL FILECAT (NIL T T) -9 NIL 839554 NIL) (-368 835978 837506 837534 "FIELD" 837574 T FIELD (NIL) -9 NIL 837654 NIL) (-367 834598 834983 835494 "FIELD-" 835499 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832448 833233 833580 "FGROUP" 834284 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831538 831702 831922 "FGLMICPK" 832280 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827370 831463 831520 "FFX" 831525 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 826971 827032 827167 "FFSLPE" 827303 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 822961 823743 824539 "FFPOLY" 826207 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822465 822501 822710 "FFPOLY2" 822919 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818311 822384 822447 "FFP" 822452 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813709 818222 818286 "FF" 818291 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 808835 813052 813242 "FFNBX" 813563 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 803763 807970 808228 "FFNBP" 808689 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798396 803047 803258 "FFNB" 803596 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797228 797426 797741 "FFINTBAS" 798193 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793297 795517 795545 "FFIELDC" 796165 T FFIELDC (NIL) -9 NIL 796541 NIL) (-353 791959 792330 792827 "FFIELDC-" 792832 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791528 791574 791698 "FFHOM" 791901 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789223 789710 790227 "FFF" 791043 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 784841 788965 789066 "FFCGX" 789166 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780463 784573 784680 "FFCGP" 784784 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775646 780190 780298 "FFCG" 780399 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757042 766123 766209 "FFCAT" 771374 NIL FFCAT (NIL T T T) -9 NIL 772825 NIL) (-346 752239 753287 754601 "FFCAT-" 755831 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751650 751693 751928 "FFCAT2" 752190 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 740973 744622 745842 "FEXPR" 750502 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 739935 740370 740411 "FEVALAB" 740495 NIL FEVALAB (NIL T) -9 NIL 740756 NIL) (-342 739094 739304 739642 "FEVALAB-" 739647 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737660 738477 738680 "FDIV" 738993 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734680 735421 735536 "FDIVCAT" 737104 NIL FDIVCAT (NIL T T T T) -9 NIL 737541 NIL) (-339 734442 734469 734639 "FDIVCAT-" 734644 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733662 733749 734026 "FDIV2" 734349 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732636 732957 733159 "FCTRDATA" 733480 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731322 731581 731870 "FCPAK1" 732367 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730421 730822 730963 "FCOMP" 731213 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714126 717571 721109 "FC" 726903 T FC (NIL) -8 NIL NIL NIL) (-333 706489 710517 710557 "FAXF" 712359 NIL FAXF (NIL T) -9 NIL 713051 NIL) (-332 703766 704423 705248 "FAXF-" 705713 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 698818 703142 703318 "FARRAY" 703623 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 693712 695779 695832 "FAMR" 696855 NIL FAMR (NIL T T) -9 NIL 697315 NIL) (-329 692602 692904 693339 "FAMR-" 693344 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 691771 692524 692577 "FAMONOID" 692582 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689557 690267 690320 "FAMONC" 691261 NIL FAMONC (NIL T T) -9 NIL 691647 NIL) (-326 688221 689311 689448 "FAGROUP" 689453 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686016 686335 686738 "FACUTIL" 687902 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685115 685300 685522 "FACTFUNC" 685826 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677537 684418 684617 "EXPUPXS" 684971 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675020 675560 676146 "EXPRTUBE" 676971 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671291 671883 672613 "EXPRODE" 674359 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 656776 669940 670369 "EXPR" 670895 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651330 651917 652723 "EXPR2UPS" 656074 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 650962 651019 651128 "EXPR2" 651267 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642350 650113 650404 "EXPEXPAN" 650798 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642150 642307 642336 "EXIT" 642341 T EXIT (NIL) -8 NIL NIL NIL) (-315 641630 641874 641965 "EXITAST" 642079 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641257 641319 641432 "EVALCYC" 641562 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 640798 640916 640957 "EVALAB" 641127 NIL EVALAB (NIL T) -9 NIL 641231 NIL) (-312 640279 640401 640622 "EVALAB-" 640627 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637647 638949 638977 "EUCDOM" 639532 T EUCDOM (NIL) -9 NIL 639882 NIL) (-310 636052 636494 637084 "EUCDOM-" 637089 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623591 626350 629100 "ESTOOLS" 633322 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623223 623280 623389 "ESTOOLS2" 623528 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 622974 623016 623096 "ESTOOLS1" 623175 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617011 618619 618647 "ES" 621415 T ES (NIL) -9 NIL 622825 NIL) (-305 611958 613245 615062 "ES-" 615226 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608332 609093 609873 "ESCONT" 611198 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608077 608109 608191 "ESCONT1" 608294 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 607752 607802 607902 "ES2" 608021 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607382 607440 607549 "ES1" 607688 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606598 606727 606903 "ERROR" 607226 T ERROR (NIL) -7 NIL NIL NIL) (-299 599990 606457 606548 "EQTBL" 606553 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592493 595304 596753 "EQ" 598574 NIL -2129 (NIL T) -8 NIL NIL NIL) (-297 592125 592182 592291 "EQ2" 592430 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587416 588463 589556 "EP" 591064 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586016 586307 586613 "ENV" 587130 T ENV (NIL) -8 NIL NIL NIL) (-294 585110 585664 585692 "ENTIRER" 585697 T ENTIRER (NIL) -9 NIL 585743 NIL) (-293 581804 583292 583653 "EMR" 584918 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 580934 581119 581173 "ELTAGG" 581553 NIL ELTAGG (NIL T T) -9 NIL 581764 NIL) (-291 580653 580715 580856 "ELTAGG-" 580861 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580417 580446 580500 "ELTAB" 580584 NIL ELTAB (NIL T T) -9 NIL 580636 NIL) (-289 579543 579689 579888 "ELFUTS" 580268 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579285 579341 579369 "ELEMFUN" 579474 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579155 579176 579244 "ELEMFUN-" 579249 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 573969 577225 577266 "ELAGG" 578206 NIL ELAGG (NIL T) -9 NIL 578669 NIL) (-285 572254 572688 573351 "ELAGG-" 573356 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571566 571703 571859 "ELABOR" 572118 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570227 570506 570800 "ELABEXPR" 571292 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563091 564894 565721 "EFUPXS" 569503 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556541 558342 559152 "EFULS" 562367 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554026 554384 554856 "EFSTRUC" 556173 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543817 545383 546931 "EF" 552541 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 542891 543302 543451 "EAB" 543688 T EAB (NIL) -8 NIL NIL NIL) (-277 542073 542850 542878 "E04UCFA" 542883 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541255 542032 542060 "E04NAFA" 542065 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540437 541214 541242 "E04MBFA" 541247 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539619 540396 540424 "E04JAFA" 540429 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538803 539578 539606 "E04GCFA" 539611 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 537987 538762 538790 "E04FDFA" 538795 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537169 537946 537974 "E04DGFA" 537979 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531342 532694 534058 "E04AGNT" 535825 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530022 530528 530568 "DVARCAT" 531043 NIL DVARCAT (NIL T) -9 NIL 531242 NIL) (-268 529226 529438 529752 "DVARCAT-" 529757 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522363 529025 529154 "DSMP" 529159 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517144 518308 519376 "DROPT" 521315 T DROPT (NIL) -8 NIL NIL NIL) (-265 516809 516868 516966 "DROPT1" 517079 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 511924 513050 514187 "DROPT0" 515692 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510269 510594 510980 "DRAWPT" 511558 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504856 505779 506858 "DRAW" 509243 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504489 504542 504660 "DRAWHACK" 504797 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503220 503489 503780 "DRAWCX" 504218 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502735 502804 502955 "DRAWCURV" 503146 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493203 495165 497280 "DRAWCFUN" 500640 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 489967 491896 491937 "DQAGG" 492566 NIL DQAGG (NIL T) -9 NIL 492840 NIL) (-256 478091 484560 484643 "DPOLCAT" 486495 NIL DPOLCAT (NIL T T T T) -9 NIL 487040 NIL) (-255 472928 474276 476234 "DPOLCAT-" 476239 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466050 472789 472887 "DPMO" 472892 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459075 465830 465997 "DPMM" 466002 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458645 458859 458948 "DOMTMPLT" 459006 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458078 458447 458527 "DOMCTOR" 458585 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457290 457558 457709 "DOMAIN" 457947 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451278 456925 457077 "DMP" 457191 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450878 450934 451078 "DLP" 451216 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444700 450205 450395 "DLIST" 450720 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441497 443553 443594 "DLAGG" 444144 NIL DLAGG (NIL T) -9 NIL 444374 NIL) (-245 440173 440837 440865 "DIVRING" 440957 T DIVRING (NIL) -9 NIL 441040 NIL) (-244 439410 439600 439900 "DIVRING-" 439905 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437512 437869 438275 "DISPLAY" 439024 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431400 437426 437489 "DIRPROD" 437494 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430248 430451 430716 "DIRPROD2" 431193 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419023 425029 425082 "DIRPCAT" 425492 NIL DIRPCAT (NIL NIL T) -9 NIL 426332 NIL) (-239 416349 416991 417872 "DIRPCAT-" 418209 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415636 415796 415982 "DIOSP" 416183 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412291 414548 414589 "DIOPS" 415023 NIL DIOPS (NIL T) -9 NIL 415252 NIL) (-236 411840 411954 412145 "DIOPS-" 412150 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410663 411291 411319 "DIFRING" 411506 T DIFRING (NIL) -9 NIL 411616 NIL) (-234 410309 410386 410538 "DIFRING-" 410543 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408045 409317 409358 "DIFEXT" 409721 NIL DIFEXT (NIL T) -9 NIL 410015 NIL) (-232 406330 406758 407424 "DIFEXT-" 407429 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403605 405862 405903 "DIAGG" 405908 NIL DIAGG (NIL T) -9 NIL 405928 NIL) (-230 402989 403146 403398 "DIAGG-" 403403 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398406 401948 402225 "DHMATRIX" 402758 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394018 394927 395937 "DFSFUN" 397416 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389097 392949 393261 "DFLOAT" 393726 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387360 387641 388030 "DFINTTLS" 388805 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384389 385381 385781 "DERHAM" 387026 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382190 384164 384253 "DEQUEUE" 384333 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381444 381577 381760 "DEGRED" 382052 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377874 378619 379465 "DEFINTRF" 380672 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375429 375898 376490 "DEFINTEF" 377393 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374779 375049 375164 "DEFAST" 375334 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368781 374372 374522 "DECIMAL" 374649 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366293 366751 367257 "DDFACT" 368325 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365889 365932 366083 "DBLRESP" 366244 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363761 364122 364482 "DBASE" 365656 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363003 363241 363387 "DATAARY" 363660 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362109 362962 362990 "D03FAFA" 362995 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361216 362068 362096 "D03EEFA" 362101 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359166 359632 360121 "D03AGNT" 360747 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358455 359125 359153 "D02EJFA" 359158 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357744 358414 358442 "D02CJFA" 358447 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357033 357703 357731 "D02BHFA" 357736 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356322 356992 357020 "D02BBFA" 357025 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349519 351108 352714 "D02AGNT" 354736 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347287 347810 348356 "D01WGTS" 348993 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346354 347246 347274 "D01TRNS" 347279 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345422 346313 346341 "D01GBFA" 346346 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344490 345381 345409 "D01FCFA" 345414 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343558 344449 344477 "D01ASFA" 344482 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342626 343517 343545 "D01AQFA" 343550 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341694 342585 342613 "D01APFA" 342618 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340762 341653 341681 "D01ANFA" 341686 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339830 340721 340749 "D01AMFA" 340754 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338898 339789 339817 "D01ALFA" 339822 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 337966 338857 338885 "D01AKFA" 338890 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337034 337925 337953 "D01AJFA" 337958 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330329 331882 333443 "D01AGNT" 335493 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329666 329794 329946 "CYCLOTOM" 330197 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326399 327114 327841 "CYCLES" 328959 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325711 325845 326016 "CVMP" 326260 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323552 323810 324179 "CTRIGMNP" 325439 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 322988 323346 323419 "CTOR" 323499 T CTOR (NIL) -8 NIL NIL NIL) (-188 322497 322719 322820 "CTORKIND" 322907 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321788 322104 322132 "CTORCAT" 322314 T CTORCAT (NIL) -9 NIL 322427 NIL) (-186 321386 321497 321656 "CTORCAT-" 321661 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320848 321060 321168 "CTORCALL" 321310 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320222 320321 320474 "CSTTOOLS" 320745 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316021 316678 317436 "CRFP" 319534 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315496 315742 315834 "CRCEAST" 315949 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314543 314728 314956 "CRAPACK" 315300 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313927 314028 314232 "CPMATCH" 314419 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313652 313680 313786 "CPIMA" 313893 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310000 310672 311391 "COORDSYS" 312987 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309412 309533 309675 "CONTOUR" 309878 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305303 307415 307907 "CONTFRAC" 308952 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305183 305204 305232 "CONDUIT" 305269 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304271 304825 304853 "COMRING" 304858 T COMRING (NIL) -9 NIL 304910 NIL) (-173 303325 303629 303813 "COMPPROP" 304107 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 302986 303021 303149 "COMPLPAT" 303284 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293277 302795 302904 "COMPLEX" 302909 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292913 292970 293077 "COMPLEX2" 293214 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292252 292373 292533 "COMPILER" 292773 T COMPILER (NIL) -8 NIL NIL NIL) (-168 291970 292005 292103 "COMPFACT" 292211 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276050 286044 286084 "COMPCAT" 287088 NIL COMPCAT (NIL T) -9 NIL 288436 NIL) (-166 265562 268489 272116 "COMPCAT-" 272472 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265291 265319 265422 "COMMUPC" 265528 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265085 265119 265178 "COMMONOP" 265252 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264641 264836 264923 "COMM" 265018 T COMM (NIL) -8 NIL NIL NIL) (-162 264217 264445 264520 "COMMAAST" 264586 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263466 263660 263688 "COMBOPC" 264026 T COMBOPC (NIL) -9 NIL 264201 NIL) (-160 262362 262572 262814 "COMBINAT" 263256 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258819 259393 260020 "COMBF" 261784 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257577 257935 258170 "COLOR" 258604 T COLOR (NIL) -8 NIL NIL NIL) (-157 257053 257298 257390 "COLONAST" 257505 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256693 256740 256865 "CMPLXRT" 257000 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256141 256393 256492 "CLLCTAST" 256614 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251643 252671 253751 "CLIP" 255081 T CLIP (NIL) -7 NIL NIL NIL) (-153 249984 250744 250984 "CLIF" 251470 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246159 248130 248171 "CLAGG" 249100 NIL CLAGG (NIL T) -9 NIL 249636 NIL) (-151 244581 245038 245621 "CLAGG-" 245626 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244125 244210 244350 "CINTSLPE" 244490 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241626 242097 242645 "CHVAR" 243653 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240800 241354 241382 "CHARZ" 241387 T CHARZ (NIL) -9 NIL 241402 NIL) (-147 240554 240594 240672 "CHARPOL" 240754 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239612 240199 240227 "CHARNZ" 240274 T CHARNZ (NIL) -9 NIL 240330 NIL) (-145 237518 238266 238619 "CHAR" 239279 T CHAR (NIL) -8 NIL NIL NIL) (-144 237244 237305 237333 "CFCAT" 237444 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236485 236596 236779 "CDEN" 237128 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232450 235638 235918 "CCLASS" 236225 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231701 231858 232035 "CATEGORY" 232293 T -10 (NIL) -8 NIL NIL NIL) (-140 231274 231620 231668 "CATCTOR" 231673 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230725 230977 231075 "CATAST" 231196 T CATAST (NIL) -8 NIL NIL NIL) (-138 230201 230446 230538 "CASEAST" 230653 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225339 226358 227102 "CARTEN" 229513 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224447 224595 224816 "CARTEN2" 225186 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222763 223597 223854 "CARD" 224210 T CARD (NIL) -8 NIL NIL NIL) (-134 222339 222567 222642 "CAPSLAST" 222708 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221843 222051 222079 "CACHSET" 222211 T CACHSET (NIL) -9 NIL 222289 NIL) (-132 221313 221635 221663 "CABMON" 221713 T CABMON (NIL) -9 NIL 221769 NIL) (-131 220786 221017 221127 "BYTEORD" 221223 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219768 220320 220462 "BYTE" 220625 T BYTE (NIL) -8 NIL NIL 220747) (-129 215118 219273 219445 "BYTEBUF" 219616 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212627 214810 214917 "BTREE" 215044 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 210076 212275 212397 "BTOURN" 212537 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207446 209546 209587 "BTCAT" 209655 NIL BTCAT (NIL T) -9 NIL 209732 NIL) (-125 207113 207193 207342 "BTCAT-" 207347 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202492 206372 206400 "BTAGG" 206514 T BTAGG (NIL) -9 NIL 206624 NIL) (-123 201982 202107 202313 "BTAGG-" 202318 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198977 201260 201475 "BSTREE" 201799 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198115 198241 198425 "BRILL" 198833 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194767 196841 196882 "BRAGG" 197531 NIL BRAGG (NIL T) -9 NIL 197789 NIL) (-119 193296 193702 194257 "BRAGG-" 194262 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186523 192640 192825 "BPADICRT" 193143 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184838 186460 186505 "BPADIC" 186510 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184536 184566 184680 "BOUNDZRO" 184802 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179764 180962 181874 "BOP" 183644 T BOP (NIL) -8 NIL NIL NIL) (-114 177545 177949 178424 "BOP1" 179322 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177246 177307 177335 "BOOLE" 177446 T BOOLE (NIL) -9 NIL 177528 NIL) (-112 176071 176820 176969 "BOOLEAN" 177117 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175350 175754 175808 "BMODULE" 175813 NIL BMODULE (NIL T T) -9 NIL 175878 NIL) (-110 171151 175148 175221 "BITS" 175297 T BITS (NIL) -8 NIL NIL NIL) (-109 170572 170691 170831 "BINDING" 171031 T BINDING (NIL) -8 NIL NIL NIL) (-108 164577 170167 170316 "BINARY" 170443 T BINARY (NIL) -8 NIL NIL NIL) (-107 162357 163832 163873 "BGAGG" 164133 NIL BGAGG (NIL T) -9 NIL 164270 NIL) (-106 162188 162220 162311 "BGAGG-" 162316 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161259 161572 161777 "BFUNCT" 162003 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159949 160127 160415 "BEZOUT" 161083 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156418 158801 159131 "BBTREE" 159652 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156152 156205 156233 "BASTYPE" 156352 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156004 156033 156106 "BASTYPE-" 156111 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155438 155514 155666 "BALFACT" 155915 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154294 154853 155039 "AUTOMOR" 155283 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154020 154025 154051 "ATTREG" 154056 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152272 152717 153069 "ATTRBUT" 153686 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151880 152100 152166 "ATTRAST" 152224 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151416 151529 151555 "ATRIG" 151756 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151225 151266 151353 "ATRIG-" 151358 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150870 151056 151082 "ASTCAT" 151087 T ASTCAT (NIL) -9 NIL 151117 NIL) (-92 150597 150656 150775 "ASTCAT-" 150780 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148746 150373 150461 "ASTACK" 150540 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147251 147548 147913 "ASSOCEQ" 148428 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146283 146910 147034 "ASP9" 147158 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146046 146231 146270 "ASP8" 146275 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144914 145651 145793 "ASP80" 145935 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143812 144549 144681 "ASP7" 144813 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142766 143489 143607 "ASP78" 143725 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141735 142446 142563 "ASP77" 142680 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140647 141373 141504 "ASP74" 141635 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139547 140282 140414 "ASP73" 140546 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138651 139373 139473 "ASP6" 139478 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137598 138328 138446 "ASP55" 138564 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136547 137272 137391 "ASP50" 137510 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135635 136248 136358 "ASP4" 136468 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134723 135336 135446 "ASP49" 135556 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133507 134262 134430 "ASP42" 134612 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132284 133040 133210 "ASP41" 133394 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131234 131961 132079 "ASP35" 132197 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130999 131182 131221 "ASP34" 131226 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130736 130803 130879 "ASP33" 130954 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129630 130371 130503 "ASP31" 130635 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129395 129578 129617 "ASP30" 129622 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129130 129199 129275 "ASP29" 129350 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128895 129078 129117 "ASP28" 129122 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128660 128843 128882 "ASP27" 128887 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127744 128358 128469 "ASP24" 128580 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126821 127546 127658 "ASP20" 127663 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125909 126522 126632 "ASP1" 126742 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124852 125583 125702 "ASP19" 125821 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124589 124656 124732 "ASP12" 124807 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123441 124188 124332 "ASP10" 124476 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121292 123285 123376 "ARRAY2" 123381 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117057 120940 121054 "ARRAY1" 121209 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116089 116262 116483 "ARRAY12" 116880 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110401 112319 112394 "ARR2CAT" 115024 NIL ARR2CAT (NIL T T T) -9 NIL 115782 NIL) (-56 107835 108579 109533 "ARR2CAT-" 109538 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107152 107462 107587 "ARITY" 107728 T ARITY (NIL) -8 NIL NIL NIL) (-54 105928 106080 106379 "APPRULE" 106988 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105579 105627 105746 "APPLYORE" 105874 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104933 105172 105292 "ANY" 105477 T ANY (NIL) -8 NIL NIL NIL) (-51 104211 104334 104491 "ANY1" 104807 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101741 102648 102975 "ANTISYM" 103935 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101233 101448 101544 "ANON" 101663 T ANON (NIL) -8 NIL NIL NIL) (-48 95482 99772 100226 "AN" 100797 T AN (NIL) -8 NIL NIL NIL) (-47 91380 92768 92819 "AMR" 93567 NIL AMR (NIL T T) -9 NIL 94167 NIL) (-46 90492 90713 91076 "AMR-" 91081 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74931 90409 90470 "ALIST" 90475 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71736 74525 74694 "ALGSC" 74849 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68292 68846 69453 "ALGPKG" 71176 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67569 67670 67854 "ALGMFACT" 68178 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63604 64183 64777 "ALGMANIP" 67153 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54974 63230 63380 "ALGFF" 63537 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54170 54301 54480 "ALGFACT" 54832 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53111 53711 53749 "ALGEBRA" 53754 NIL ALGEBRA (NIL T) -9 NIL 53795 NIL) (-37 52829 52888 53020 "ALGEBRA-" 53025 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34892 50801 50853 "ALAGG" 50989 NIL ALAGG (NIL T T) -9 NIL 51150 NIL) (-35 34428 34541 34567 "AHYP" 34768 T AHYP (NIL) -9 NIL NIL NIL) (-34 33359 33607 33633 "AGG" 34132 T AGG (NIL) -9 NIL 34411 NIL) (-33 32793 32955 33169 "AGG-" 33174 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30599 31022 31427 "AF" 32435 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30079 30324 30414 "ADDAST" 30527 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29347 29606 29762 "ACPLOT" 29941 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18670 26474 26512 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358 NIL) (-28 16697 17187 17949 "ACFS-" 17954 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12815 14744 14770 "ACF" 15649 T ACF (NIL) -9 NIL 16062 NIL) (-26 11519 11853 12346 "ACF-" 12351 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11091 11286 11312 "ABELSG" 11404 T ABELSG (NIL) -9 NIL 11469 NIL) (-24 10958 10983 11049 "ABELSG-" 11054 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10301 10588 10614 "ABELMON" 10784 T ABELMON (NIL) -9 NIL 10896 NIL) (-22 9965 10049 10187 "ABELMON-" 10192 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9313 9685 9711 "ABELGRP" 9783 T ABELGRP (NIL) -9 NIL 9858 NIL) (-20 8776 8905 9121 "ABELGRP-" 9126 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8085 8124 "A1AGG" 8129 NIL A1AGG (NIL T) -9 NIL 8169 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 288cd220..813a907e 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,32 +1,10 @@ -(732524 . 3481463046) -(((*1 *2 *2) - (-12 (-5 *2 (-1166 *3)) (-4 *3 (-1058)) (-5 *1 (-1170 *3)))) - ((*1 *1 *1) - (-12 (-5 *1 (-1269 *2 *3 *4)) (-4 *2 (-1058)) (-14 *3 (-1186)) - (-14 *4 *2)))) -(((*1 *2 *1) - (-12 (-4 *3 (-368)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *2 (-112)) - (-5 *1 (-510 *3 *4 *5 *6)) (-4 *6 (-956 *3 *4 *5))))) -(((*1 *1) (-5 *1 (-443)))) -(((*1 *1 *2 *2 *2) - (-12 (-5 *1 (-229 *2)) (-4 *2 (-13 (-368) (-1212))))) - ((*1 *1 *1 *2) (-12 (-5 *1 (-724 *2)) (-4 *2 (-368)))) - ((*1 *1 *2) (-12 (-5 *1 (-724 *2)) (-4 *2 (-368)))) - ((*1 *2 *1 *3 *4 *4) - (-12 (-5 *3 (-928)) (-5 *4 (-384)) (-5 *2 (-1282)) (-5 *1 (-1278))))) -(((*1 *1 *2) - (-12 (-5 *2 (-928)) (-4 *1 (-240 *3 *4)) (-4 *4 (-1058)) - (-4 *4 (-1227)))) - ((*1 *1 *2) - (-12 (-14 *3 (-650 (-1186))) (-4 *4 (-174)) - (-4 *5 (-240 (-2589 *3) (-777))) - (-14 *6 - (-1 (-112) (-2 (|:| -2283 *2) (|:| -3227 *5)) - (-2 (|:| -2283 *2) (|:| -3227 *5)))) - (-5 *1 (-467 *3 *4 *2 *5 *6 *7)) (-4 *2 (-856)) - (-4 *7 (-956 *4 *5 (-870 *3))))) - ((*1 *2 *2) (-12 (-5 *2 (-950 (-227))) (-5 *1 (-1223))))) +(732524 . 3481665222) +(((*1 *2 *3) (-12 (-5 *3 (-928)) (-5 *2 (-1168)) (-5 *1 (-792))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-880)) (-5 *3 (-650 (-266))) (-5 *1 (-264))))) +(((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-695 *3)) (-4 *3 (-1058)) (-5 *1 (-696 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-1134 (-570) (-618 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-311)) (-4 *4 (-1001 *3)) (-4 *5 (-1253 *4)) @@ -43,71 +21,41 @@ (-12 (-4 *3 (-174)) (-4 *2 (-723 *3)) (-5 *1 (-668 *2 *3 *4)) (-4 *4 (|SubsetCategory| (-732) *3)))) ((*1 *2 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-562))))) -(((*1 *2 *2 *3 *3) - (-12 (-5 *3 (-570)) (-4 *4 (-13 (-562) (-148))) (-5 *1 (-543 *4 *2)) - (-4 *2 (-1268 *4)))) - 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*1 (-678 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-683 *2)) (-4 *2 (-856)))) @@ -116,24 +64,30 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-854) (-368))) (-5 *1 (-1070 *2 *3)) (-4 *3 (-1253 *2))))) -(((*1 *2 *1) (-12 (-5 *2 (-650 (-879 (-928) (-928)))) (-5 *1 (-980))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-562) (-1047 (-570)))) (-5 *2 (-171 (-320 *4))) - (-5 *1 (-190 *4 *3)) (-4 *3 (-13 (-27) (-1212) (-436 (-171 *4)))))) - ((*1 *2 *3) - (-12 (-4 *4 (-13 (-458) (-1047 (-570)) (-645 (-570)))) - (-5 *2 (-171 *3)) (-5 *1 (-1216 *4 *3)) - (-4 *3 (-13 (-27) (-1212) (-436 *4)))))) (((*1 *1 *1 *1) (-4 *1 (-667)))) -(((*1 *1 *1) - (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) -(((*1 *1 *1) (-5 *1 (-542)))) -(((*1 *2 *3 *4 *3 *5) - (-12 (-5 *3 (-1168)) (-5 *4 (-171 (-227))) (-5 *5 (-570)) - (-5 *2 (-1044)) (-5 *1 (-764))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) + (-5 *1 (-753))))) (((*1 *2 *3) - (-12 (-5 *2 (-570)) (-5 *1 (-451 *3)) (-4 *3 (-410)) (-4 *3 (-1058))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) + (-12 + (-5 *3 + (-650 (-2 (|:| -4402 (-413 (-570))) (|:| -4415 (-413 (-570)))))) + (-5 *2 (-650 (-413 (-570)))) (-5 *1 (-1029 *4)) + (-4 *4 (-1253 (-570)))))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-1109)) + (-5 *2 (-2 (|:| |lm| *1) (|:| |mm| *1) (|:| |rm| *1))) + (-4 *1 (-391 *3))))) +(((*1 *1 *2 *3 *4) + (-12 (-5 *2 (-1 (-1135 *4 *3 *5))) (-4 *4 (-38 (-413 (-570)))) + (-4 *4 (-1058)) (-4 *3 (-856)) (-5 *1 (-1135 *4 *3 *5)) + (-4 *5 (-956 *4 (-537 *3) *3)))) + ((*1 *1 *2 *3 *4) + (-12 (-5 *2 (-1 (-1221 *4))) (-5 *3 (-1186)) (-5 *1 (-1221 *4)) + (-4 *4 (-38 (-413 (-570)))) (-4 *4 (-1058))))) +(((*1 *1 *1) + (-12 (-4 *1 (-693 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-378 *2)) + (-4 *4 (-378 *2))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) @@ -209,26 +163,26 @@ (-4 *1 (-985 *3 *4 *5 *6)))) ((*1 *2 *1) (|partial| -12 (-4 *1 (-1047 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) - (|partial| -2905 + (|partial| -2854 (-12 (-5 *2 (-959 *3)) - (-12 (-1780 (-4 *3 (-38 (-413 (-570))))) - (-1780 (-4 *3 (-38 (-570)))) (-4 *5 (-620 (-1186)))) + (-12 (-1741 (-4 *3 (-38 (-413 (-570))))) + (-1741 (-4 *3 (-38 (-570)))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 *3)) - (-12 (-1780 (-4 *3 (-551))) (-1780 (-4 *3 (-38 (-413 (-570))))) + (-12 (-1741 (-4 *3 (-551))) (-1741 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 *3)) - (-12 (-1780 (-4 *3 (-1001 (-570)))) (-4 *3 (-38 (-413 (-570)))) + (-12 (-1741 (-4 *3 (-1001 (-570)))) (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))))) ((*1 *1 *2) - (|partial| -2905 + (|partial| -2854 (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) - (-12 (-1780 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) + (-12 (-1741 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) @@ -238,17 +192,59 @@ (|partial| -12 (-5 *2 (-959 (-413 (-570)))) (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-989 *2)) (-4 *2 (-1058)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-950 (-227))) (-5 *1 (-1223)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1227)) (-4 *2 (-1058))))) -(((*1 *1 *1 *1) (-5 *1 (-868)))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-1035 (-849 (-570)))) - (-5 *3 (-1166 (-2 (|:| |k| (-570)) (|:| |c| *4)))) (-4 *4 (-1058)) - (-5 *1 (-601 *4))))) -(((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570)))))) +(((*1 *2 *3) + (-12 (-4 *4 (-38 (-413 (-570)))) + (-5 *2 (-2 (|:| -1722 (-1166 *4)) (|:| -1735 (-1166 *4)))) + (-5 *1 (-1172 *4)) (-5 *3 (-1166 *4))))) +(((*1 *2 *1) + (-12 (-4 *1 (-167 *3)) (-4 *3 (-174)) (-4 *3 (-551)) (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-424 *3)) (-4 *3 (-551)) (-4 *3 (-562)))) + ((*1 *2 *1) (-12 (-4 *1 (-551)) (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-4 *1 (-803 *3)) (-4 *3 (-174)) (-4 *3 (-551)) (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-839 *3)) (-4 *3 (-551)) (-4 *3 (-1109)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-849 *3)) (-4 *3 (-551)) (-4 *3 (-1109)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1006 *3)) (-4 *3 (-174)) (-4 *3 (-551)) (-5 *2 (-112)))) + ((*1 *2 *3) + (-12 (-5 *2 (-112)) (-5 *1 (-1017 *3)) (-4 *3 (-1047 (-413 (-570))))))) +(((*1 *1) + (-12 (-4 *1 (-410)) (-1741 (|has| *1 (-6 -4443))) + (-1741 (|has| *1 (-6 -4435))))) + ((*1 *2 *1) (-12 (-4 *1 (-431 *2)) (-4 *2 (-1109)) (-4 *2 (-856)))) + ((*1 *2 *1) (-12 (-4 *1 (-836 *2)) (-4 *2 (-856)))) + ((*1 *1) (-4 *1 (-850))) ((*1 *1 *1 *1) (-4 *1 (-856)))) +(((*1 *2 *1) + (|partial| -12 (-4 *1 (-167 *3)) (-4 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*1) (-12 (-5 *1 (-678 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-683 *2)) (-4 *2 (-856)))) @@ -257,115 +253,11 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-854) (-368))) (-5 *1 (-1070 *2 *3)) (-4 *3 (-1253 *2))))) -(((*1 *2) (-12 (-5 *2 (-880)) (-5 *1 (-1280)))) - ((*1 *2 *2) (-12 (-5 *2 (-880)) (-5 *1 (-1280))))) -(((*1 *2 *1) (-12 (-4 *1 (-1102 *2)) (-4 *2 (-1227))))) -(((*1 *2 *3 *3 *3 *4 *5 *5 *3) - (-12 (-5 *3 (-570)) (-5 *5 (-695 (-227))) (-5 *4 (-227)) - (-5 *2 (-1044)) (-5 *1 (-758))))) -(((*1 *1 *1) - (-12 (-4 *1 (-330 *2 *3)) (-4 *2 (-1058)) (-4 *3 (-798)) - (-4 *2 (-458)))) - ((*1 *1 *1) - (-12 (-4 *1 (-347 *2 *3 *4)) (-4 *2 (-1231)) (-4 *3 (-1253 *2)) - (-4 *4 (-1253 (-413 *3))))) - ((*1 *1 *1) (-12 (-4 *1 (-858 *2)) (-4 *2 (-1058)) (-4 *2 (-458)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-956 *3 *4 *2)) (-4 *3 (-1058)) (-4 *4 (-799)) - (-4 *2 (-856)) (-4 *3 (-458)))) - ((*1 *1 *1) - (-12 (-4 *1 (-956 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) - (-4 *4 (-856)) (-4 *2 (-458)))) - ((*1 *2 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(-650 (-868))) - (|:| |args| (-650 (-868))))) - (-5 *1 (-1186)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-650 (-650 (-868)))) (-5 *1 (-1186))))) -(((*1 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-567))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-695 *4)) (-5 *3 (-928)) (|has| *4 (-6 (-4454 "*"))) - (-4 *4 (-1058)) (-5 *1 (-1037 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-650 (-695 *4))) (-5 *3 (-928)) - (|has| *4 (-6 (-4454 "*"))) (-4 *4 (-1058)) (-5 *1 (-1037 *4))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-311) (-148))) (-4 *4 (-13 (-856) (-620 (-1186)))) - (-4 *5 (-799)) (-5 *1 (-931 *3 *4 *5 *2)) (-4 *2 (-956 *3 *5 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-512)) (-5 *1 (-531)))) - ((*1 *2 *1) (-12 (-5 *2 (-512)) (-5 *1 (-1160))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-650 *2)) (-4 *2 (-956 *4 *5 *6)) (-4 *4 (-368)) - (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) - (-5 *1 (-456 *4 *5 *6 *2)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-99 *6)) (-5 *5 (-1 *6 *6)) (-4 *6 (-368)) - (-5 *2 - (-2 (|:| R (-695 *6)) (|:| A (-695 *6)) (|:| |Ainv| (-695 *6)))) - (-5 *1 (-987 *6)) (-5 *3 (-695 *6))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-311)) (-5 *1 (-461 *3 *2)) (-4 *2 (-1253 *3)))) - ((*1 *2 *2 *3) - (-12 (-4 *3 (-311)) (-5 *1 (-466 *3 *2)) (-4 *2 (-1253 *3)))) - ((*1 *2 *2 *3) - (-12 (-4 *3 (-311)) (-14 *4 *3) (-14 *5 (-1 *3 *3 (-777))) - (-5 *1 (-545 *3 *2 *4 *5)) (-4 *2 (-1253 *3))))) -(((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1227)) (-4 *1 (-107 *3))))) -(((*1 *2 *3 *3 *4 *3) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) - (-5 *1 (-753))))) (((*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -2271 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -1861 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-3 (|:| |finite| "The range is finite") @@ -374,14 +266,239 @@ (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))) (-5 *1 (-194))))) +(((*1 *2 *1) + (-12 (-5 *2 (-650 (-1191))) (-5 *1 (-185 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(-5 *1 (-1123 *4 *5))))) +(((*1 *2 *1 *2) + (-12 (|has| *1 (-6 -4453)) (-4 *1 (-1019 *2)) (-4 *2 (-1227))))) +(((*1 *1 *2 *3 *1) (-12 (-5 *2 (-512)) (-5 *3 (-603)) (-5 *1 (-591))))) +(((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-1174 *3 *4)) (-14 *3 (-928)) + (-4 *4 (-1058))))) +(((*1 *2 *1) + (|partial| -12 (-4 *1 (-956 *3 *4 *2)) (-4 *3 (-1058)) (-4 *4 (-799)) + (-4 *2 (-856)))) + ((*1 *2 *3) + (|partial| -12 (-4 *4 (-799)) (-4 *5 (-1058)) (-4 *6 (-956 *5 *4 *2)) + (-4 *2 (-856)) (-5 *1 (-957 *4 *2 *5 *6 *3)) + (-4 *3 + (-13 (-368) + (-10 -8 (-15 -3838 ($ *6)) (-15 -4429 (*6 $)) + (-15 -1317 (*6 $))))))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-413 (-959 *4))) (-4 *4 (-562)) + (-5 *2 (-1186)) (-5 *1 (-1052 *4))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-650 (-48))) (-5 *2 (-424 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1253 (-48))))) @@ -3146,8 +3001,8 @@ (-12 (-4 *4 (-13 (-856) - (-10 -8 (-15 -1450 ((-1186) $)) - (-15 -2811 ((-3 $ "failed") (-1186)))))) + (-10 -8 (-15 -1436 ((-1186) $)) + (-15 -2750 ((-3 $ 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+ (-5 *1 (-454 *4 *5 *6 *7)) (-5 *3 (-650 *7)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-112)) (-4 *5 (-13 (-311) (-148))) (-4 *6 (-799)) + (-4 *7 (-856)) (-4 *8 (-956 *5 *6 *7)) (-5 *2 (-650 (-650 *8))) + (-5 *1 (-454 *5 *6 *7 *8)) (-5 *3 (-650 *8))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-997 *4 *5 *6 *7 *3)) (-4 *3 (-1080 *4 *5 *6 *7)))) + ((*1 *2 *3 *3) + (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-1116 *4 *5 *6 *7 *3)) (-4 *3 (-1080 *4 *5 *6 *7))))) (((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1227)) (-4 *1 (-152 *3)))) ((*1 *1 *2) (-12 - (-5 *2 (-650 (-2 (|:| -3227 (-777)) (|:| -2919 *4) (|:| |num| *4)))) + (-5 *2 (-650 (-2 (|:| -3229 (-777)) (|:| -2987 *4) (|:| |num| *4)))) (-4 *4 (-1253 *3)) (-4 *3 (-13 (-368) (-148))) (-5 *1 (-405 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2749 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2682 "void"))) (-5 *3 (-650 (-959 (-570)))) (-5 *4 (-112)) (-5 *1 (-443)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2749 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2682 "void"))) (-5 *3 (-650 (-1186))) (-5 *4 (-112)) (-5 *1 (-443)))) ((*1 *2 *1) (-12 (-5 *2 (-1166 *3)) (-5 *1 (-607 *3)) (-4 *3 (-1227)))) @@ -3297,24 +3185,24 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-719 *2 *3 *4)) (-4 *2 (-856)) (-4 *3 (-1109)) (-14 *4 - (-1 (-112) (-2 (|:| -2283 *2) (|:| -3227 *3)) - (-2 (|:| -2283 *2) (|:| -3227 *3)))))) + (-1 (-112) (-2 (|:| -2190 *2) (|:| -3229 *3)) + (-2 (|:| -2190 *2) (|:| -3229 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-512)) (-5 *3 (-1127)) (-5 *1 (-844)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-879 *2 *3)) (-4 *2 (-1227)) (-4 *3 (-1227)))) ((*1 *1 *2) - (-12 (-5 *2 (-650 (-2 (|:| -2106 (-1186)) (|:| -2361 *4)))) + (-12 (-5 *2 (-650 (-2 (|:| -2046 (-1186)) (|:| -2254 *4)))) (-4 *4 (-1109)) (-5 *1 (-896 *3 *4)) (-4 *3 (-1109)))) ((*1 *2 *3 *4) (-12 (-5 *4 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(-3 (|:| |fst| (-440)) (|:| -2749 "void"))) + (-14 *4 (-3 (|:| |fst| (-440)) (|:| -2682 "void"))) (-14 *5 (-650 (-1186))) (-14 *6 (-1190)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-334))) (-5 *1 (-404 *3 *4 *5 *6)) - (-14 *3 (-1186)) (-14 *4 (-3 (|:| |fst| (-440)) (|:| -2749 "void"))) + (-14 *3 (-1186)) (-14 *4 (-3 (|:| |fst| (-440)) (|:| -2682 "void"))) (-14 *5 (-650 (-1186))) (-14 *6 (-1190)))) ((*1 *1 *2) (-12 (-5 *2 (-334)) (-5 *1 (-404 *3 *4 *5 *6)) (-14 *3 (-1186)) - (-14 *4 (-3 (|:| |fst| (-440)) (|:| -2749 "void"))) + (-14 *4 (-3 (|:| |fst| (-440)) (|:| -2682 "void"))) (-14 *5 (-650 (-1186))) (-14 *6 (-1190)))) ((*1 *1 *2) (-12 (-5 *2 (-335 *4)) (-4 *4 (-13 (-856) (-21))) @@ -3574,14 +3476,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-440)) (-5 *1 (-443)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3274 (-650 (-334))))) + (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3280 (-650 (-334))))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-334)) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-334))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-1277 (-705))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3274 (-650 (-334))))) + (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3280 (-650 (-334))))) (-4 *1 (-447)))) ((*1 *1 *2) (-12 (-5 *2 (-334)) (-4 *1 (-447)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-334))) (-4 *1 (-447)))) @@ -3650,7 +3552,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-650 (-2 (|:| -1474 *3) (|:| -3418 *4)))) + (-12 (-5 *2 (-650 (-2 (|:| -1458 *3) (|:| -3436 *4)))) (-4 *3 (-1058)) (-4 *4 (-732)) (-5 *1 (-741 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-570)) (-4 *1 (-769)))) ((*1 *1 *2) @@ -3659,25 +3561,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -2271 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -1861 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-320 (-227))) - (|:| -2271 (-650 (-1103 (-849 (-227))))) + (|:| -1861 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-775)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-320 (-227))) - (|:| -2271 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) + (|:| -1861 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-775)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -2271 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -1861 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-775)))) ((*1 *2 *3) (-12 (-5 *2 (-780)) (-5 *1 (-779 *3)) (-4 *3 (-1227)))) @@ -3695,23 +3597,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-320 (-227))) (|:| -2478 (-650 (-227))) + (-2 (|:| |fn| (-320 (-227))) (|:| -3148 (-650 (-227))) (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) (|:| |ub| (-650 (-849 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-650 (-320 (-227)))) - (|:| -2478 (-650 (-227))))))) + (|:| -3148 (-650 (-227))))))) (-5 *1 (-847)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -2478 (-650 (-227))))) + (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -3148 (-650 (-227))))) (-5 *1 (-847)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-320 (-227))) (|:| -2478 (-650 (-227))) + (-2 (|:| |fn| (-320 (-227))) (|:| -3148 (-650 (-227))) (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) (|:| |ub| (-650 (-849 (-227)))))) (-5 *1 (-847)))) @@ -3812,47 +3714,40 @@ ((*1 *1 *2) (-12 (-5 *2 (-670 *3 *4)) (-4 *3 (-856)) (-4 *4 (-174)) (-5 *1 (-1297 *3 *4))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) - (-4 *4 (-856))))) -(((*1 *1 *1) (-5 *1 (-1072)))) -(((*1 *2 *3 *2) (-12 (-5 *3 (-777)) (-5 *1 (-862 *2)) (-4 *2 (-174)))) - ((*1 *2 *3 *3 *2) - (-12 (-5 *3 (-777)) (-5 *1 (-862 *2)) (-4 *2 (-174))))) -(((*1 *2 *3) - (-12 (|has| *6 (-6 -4453)) (-4 *4 (-368)) (-4 *5 (-378 *4)) - (-4 *6 (-378 *4)) (-5 *2 (-650 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(-5 *1 (-899 *3)) (-4 *3 (-1109))))) +(((*1 *1 *2) (-12 (-5 *1 (-697 *2)) (-4 *2 (-619 (-868)))))) +(((*1 *2 *1) (-12 (-4 *1 (-562)) (-5 *2 (-112))))) +(((*1 *1 *2) (-12 (-5 *2 (-650 (-868))) (-5 *1 (-868))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 (-650 *5) *6)) + (-4 *5 (-13 (-368) (-148) (-1047 (-413 (-570))))) (-4 *6 (-1253 *5)) + (-5 *2 (-650 (-2 (|:| -1864 *5) (|:| -4334 *3)))) + (-5 *1 (-815 *5 *6 *3 *7)) (-4 *3 (-662 *6)) + (-4 *7 (-662 (-413 *6)))))) (((*1 *2 *2) (-12 (-4 *3 (-1109)) (-5 *1 (-936 *3 *2)) (-4 *2 (-436 *3)))) ((*1 *2 *3) @@ -4851,35 +4664,83 @@ ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-1084 *3)) (-14 *3 *2))) ((*1 *2 *1) (-12 (-5 *2 (-512)) (-5 *1 (-1124)))) ((*1 *1 *1) (-5 *1 (-1186)))) -(((*1 *1 *1 *1) (-4 *1 (-551)))) -(((*1 *2 *1) (-12 (-4 *1 (-533)) (-5 *2 (-697 (-1232)))))) -(((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-591)) (-5 *3 (-603)) (-5 *4 (-295)) (-5 *1 (-284))))) (((*1 *2 *3) - (-12 (-5 *3 (-650 *2)) (-4 *2 (-436 *4)) (-5 *1 (-159 *4 *2)) - (-4 *4 (-562))))) 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(-645 (-570)))) + (-5 *2 (-2 (|:| -4007 *3) (|:| |coeff| *3))) + (-5 *1 (-566 *6 *3 *7)) (-4 *7 (-1109))))) +(((*1 *1 *2) (-12 (-5 *2 (-158)) (-5 *1 (-880))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-115))))) (((*1 *1 *1) (-12 (-5 *1 (-683 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-825 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-900 *2)) (-4 *2 (-856)))) @@ -5010,7 +4799,18 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-777)) (-4 *1 (-1265 *3)) (-4 *3 (-1227)))) ((*1 *1 *1) (-12 (-4 *1 (-1265 *2)) (-4 *2 (-1227))))) -(((*1 *1 *1) (-12 (-4 *1 (-680 *2)) (-4 *2 (-1227))))) +(((*1 *1 *2) + (-12 (-5 *2 (-650 *1)) (-4 *1 (-1143 *3)) (-4 *3 (-1058)))) + ((*1 *2 *2 *1) + (|partial| -12 (-5 *2 (-413 *1)) (-4 *1 (-1253 *3)) (-4 *3 (-1058)) + (-4 *3 (-562)))) + ((*1 *1 *1 *1) + (|partial| -12 (-4 *1 (-1253 *2)) (-4 *2 (-1058)) (-4 *2 (-562))))) +(((*1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-1196))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1 *5 (-650 *5))) (-4 *5 (-1268 *4)) + (-4 *4 (-38 (-413 (-570)))) + (-5 *2 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(-1246 *2 *4 *3)) + (-4 *3 (-1253 *4))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) + (-4 *3 (-1074 *5 *6 *7)) + (-5 *2 (-650 (-2 (|:| |val| *3) (|:| -3730 *4)))) + (-5 *1 (-1117 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-650 (-849 (-227)))) (-5 *4 (-227)) (-5 *2 (-650 *4)) + (-5 *1 (-270))))) (((*1 *2 *3 *2) - (-12 (-5 *2 (-928)) (-5 *3 (-650 (-266))) (-5 *1 (-264)))) - ((*1 *1 *2) (-12 (-5 *2 (-928)) (-5 *1 (-266))))) -(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-933))))) -(((*1 *2 *1) - (-12 (-4 *1 (-256 *3 *4 *2 *5)) (-4 *3 (-1058)) (-4 *4 (-856)) - (-4 *5 (-799)) (-4 *2 (-269 *4))))) + (-12 (-5 *2 (-1166 *3)) (-4 *3 (-368)) (-4 *3 (-1058)) + (-5 *1 (-1170 *3))))) +(((*1 *2) + (-12 (-4 *1 (-347 *3 *4 *5)) (-4 *3 (-1231)) (-4 *4 (-1253 *3)) + (-4 *5 (-1253 (-413 *4))) (-5 *2 (-112))))) (((*1 *1 *2) (-12 (-5 *2 (-650 (-570))) (-5 *1 (-50 *3 *4)) (-4 *3 (-1058)) (-14 *4 (-650 (-1186))))) @@ -6498,12 +6365,6 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-777)) (-5 *1 (-1297 *3 *4)) (-4 *4 (-723 (-413 (-570)))) (-4 *3 (-856)) (-4 *4 (-174))))) -(((*1 *2 *1 *1) - (|partial| -12 (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-1058)) - (-4 *4 (-799)) (-4 *5 (-856)) (-5 *2 (-112))))) -(((*1 *2 *3) - (-12 (-5 *3 (-570)) (-4 *4 (-1253 (-413 *3))) (-5 *2 (-928)) - (-5 *1 (-920 *4 *5)) (-4 *5 (-1253 (-413 *4)))))) (((*1 *2 *3) (-12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) (-12 (-5 *2 (-959 (-384))) (-5 *1 (-344 *3 *4 *5)) @@ -6559,11 +6420,11 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -2271 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -1861 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-320 (-227))) - (|:| -2271 (-650 (-1103 (-849 (-227))))) + (|:| -1861 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-775)))) ((*1 *2 *1) @@ -6579,13 +6440,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-320 (-227))) (|:| -2478 (-650 (-227))) + (-2 (|:| |fn| (-320 (-227))) (|:| -3148 (-650 (-227))) (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) (|:| |ub| (-650 (-849 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-650 (-320 (-227)))) - (|:| -2478 (-650 (-227))))))) + (|:| -3148 (-650 (-227))))))) (-5 *1 (-847)))) ((*1 *2 *1) (-12 @@ -6604,26 +6465,26 @@ (-4 *4 (-799)) (-4 *5 (-856)) (-4 *1 (-985 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1047 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) - (-2905 + (-2854 (-12 (-5 *2 (-959 *3)) - (-12 (-1780 (-4 *3 (-38 (-413 (-570))))) - (-1780 (-4 *3 (-38 (-570)))) (-4 *5 (-620 (-1186)))) + (-12 (-1741 (-4 *3 (-38 (-413 (-570))))) + (-1741 (-4 *3 (-38 (-570)))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 *3)) - (-12 (-1780 (-4 *3 (-551))) (-1780 (-4 *3 (-38 (-413 (-570))))) + (-12 (-1741 (-4 *3 (-551))) (-1741 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 *3)) - (-12 (-1780 (-4 *3 (-1001 (-570)))) (-4 *3 (-38 (-413 (-570)))) + (-12 (-1741 (-4 *3 (-1001 (-570)))) (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))))) ((*1 *1 *2) - (-2905 + (-2854 (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) - (-12 (-1780 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) + (-12 (-1741 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) @@ -6633,47 +6494,73 @@ (-12 (-5 *2 (-959 (-413 (-570)))) (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))))) -(((*1 *2 *3 *3 *3 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) -(((*1 *2 *2) (-12 (-5 *2 (-320 (-227))) (-5 *1 (-212))))) -(((*1 *2 *2) - (-12 (-4 *3 (-1047 (-570))) (-4 *3 (-562)) (-5 *1 (-32 *3 *2)) - (-4 *2 (-436 *3)))) - ((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-1182 *4)) (-5 *1 (-166 *3 *4)) - (-4 *3 (-167 *4)))) - ((*1 *1 *1) (-12 (-4 *1 (-1058)) (-4 *1 (-306)))) - ((*1 *2) (-12 (-4 *1 (-333 *3)) (-4 *3 (-368)) (-5 *2 (-1182 *3)))) - ((*1 *2) (-12 (-4 *1 (-730 *3 *2)) (-4 *3 (-174)) (-4 *2 (-1253 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1077 *3 *2)) (-4 *3 (-13 (-854) (-368))) - (-4 *2 (-1253 *3))))) -(((*1 *2 *1) - (-12 (-5 *2 (-697 (-879 (-973 *3) (-973 *3)))) (-5 *1 (-973 *3)) +(((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-1186)) (-5 *4 (-959 (-570))) (-5 *2 (-334)) + (-5 *1 (-336)))) + ((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-1186)) (-5 *4 (-1101 (-959 (-570)))) (-5 *2 (-334)) + (-5 *1 (-336)))) + ((*1 *1 *2 *2 *2) + (-12 (-5 *2 (-777)) (-5 *1 (-681 *3)) (-4 *3 (-1058)) (-4 *3 (-1109))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-384) (-384))) (-5 *4 (-384)) +(((*1 *2 *1) (-12 (-5 *2 (-650 (-1226))) (-5 *1 (-530))))) +(((*1 *2 *3) (-12 (-5 *3 (-227)) (-5 *2 (-320 (-384))) (-5 *1 (-309))))) +(((*1 *2) (-12 (-5 *2 (-650 (-1186))) (-5 *1 (-105))))) +(((*1 *2 *1) + (-12 (-4 *1 (-701 *3)) (-4 *3 (-1109)) + (-5 *2 (-650 (-2 (|:| -2254 *3) (|:| -3622 (-777)))))))) +(((*1 *2 *3 *3) + (-12 (-4 *2 (-562)) (-5 *1 (-978 *2 *3)) (-4 *3 (-1253 *2))))) +(((*1 *2 *3 *4 *5 *3) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 + (-1 (-2 (|:| |ans| *6) (|:| -4415 *6) (|:| |sol?| (-112))) (-570) + *6)) + (-4 *6 (-368)) (-4 *7 (-1253 *6)) (-5 *2 - (-2 (|:| -2329 *4) (|:| -3670 *4) (|:| |totalpts| (-570)) - (|:| |success| (-112)))) - (-5 *1 (-795)) (-5 *5 (-570))))) -(((*1 *1 *1) (-4 *1 (-635))) - ((*1 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-636 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1011) (-1212)))))) + (-3 (-2 (|:| |answer| (-413 *7)) (|:| |a0| *6)) + (-2 (|:| -4007 (-413 *7)) (|:| |coeff| (-413 *7))) "failed")) + (-5 *1 (-580 *6 *7)) (-5 *3 (-413 *7))))) +(((*1 *2 *3 *4 *4 *5) + (-12 (-5 *3 (-1 (-171 (-227)) (-171 (-227)))) (-5 *4 (-1103 (-227))) + (-5 *5 (-112)) (-5 *2 (-1279)) (-5 *1 (-260))))) +(((*1 *2 *2) + (-12 (-5 *2 (-650 *6)) (-4 *6 (-1074 *3 *4 *5)) (-4 *3 (-562)) + (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-986 *3 *4 *5 *6))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-650 + (-2 (|:| -1629 (-777)) + (|:| |eqns| + (-650 + (-2 (|:| |det| *7) (|:| |rows| (-650 (-570))) + (|:| |cols| (-650 (-570)))))) + (|:| |fgb| (-650 *7))))) + (-4 *7 (-956 *4 *6 *5)) (-4 *4 (-13 (-311) (-148))) + (-4 *5 (-13 (-856) (-620 (-1186)))) (-4 *6 (-799)) (-5 *2 (-777)) + (-5 *1 (-931 *4 *5 *6 *7))))) +(((*1 *2 *3) + (-12 (-4 *4 (-1058)) (-5 *2 (-570)) (-5 *1 (-449 *4 *3 *5)) + (-4 *3 (-1253 *4)) + (-4 *5 (-13 (-410) (-1047 *4) (-368) (-1212) (-288)))))) +(((*1 *2 *3) + (-12 (-4 *4 (-562)) (-5 *2 (-112)) (-5 *1 (-279 *4 *3)) + (-4 *3 (-13 (-436 *4) (-1011)))))) +(((*1 *1 *2 *1) (-12 (-5 *2 (-109)) (-5 *1 (-1094))))) (((*1 *2 *1) - (-12 (-5 *2 (-1166 (-2 (|:| |k| (-570)) (|:| |c| *3)))) - (-5 *1 (-601 *3)) (-4 *3 (-1058))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) + (-12 (-5 *2 (-1262 *3 *4 *5)) (-5 *1 (-323 *3 *4 *5)) (-4 *3 (-368)) + (-14 *4 (-1186)) (-14 *5 *3))) + ((*1 *2 *1) (-12 (-4 *1 (-410)) (-5 *2 (-570)))) + ((*1 *2 *1) (-12 (-5 *2 (-570)) (-5 *1 (-424 *3)) (-4 *3 (-562)))) + ((*1 *2 *1) (-12 (-5 *2 (-570)) (-5 *1 (-705)))) + ((*1 *2 *1) + (-12 (-4 *2 (-1109)) (-5 *1 (-719 *3 *2 *4)) (-4 *3 (-856)) + (-14 *4 + (-1 (-112) (-2 (|:| -2190 *3) (|:| -3229 *2)) + (-2 (|:| -2190 *3) (|:| -3229 *2))))))) (((*1 *2 *3) - (-12 (-5 *3 (-1 *5 *5)) (-4 *1 (-347 *4 *5 *6)) (-4 *4 (-1231)) - (-4 *5 (-1253 *4)) (-4 *6 (-1253 (-413 *5))) - (-5 *2 (-2 (|:| |num| (-695 *5)) (|:| |den| *5)))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) - (-4 *4 (-856)) (-4 *2 (-562))))) + (-12 (-5 *3 (-650 (-227))) (-5 *2 (-1277 (-705))) (-5 *1 (-309))))) (((*1 *2 *3 *2) (-12 (-5 *2 (-650 (-384))) (-5 *3 (-650 (-266))) (-5 *1 (-264)))) ((*1 *2 *1 *2) (-12 (-5 *2 (-650 (-384))) (-5 *1 (-474)))) @@ -6682,28 +6569,41 @@ (-12 (-5 *3 (-928)) (-5 *4 (-880)) (-5 *2 (-1282)) (-5 *1 (-1278)))) ((*1 *2 *1 *3 *4) (-12 (-5 *3 (-928)) (-5 *4 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1278))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *2 (-695 *3)) (-4 *3 (-1058)) (-5 *1 (-696 *3))))) -(((*1 *1 *2 *3 *4) - (-12 (-5 *3 (-570)) (-5 *4 (-3 "nil" "sqfr" "irred" "prime")) - (-5 *1 (-424 *2)) (-4 *2 (-562))))) -(((*1 *1) (-12 (-4 *1 (-333 *2)) (-4 *2 (-373)) (-4 *2 (-368))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-311) (-148))) (-4 *5 (-13 (-856) (-620 (-1186)))) - (-4 *6 (-799)) (-5 *2 (-650 *3)) (-5 *1 (-931 *4 *5 *6 *3)) - (-4 *3 (-956 *4 *6 *5))))) -(((*1 *2 *3) (-12 (-5 *3 (-227)) (-5 *2 (-320 (-384))) (-5 *1 (-309))))) +(((*1 *1) (-5 *1 (-584)))) (((*1 *2 *1) - (-12 (-5 *2 (-1262 *3 *4 *5)) (-5 *1 (-323 *3 *4 *5)) (-4 *3 (-368)) - (-14 *4 (-1186)) (-14 *5 *3))) - ((*1 *2 *1) (-12 (-4 *1 (-410)) (-5 *2 (-570)))) - ((*1 *2 *1) (-12 (-5 *2 (-570)) (-5 *1 (-424 *3)) (-4 *3 (-562)))) - ((*1 *2 *1) (-12 (-5 *2 (-570)) (-5 *1 (-705)))) + (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1227)) (-4 *4 (-378 *3)) + (-4 *5 (-378 *3)) (-5 *2 (-650 *3)))) ((*1 *2 *1) - (-12 (-4 *2 (-1109)) (-5 *1 (-719 *3 *2 *4)) (-4 *3 (-856)) - (-14 *4 - (-1 (-112) (-2 (|:| -2283 *3) (|:| -3227 *2)) - (-2 (|:| -2283 *3) (|:| -3227 *2))))))) + (-12 (|has| *1 (-6 -4452)) (-4 *1 (-495 *3)) (-4 *3 (-1227)) + (-5 *2 (-650 *3)))) + ((*1 *2 *1) (-12 (-5 *2 (-650 (-928))) (-5 *1 (-980))))) +(((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-688 *3)) (-4 *3 (-1109))))) +(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) +(((*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1168)) + (-4 *4 (-13 (-458) (-1047 (-570)) (-645 (-570)))) (-5 *2 (-112)) + (-5 *1 (-226 *4 *5)) (-4 *5 (-13 (-1212) (-29 *4)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-695 (-413 (-570)))) (-5 *2 (-650 *4)) (-5 *1 (-785 *4)) + (-4 *4 (-13 (-368) (-854)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-372 *3)) (-4 *3 (-174)) (-4 *3 (-562)) + (-5 *2 (-1182 *3))))) +(((*1 *1 *2 *1) (-12 (-5 *2 (-570)) (-5 *1 (-118 *3)) (-14 *3 *2))) + ((*1 *1 *1) (-12 (-5 *1 (-118 *2)) (-14 *2 (-570)))) + ((*1 *1 *2 *1) (-12 (-5 *2 (-570)) (-5 *1 (-877 *3)) (-14 *3 *2))) + ((*1 *1 *1) (-12 (-5 *1 (-877 *2)) (-14 *2 (-570)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-570)) (-14 *3 *2) (-5 *1 (-878 *3 *4)) + (-4 *4 (-875 *3)))) + ((*1 *1 *1) + (-12 (-14 *2 (-570)) (-5 *1 (-878 *2 *3)) (-4 *3 (-875 *2)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-570)) (-4 *1 (-1239 *3 *4)) (-4 *3 (-1058)) + (-4 *4 (-1268 *3)))) + ((*1 *1 *1) + (-12 (-4 *1 (-1239 *2 *3)) (-4 *2 (-1058)) (-4 *3 (-1268 *2))))) (((*1 *1) (-4 *1 (-34))) ((*1 *1) (-5 *1 (-295))) ((*1 *1) (-5 *1 (-868))) ((*1 *1) @@ -6714,26 +6614,26 @@ (-12 (-5 *1 (-1149 *2 *3)) (-4 *2 (-13 (-1109) (-34))) (-4 *3 (-13 (-1109) (-34))))) ((*1 *1) (-5 *1 (-1189))) ((*1 *1) (-5 *1 (-1190)))) -(((*1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-243))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) (((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-650 (-1182 *5))) (-5 *3 (-1182 *5)) - (-4 *5 (-167 *4)) (-4 *4 (-551)) (-5 *1 (-150 *4 *5)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-650 *3)) (-4 *3 (-1253 *5)) - (-4 *5 (-1253 *4)) (-4 *4 (-354)) (-5 *1 (-363 *4 *5 *3)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-650 (-1182 (-570)))) (-5 *3 (-1182 (-570))) - (-5 *1 (-578)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-650 (-1182 *1))) (-5 *3 (-1182 *1)) - (-4 *1 (-916))))) + (-12 (-5 *2 (-1277 *4)) (-5 *3 (-570)) (-4 *4 (-354)) + (-5 *1 (-534 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-424 *5)) (-4 *5 (-562)) + (-5 *2 + (-2 (|:| -3229 (-777)) (|:| -1458 *5) (|:| |radicand| (-650 *5)))) + (-5 *1 (-324 *5)) (-5 *4 (-777)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-1011)) (-5 *2 (-570))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1220 *3 *4 *5 *6)) (-4 *3 (-562)) (-4 *4 (-799)) + (-4 *5 (-856)) (-4 *6 (-1074 *3 *4 *5)) (-5 *2 (-650 *6))))) +(((*1 *2) + (-12 (-5 *2 (-112)) (-5 *1 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*5 (-650 *2)) @@ -11547,40 +12264,40 @@ (-12 (-5 *3 (-695 *5)) (-4 *5 (-368)) (-5 *2 (-2 (|:| |particular| (-3 (-1277 *5) "failed")) - (|:| -2249 (-650 (-1277 *5))))) + (|:| -2856 (-650 (-1277 *5))))) (-5 *1 (-673 *5)) (-5 *4 (-1277 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-650 (-650 *5))) (-4 *5 (-368)) (-5 *2 (-2 (|:| |particular| (-3 (-1277 *5) "failed")) - (|:| -2249 (-650 (-1277 *5))))) + (|:| -2856 (-650 (-1277 *5))))) (-5 *1 (-673 *5)) (-5 *4 (-1277 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-695 *5)) (-4 *5 (-368)) (-5 *2 (-650 (-2 (|:| |particular| (-3 (-1277 *5) "failed")) - (|:| -2249 (-650 (-1277 *5)))))) + (|:| -2856 (-650 (-1277 *5)))))) (-5 *1 (-673 *5)) (-5 *4 (-650 (-1277 *5))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-650 (-650 *5))) (-4 *5 (-368)) (-5 *2 (-650 (-2 (|:| |particular| (-3 (-1277 *5) "failed")) - (|:| -2249 (-650 (-1277 *5)))))) + (|:| -2856 (-650 (-1277 *5)))))) (-5 *1 (-673 *5)) (-5 *4 (-650 (-1277 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-368)) (-4 *6 (-13 (-378 *5) (-10 -7 (-6 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(-1058)))) ((*1 *2 *1) (-12 (-4 *2 (-1058)) (-5 *1 (-50 *2 *3)) (-14 *3 (-650 (-1186))))) @@ -13234,10 +13183,10 @@ ((*1 *2 *1) (-12 (-4 *1 (-387 *2 *3)) (-4 *3 (-1109)) (-4 *2 (-1058)))) ((*1 *2 *1) - (-12 (-14 *3 (-650 (-1186))) (-4 *5 (-240 (-2589 *3) (-777))) + (-12 (-14 *3 (-650 (-1186))) (-4 *5 (-240 (-2473 *3) (-777))) (-14 *6 - (-1 (-112) (-2 (|:| -2283 *4) (|:| -3227 *5)) - (-2 (|:| -2283 *4) (|:| -3227 *5)))) + (-1 (-112) (-2 (|:| -2190 *4) (|:| -3229 *5)) + (-2 (|:| -2190 *4) (|:| -3229 *5)))) (-4 *2 (-174)) (-5 *1 (-467 *3 *2 *4 *5 *6 *7)) (-4 *4 (-856)) (-4 *7 (-956 *2 *5 (-870 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-515 *2 *3)) (-4 *3 (-856)) (-4 *2 (-1109)))) @@ -13255,53 +13204,99 @@ (-12 (-4 *1 (-1074 *3 *4 *2)) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *2 (-856))))) (((*1 *1) (-4 *1 (-976)))) -(((*1 *2 *3 *3 *4) - (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) - (-4 *3 (-1074 *5 *6 *7)) - (-5 *2 (-650 (-2 (|:| |val| (-650 *3)) (|:| -3702 *4)))) - (-5 *1 (-1117 *5 *6 *7 *3 *4)) 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(|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1861 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))))) + (-5 *1 (-565)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-777)) (-4 *1 (-701 *2)) (-4 *2 (-1109)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -2046 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1277 (-320 (-227)))) (|:| |yinit| (-650 (-227))) + (|:| |intvals| (-650 (-227))) (|:| |g| (-320 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (|:| -2254 + (-2 (|:| |stiffness| (-384)) (|:| |stability| (-384)) + (|:| |expense| (-384)) (|:| |accuracy| (-384)) + (|:| |intermediateResults| (-384)))))) + (-5 *1 (-809)))) + ((*1 *2 *3 *4) + (-12 (-5 *2 (-1282)) (-5 *1 (-1204 *3 *4)) (-4 *3 (-1109)) + (-4 *4 (-1109))))) 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(-115)))))) (((*1 *1 *2 *3) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1058)) (-4 *3 (-798)))) ((*1 *1 *2 *3) @@ -14498,10 +14892,10 @@ (-4 *2 (-368)) (-14 *5 (-1002 *4 *2)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-719 *5 *6 *7)) (-4 *5 (-856)) - (-4 *6 (-240 (-2589 *4) (-777))) + (-4 *6 (-240 (-2473 *4) (-777))) (-14 *7 - (-1 (-112) (-2 (|:| -2283 *5) (|:| -3227 *6)) - (-2 (|:| -2283 *5) (|:| -3227 *6)))) + (-1 (-112) (-2 (|:| -2190 *5) (|:| -3229 *6)) + (-2 (|:| -2190 *5) (|:| -3229 *6)))) (-14 *4 (-650 (-1186))) (-4 *2 (-174)) (-5 *1 (-467 *4 *2 *5 *6 *7 *8)) (-4 *8 (-956 *2 *6 (-870 *4))))) ((*1 *1 *2 *3) @@ -14531,21 +14925,204 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-982 *4 *3 *2)) (-4 *4 (-1058)) (-4 *3 (-798)) (-4 *2 (-856))))) +(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) +(((*1 *2 *2) + (-12 (-4 *3 (-368)) (-4 *4 (-378 *3)) (-4 *5 (-378 *3)) + (-5 *1 (-527 *3 *4 *5 *2)) (-4 *2 (-693 *3 *4 *5))))) +(((*1 *2 *3) + (-12 (-5 *3 (-570)) (|has| *1 (-6 -4443)) (-4 *1 (-410)) + (-5 *2 (-928))))) (((*1 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(-1186))) (-4 *4 (-799)) (-4 *5 (-856)))) ((*1 *1 *2) - (-2905 + (-2854 (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) - (-12 (-1780 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) + (-12 (-1741 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) @@ -16430,12 +16417,12 @@ (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -3702 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -3730 *8))) (-4 *7 (-1074 *4 *5 *6)) (-4 *8 (-1080 *4 *5 *6 *7)) (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-1168)) (-5 *1 (-1078 *4 *5 *6 *7 *8)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -3702 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -3730 *8))) (-4 *7 (-1074 *4 *5 *6)) (-4 *8 (-1118 *4 *5 *6 *7)) (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-1168)) (-5 *1 (-1154 *4 *5 *6 *7 *8)))) @@ -16467,136 +16454,214 @@ (-4 *4 (-13 (-854) (-311) (-148) (-1031))) (-14 *6 (-650 (-1186))) (-5 *2 (-650 (-786 *4 (-870 *6)))) (-5 *1 (-1304 *4 *5 *6)) (-14 *5 (-650 (-1186)))))) -(((*1 *2 *2) (-12 (-5 *2 (-384)) (-5 *1 (-1279)))) - ((*1 *2) (-12 (-5 *2 (-384)) (-5 *1 (-1279))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1298 *3 *4)) (-4 *3 (-856)) (-4 *4 (-1058)) - (-5 *2 (-825 *3)))) - ((*1 *2 *1) - (-12 (-4 *2 (-852)) (-5 *1 (-1300 *3 *2)) (-4 *3 (-1058))))) -(((*1 *1 *2) (-12 (-5 *1 (-697 *2)) (-4 *2 (-619 (-868)))))) -(((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-371 *3 *4)) - (-4 *3 (-372 *4)))) - ((*1 *2) (-12 (-4 *1 (-372 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) +(((*1 *2 *3) + (-12 (-5 *2 (-112)) (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570)))))) (((*1 *2 *1) - (-12 (-5 *2 (-650 (-1191))) (-5 *1 (-185 *3)) (-4 *3 (-187))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-950 (-227))) (-5 *2 (-1282)) (-5 *1 (-474))))) + (-12 (-4 *1 (-985 *3 *4 *5 *6)) (-4 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