diff options
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 640 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1396 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1313 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8950 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 31052 |
5 files changed, 21679 insertions, 21672 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 0506e175..20f43bb5 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2264570 . 3467417890) +(2264863 . 3474699321) (-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 -3888) +(-32 R -1676) ((|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 -1040) (QUOTE (-567))))) @@ -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 -3888 UP UPUP -3054) +(-40 -1676 UP UPUP -4190) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4415 |has| (-410 |#2|) (-365)) (-4420 |has| (-410 |#2|) (-365)) (-4414 |has| (-410 |#2|) (-365)) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| (-410 |#2|) (QUOTE (-145))) (|HasCategory| (-410 |#2|) (QUOTE (-147))) (|HasCategory| (-410 |#2|) (QUOTE (-351))) (-2811 (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-370))) (-2811 (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (-2811 (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-410 |#2|) (QUOTE (-351))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -640) (QUOTE (-567)))) (-2811 (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365))))) -(-41 R -3888) +((|HasCategory| (-410 |#2|) (QUOTE (-145))) (|HasCategory| (-410 |#2|) (QUOTE (-147))) (|HasCategory| (-410 |#2|) (QUOTE (-351))) (-2836 (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-370))) (-2836 (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (-2836 (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-410 |#2|) (QUOTE (-351))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -640) (QUOTE (-567)))) (-2836 (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365))))) +(-41 R -1676) ((|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 (-455))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -433) (|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."))) ((-4422 . T) (-4423 . T)) -((-2811 (-12 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1809) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4236) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1809) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4236) (|devaluate| |#2|))))))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1809) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4236) (|devaluate| |#2|))))))) +((-2836 (-12 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2025) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2265) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2025) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2265) (|devaluate| |#2|))))))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2025) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2265) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3888) +(-54 |Base| R -1676) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|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}."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) -(-61 -2007) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +(-61 -1646) ((|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 -2007) +(-62 -1646) ((|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 -2007) +(-63 -1646) ((|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 -2007) +(-64 -1646) ((|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 -2007) +(-65 -1646) ((|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 -2007) +(-66 -1646) ((|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 -2007) +(-67 -1646) ((|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 -2007) +(-68 -1646) ((|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 -2007) +(-69 -1646) ((|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 -2007) +(-70 -1646) ((|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 -2007) +(-71 -1646) ((|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 -2007) +(-72 -1646) ((|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 -2007) +(-73 -1646) ((|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 -2007) +(-74 -1646) ((|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 -2007) +(-77 -1646) ((|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 -2007) +(-78 -1646) ((|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 -2007) +(-79 -1646) ((|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 -2007) +(-80 -1646) ((|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 -2007) +(-81 -1646) ((|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 -2007) +(-82 -1646) ((|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 -2007) +(-83 -1646) ((|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 -2007) +(-84 -1646) ((|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 -2007) +(-85 -1646) ((|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 -2007) +(-86 -1646) ((|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 -2007) +(-87 -1646) ((|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 -2007) +(-88 -1646) ((|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 -2007) +(-89 -1646) ((|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}."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-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}."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-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."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| (-567) (QUOTE (-911))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1024))) (|HasCategory| (-567) (QUOTE (-821))) (-2811 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1154))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1179)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (|HasCategory| (-567) (QUOTE (-145))))) +((|HasCategory| (-567) (QUOTE (-911))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1024))) (|HasCategory| (-567) (QUOTE (-821))) (-2836 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1154))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1179)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (|HasCategory| (-567) (QUOTE (-145))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -388,7 +388,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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 -(-115 -3888 UP) +(-115 -1676 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 @@ -399,7 +399,7 @@ NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-911))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-116 |#1|) (QUOTE (-1024))) (|HasCategory| (-116 |#1|) (QUOTE (-821))) (-2811 (|HasCategory| (-116 |#1|) (QUOTE (-821))) (|HasCategory| (-116 |#1|) (QUOTE (-851)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-116 |#1|) (QUOTE (-1154))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -517) (QUOTE (-1179)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-308))) (|HasCategory| (-116 |#1|) (QUOTE (-548))) (|HasCategory| (-116 |#1|) (QUOTE (-851))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-911)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((|HasCategory| (-116 |#1|) (QUOTE (-911))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-116 |#1|) (QUOTE (-1024))) (|HasCategory| (-116 |#1|) (QUOTE (-821))) (-2836 (|HasCategory| (-116 |#1|) (QUOTE (-821))) (|HasCategory| (-116 |#1|) (QUOTE (-851)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-116 |#1|) (QUOTE (-1154))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -517) (QUOTE (-1179)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-308))) (|HasCategory| (-116 |#1|) (QUOTE (-548))) (|HasCategory| (-116 |#1|) (QUOTE (-851))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-911)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -415,7 +415,7 @@ NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL @@ -435,15 +435,15 @@ NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-128) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|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."))) ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| (-129) (QUOTE (-851))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1102))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) (-2811 (-12 (|HasCategory| (-129) (QUOTE (-1102))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-129) (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| (-129) (QUOTE (-851))) (|HasCategory| (-129) (QUOTE (-1102)))) (|HasCategory| (-129) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-129) (QUOTE (-1102))) (|HasCategory| (-129) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-129) (QUOTE (-1102))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) +((-2836 (-12 (|HasCategory| (-129) (QUOTE (-851))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1102))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) (-2836 (-12 (|HasCategory| (-129) (QUOTE (-1102))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-129) (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| (-129) (QUOTE (-851))) (|HasCategory| (-129) (QUOTE (-1102)))) (|HasCategory| (-129) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-129) (QUOTE (-1102))) (|HasCategory| (-129) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-129) (QUOTE (-1102))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) (-129) ((|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 @@ -468,11 +468,11 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4424 "*") . T)) NIL -(-135 |minix| -2622 S T$) +(-135 |minix| -2424 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -2622 R) +(-136 |minix| -2424 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -495,7 +495,7 @@ NIL (-141) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4422 . T) (-4412 . T) (-4423 . T)) -((-2811 (-12 (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) +((-2836 (-12 (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-142 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{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 @@ -520,7 +520,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4419 . T)) NIL -(-148 -3888 UP UPUP) +(-148 -1676 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 @@ -560,7 +560,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-158 R -3888) +(-158 R -1676) ((|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 @@ -594,7 +594,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-911))) (|HasCategory| |#2| (QUOTE (-548))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-1204))) (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (QUOTE (-1024))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4418)) (|HasAttribute| |#2| (QUOTE -4421)) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-559)))) (-166 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4415 -2811 (|has| |#1| (-559)) (-12 (|has| |#1| (-308)) (|has| |#1| (-911)))) (-4420 |has| |#1| (-365)) (-4414 |has| |#1| (-365)) (-4418 |has| |#1| (-6 -4418)) (-4421 |has| |#1| (-6 -4421)) (-3065 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) +((-4415 -2836 (|has| |#1| (-559)) (-12 (|has| |#1| (-308)) (|has| |#1| (-911)))) (-4420 |has| |#1| (-365)) (-4414 |has| |#1| (-365)) (-4418 |has| |#1| (-6 -4418)) (-4421 |has| |#1| (-6 -4421)) (-3100 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL (-167 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -606,8 +606,8 @@ NIL NIL (-169 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4415 -2811 (|has| |#1| (-559)) (-12 (|has| |#1| (-308)) (|has| |#1| (-911)))) (-4420 |has| |#1| (-365)) (-4414 |has| |#1| (-365)) (-4418 |has| |#1| (-6 -4418)) (-4421 |has| |#1| (-6 -4421)) (-3065 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . 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T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2836 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2836 (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1179)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| 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(|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-911)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-911))))) (-2836 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-1204)))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-559)))) (-2836 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1179)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-829))) (|HasCategory| |#1| (QUOTE (-1062))) (-12 (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (QUOTE (-1204)))) (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-911))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-365)))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasAttribute| |#1| (QUOTE -4418)) (|HasAttribute| |#1| (QUOTE -4421)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179))))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-351))))) (-170 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -680,7 +680,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -3888) +(-188 R -1676) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-215 -3888 UP UPUP R) +(-215 -1676 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-216 -3888 FP) +(-216 -1676 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-217) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| (-567) (QUOTE (-911))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1024))) (|HasCategory| (-567) (QUOTE (-821))) (-2811 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1154))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1179)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (|HasCategory| (-567) (QUOTE (-145))))) +((|HasCategory| (-567) (QUOTE (-911))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1024))) (|HasCategory| (-567) (QUOTE (-821))) (-2836 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1154))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1179)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (|HasCategory| (-567) (QUOTE (-145))))) (-218) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -3888) +(-219 R -1676) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -819,18 +819,18 @@ NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-223 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4419 . T)) NIL -(-224 R -3888) +(-224 R -1676) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-225) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3058 . T) (-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) +((-3092 . T) (-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL (-226) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{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)}.}"))) @@ -839,7 +839,7 @@ NIL (-227 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-559))) (|HasAttribute| |#1| (QUOTE (-4424 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-559))) (|HasAttribute| |#1| (QUOTE (-4424 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-228 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL @@ -876,22 +876,22 @@ 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 -(-237 S -2622 R) +(-237 S -2424 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 (-365))) (|HasCategory| |#3| (QUOTE (-794))) (|HasCategory| |#3| (QUOTE (-849))) (|HasAttribute| |#3| (QUOTE -4419)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (QUOTE (-727))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (QUOTE (-1102)))) -(-238 -2622 R) +(-238 -2424 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"))) ((-4416 |has| |#2| (-1051)) (-4417 |has| |#2| (-1051)) (-4419 |has| |#2| (-6 -4419)) ((-4424 "*") |has| |#2| (-172)) (-4422 . T)) NIL -(-239 -2622 A B) +(-239 -2424 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 -(-240 -2622 R) +(-240 -2424 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."))) ((-4416 |has| |#2| (-1051)) (-4417 |has| |#2| (-1051)) (-4419 |has| |#2| (-6 -4419)) ((-4424 "*") |has| |#2| (-172)) (-4422 . T)) -((-2811 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-727))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-794))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-849))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1051))) (|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 @@ -911,7 +911,7 @@ NIL (-245 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-246 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -919,7 +919,7 @@ NIL (-247 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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T)) -((|HasCategory| |#2| (QUOTE (-911))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2811 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2811 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4420)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-911))) (-2836 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2836 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2836 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2836 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2836 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4420)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) (-248) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\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 -902) (QUOTE (-1179))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1051)))) (-2836 (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1051)))) (|HasCategory| |#3| (QUOTE (-727))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -902) (QUOTE (-1179)))))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-2836 (|HasCategory| |#3| (QUOTE (-1051))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#3| (QUOTE (-1102)))) (-2836 (|HasAttribute| |#3| (QUOTE -4419)) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1051)))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -902) (QUOTE (-1179)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (-253 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 @@ -991,7 +991,7 @@ NIL (-265 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"))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-6 -4420)) (-4417 . T) (-4416 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-911))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#3| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#3| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#3| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#3| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-911))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#3| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#3| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#3| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#3| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) (-266 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 @@ -1036,11 +1036,11 @@ 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 -(-277 R -3888) +(-277 R -1676) ((|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 -(-278 R -3888) +(-278 R -1676) ((|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 @@ -1088,7 +1088,7 @@ 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 -(-290 S R |Mod| -3438 -2473 |exactQuo|) +(-290 S R |Mod| -3461 -1315 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL @@ -1110,21 +1110,21 @@ NIL NIL (-295 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1809) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4236) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2025) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2265) (|devaluate| |#2|)))))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) (-297) ((|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 -(-298 -3888 S) +(-298 -1676 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 -(-299 E -3888) +(-299 E -1676) ((|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 @@ -1172,7 +1172,7 @@ 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 -(-311 -3888) +(-311 -1676) ((|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 @@ -1187,7 +1187,7 @@ NIL (-314 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))}."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-911))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-1024))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (-2811 (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-851)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-1154))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -517) (QUOTE (-1179)) (LIST (QUOTE -1255) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -310) (LIST (QUOTE -1255) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -287) (LIST (QUOTE -1255) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1255) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-308))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-548))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-851))) (-12 (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-911))) (|HasCategory| $ (QUOTE (-145)))) (-2811 (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-911))) (|HasCategory| $ (QUOTE (-145)))))) +((|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-911))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-1024))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (-2836 (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-851)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-1154))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -517) (QUOTE (-1179)) (LIST (QUOTE -1255) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -310) (LIST (QUOTE -1255) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (LIST (QUOTE -287) (LIST (QUOTE -1255) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1255) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-308))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-548))) (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-851))) (-12 (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-911))) (|HasCategory| $ (QUOTE (-145)))) (-2836 (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1255 |#1| |#2| |#3| |#4|) (QUOTE (-911))) (|HasCategory| $ (QUOTE (-145)))))) (-315 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 @@ -1198,9 +1198,9 @@ NIL NIL (-317 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."))) -((-4419 -2811 (-1686 (|has| |#1| (-1051)) (|has| |#1| (-640 (-567)))) (-12 (|has| |#1| (-559)) (-2811 (-1686 (|has| |#1| (-1051)) (|has| |#1| (-640 (-567)))) (|has| |#1| (-1051)) (|has| |#1| (-476)))) (|has| |#1| (-1051)) (|has| |#1| (-476))) (-4417 |has| |#1| (-172)) (-4416 |has| |#1| (-172)) ((-4424 "*") |has| |#1| (-559)) (-4415 |has| |#1| (-559)) (-4420 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(-25))) (-12 (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))))) (-2811 (|HasCategory| |#1| (QUOTE (-476))) (|HasCategory| |#1| (QUOTE (-1051)))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| $ (QUOTE (-1051))) (|HasCategory| $ (LIST (QUOTE -1040) (QUOTE (-567))))) -(-318 R -3888) +((-4419 -2836 (-1750 (|has| |#1| (-1051)) (|has| |#1| (-640 (-567)))) (-12 (|has| |#1| (-559)) (-2836 (-1750 (|has| |#1| (-1051)) (|has| |#1| (-640 (-567)))) (|has| |#1| (-1051)) (|has| |#1| (-476)))) (|has| |#1| (-1051)) (|has| |#1| (-476))) (-4417 |has| |#1| (-172)) (-4416 |has| |#1| (-172)) ((-4424 "*") |has| |#1| (-559)) 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(|HasCategory| |#1| (QUOTE (-1051)))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-1051)))) (-12 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559)))) (-2836 (|HasCategory| |#1| (QUOTE (-476))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567))))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-1114)))) (-2836 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))))) (-2836 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-1114)))) (-2836 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))))) (-2836 (|HasCategory| |#1| (QUOTE (-476))) (|HasCategory| |#1| (QUOTE (-1051)))) (-2836 (-12 (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| $ (QUOTE (-1051))) (|HasCategory| $ (LIST (QUOTE -1040) (QUOTE (-567))))) +(-318 R -1676) ((|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 @@ -1211,7 +1211,7 @@ NIL (-320 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."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-365)) (-4414 |has| |#1| (-365)) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2811 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -4083) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -2859) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2836 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -2504) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2836 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -3670) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -3783) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|))))))) (-321 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 @@ -1243,12 +1243,12 @@ NIL (-328 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."))) ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) -(-329 S -3888) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +(-329 S -1676) ((|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 (-370)))) -(-330 -3888) +(-330 -1676) ((|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."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL @@ -1272,15 +1272,15 @@ 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 -(-336 S -3888 UP UPUP R) +(-336 S -1676 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 -(-337 -3888 UP UPUP R) +(-337 -1676 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 -(-338 -3888 UP UPUP R) +(-338 -1676 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 @@ -1300,26 +1300,26 @@ 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 -(-343 S -3888 UP UPUP) +(-343 S -1676 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 (-370))) (|HasCategory| |#2| (QUOTE (-365)))) -(-344 -3888 UP UPUP) +(-344 -1676 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."))) ((-4415 |has| (-410 |#2|) (-365)) (-4420 |has| (-410 |#2|) (-365)) (-4414 |has| (-410 |#2|) (-365)) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL (-345 |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."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((-2811 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-370)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-370))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) +((-2836 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-370)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-370))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) (-346 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."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2836 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) (-347 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."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2836 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) (-348 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 @@ -1336,31 +1336,31 @@ 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."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL -(-352 R UP -3888) +(-352 R UP -1676) ((|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 (-353 |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."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((-2811 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-370)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-370))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) +((-2836 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-370)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-370))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) (-354 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."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2836 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) (-355 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."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2836 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) (-356 |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}."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((-2811 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-370)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-370))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) +((-2836 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-370)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-370))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) (-357 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."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) -(-358 -3888 GF) +((-2836 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +(-358 -1676 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 @@ -1368,14 +1368,14 @@ 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 -(-360 -3888 FP FPP) +(-360 -1676 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 (-361 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}."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2836 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) (-362 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 @@ -1454,7 +1454,7 @@ NIL NIL (-381) ((|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}."))) -((-4405 . T) (-4413 . T) (-3058 . T) (-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) +((-4405 . T) (-4413 . T) (-3092 . T) (-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL (-382 |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}."))) @@ -1508,7 +1508,7 @@ 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 -(-395 -3888 UP UPUP R) +(-395 -1676 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 @@ -1532,11 +1532,11 @@ 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 -(-401 -2007 |returnType| -4176 |symbols|) +(-401 -1646 |returnType| -4028 |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 -(-402 -3888 UP) +(-402 -1676 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1558,7 +1558,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4405)) (|HasAttribute| |#1| (QUOTE -4413))) (-407) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-3058 . T) (-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) +((-3092 . T) (-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL (-408 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."))) @@ -1571,7 +1571,7 @@ NIL (-410 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."))) ((-4409 -12 (|has| |#1| (-6 -4420)) (|has| |#1| (-455)) (|has| |#1| (-6 -4409))) (-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-911))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-821))) (-2811 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-851)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-1154))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829))))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1179)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-548))) (-12 (|HasAttribute| |#1| (QUOTE -4420)) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-455)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-911))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-821))) (-2836 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-851)))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-1154))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381)))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829))))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1179)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-548))) (-12 (|HasAttribute| |#1| (QUOTE -4420)) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-455)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) (-411 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1592,11 +1592,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-416 R -3888 UP A) +(-416 R -1676 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4419 . T)) NIL -(-417 R -3888 UP A |ibasis|) +(-417 R -1676 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 -1040) (|devaluate| |#2|)))) @@ -1615,7 +1615,7 @@ NIL (-421 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."))) ((-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1179)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -310) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -287) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-1223))) (-2811 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-1223)))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1179)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-455)))) +((|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1179)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -310) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -287) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-1223))) (-2836 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-1223)))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1179)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-455)))) (-422 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 @@ -1644,7 +1644,7 @@ 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4422 . T) (-4412 . T) (-4423 . T)) NIL -(-429 R -3888) +(-429 R -1676) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1652,7 +1652,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4409 -12 (|has| |#1| (-6 -4409)) (|has| |#2| (-6 -4409))) (-4416 . T) (-4417 . T) (-4419 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4409)) (|HasAttribute| |#2| (QUOTE -4409)))) -(-431 R -3888) +(-431 R -1676) ((|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 @@ -1662,17 +1662,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-476))) (|HasCategory| |#2| (QUOTE (-1114))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (-433 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}."))) -((-4419 -2811 (|has| |#1| (-1051)) (|has| |#1| (-476))) (-4417 |has| |#1| (-172)) (-4416 |has| |#1| (-172)) ((-4424 "*") |has| |#1| (-559)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-559)) (-4414 |has| |#1| (-559))) +((-4419 -2836 (|has| |#1| (-1051)) (|has| |#1| (-476))) (-4417 |has| |#1| (-172)) (-4416 |has| |#1| (-172)) ((-4424 "*") |has| |#1| (-559)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-559)) (-4414 |has| |#1| (-559))) NIL -(-434 R -3888) +(-434 R -1676) ((|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 -(-435 R -3888) +(-435 R -1676) ((|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)))) -(-436 R -3888) +(-436 R -1676) ((|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 @@ -1680,7 +1680,7 @@ 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 -(-438 R -3888 UP) +(-438 R -1676 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 -1040) (QUOTE (-48))))) @@ -1712,7 +1712,7 @@ 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 -(-446 R UP -3888) +(-446 R UP -1676) ((|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 @@ -1759,7 +1759,7 @@ NIL (-457 |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"))) (((-4424 "*") |has| |#2| (-172)) (-4415 |has| |#2| (-559)) (-4420 |has| |#2| (-6 -4420)) (-4417 . T) (-4416 . T) (-4419 . T)) -((|HasCategory| |#2| (QUOTE (-911))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2811 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2811 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4420)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-911))) (-2836 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2836 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2836 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2836 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2836 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4420)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) (-458 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 @@ -1824,7 +1824,7 @@ 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 -(-474 |lv| -3888 R) +(-474 |lv| -1676 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 @@ -1839,11 +1839,11 @@ NIL (-477 |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."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-365)) (-4414 |has| |#1| (-365)) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2811 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -4083) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -2859) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2836 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -2504) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2836 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -3670) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -3783) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|))))))) (-478 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4423 . T)) -((-12 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1809) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4236) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-851))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102)))) +((-12 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2025) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2265) (|devaluate| |#2|)))))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-851))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102)))) (-479 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)}"))) ((-4423 . T) (-4422 . T)) @@ -1859,7 +1859,7 @@ NIL (-482 |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."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1809) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4236) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2025) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2265) (|devaluate| |#2|)))))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) (-483) ((|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 @@ -1867,11 +1867,11 @@ NIL (-484 |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"))) (((-4424 "*") |has| |#2| (-172)) (-4415 |has| |#2| (-559)) (-4420 |has| |#2| (-6 -4420)) (-4417 . T) (-4416 . T) (-4419 . 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(QUOTE (-567))))) (-12 (|HasCategory| |#2| (QUOTE (-794))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (QUOTE (-849))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))))) (|HasCategory| (-567) (QUOTE (-851))) (-12 (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1051)))) (-12 (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179))))) (-2836 (|HasCategory| |#2| (QUOTE (-1051))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-1102)))) (|HasAttribute| |#2| (QUOTE -4419)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))))) (-486) ((|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 @@ -1879,8 +1879,8 @@ NIL (-487 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}."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) -(-488 -3888 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +(-488 -1676 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 @@ -1891,7 +1891,7 @@ NIL (-490) ((|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."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| (-567) (QUOTE (-911))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1024))) (|HasCategory| (-567) (QUOTE (-821))) (-2811 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1154))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1179)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (|HasCategory| (-567) (QUOTE (-145))))) +((|HasCategory| (-567) (QUOTE (-911))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1024))) (|HasCategory| (-567) (QUOTE (-821))) (-2836 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1154))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1179)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (|HasCategory| (-567) (QUOTE (-145))))) (-491 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1916,7 +1916,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-497 -3888 UP |AlExt| |AlPol|) +(-497 -1676 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 @@ -1927,16 +1927,16 @@ NIL (-499 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-500 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."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-501 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 -(-502 R UP -3888) +(-502 R UP -1676) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1956,7 +1956,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-507 -3888 |Expon| |VarSet| |DPoly|) +(-507 -1676 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-1179))))) @@ -2007,7 +2007,7 @@ NIL (-519 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-520) ((|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 @@ -2015,15 +2015,15 @@ NIL (-521 |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}."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((-2811 (|HasCategory| (-584 |#1|) (QUOTE (-145))) (|HasCategory| (-584 |#1|) (QUOTE (-370)))) (|HasCategory| (-584 |#1|) (QUOTE (-147))) (|HasCategory| (-584 |#1|) (QUOTE (-370))) (|HasCategory| (-584 |#1|) (QUOTE (-145)))) +((-2836 (|HasCategory| (-584 |#1|) (QUOTE (-145))) (|HasCategory| (-584 |#1|) (QUOTE (-370)))) (|HasCategory| (-584 |#1|) (QUOTE (-147))) (|HasCategory| (-584 |#1|) (QUOTE (-370))) (|HasCategory| (-584 |#1|) (QUOTE (-145)))) (-522 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}."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-523 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."))) ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-524 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 @@ -2035,7 +2035,7 @@ NIL (-526 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."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-559))) (|HasAttribute| |#1| (QUOTE (-4424 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-559))) (|HasAttribute| |#1| (QUOTE (-4424 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-527) ((|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 @@ -2068,7 +2068,7 @@ 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 -(-535 K -3888 |Par|) +(-535 K -1676 |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 @@ -2092,7 +2092,7 @@ 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 -(-541 K -3888 |Par|) +(-541 K -1676 |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 @@ -2143,12 +2143,12 @@ NIL (-553 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1809) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4236) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) -(-554 R -3888) +((-12 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2025) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2265) (|devaluate| |#2|)))))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) +(-554 R -1676) ((|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 -(-555 R0 -3888 UP UPUP R) +(-555 R0 -1676 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 @@ -2158,7 +2158,7 @@ NIL NIL (-557 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."))) -((-3058 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) +((-3092 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL (-558 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."))) @@ -2168,7 +2168,7 @@ 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."))) ((-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL -(-560 R -3888) +(-560 R -1676) ((|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 @@ -2180,7 +2180,7 @@ 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 -(-563 R -3888 L) +(-563 R -1676 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 -657) (|devaluate| |#2|)))) @@ -2188,11 +2188,11 @@ 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 -(-565 -3888 UP UPUP R) +(-565 -1676 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 -(-566 -3888 UP) +(-566 -1676 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 @@ -2204,15 +2204,15 @@ 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 -(-569 R -3888 L) +(-569 R -1676 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 -657) (|devaluate| |#2|)))) -(-570 R -3888) +(-570 R -1676) ((|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 -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-1141)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-630))))) -(-571 -3888 UP) +(-571 -1676 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 @@ -2220,27 +2220,27 @@ 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 -(-573 -3888) +(-573 -1676) ((|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 (-574 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."))) -((-3058 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) +((-3092 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL (-575) ((|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 -(-576 R -3888) +(-576 R -1676) ((|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 -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-285))) (|HasCategory| |#2| (QUOTE (-630))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1179))))) (-12 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-285)))) (|HasCategory| |#1| (QUOTE (-559)))) -(-577 -3888 UP) +(-577 -1676 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 -(-578 R -3888) +(-578 R -1676) ((|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 @@ -2272,15 +2272,15 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-586 R -3888) +(-586 R -1676) ((|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 -(-587 E -3888) +(-587 E -1676) ((|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 -(-588 -3888) +(-588 -1676) ((|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}."))) ((-4417 . T) (-4416 . T)) ((|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-1179))))) @@ -2311,7 +2311,7 @@ NIL (-595 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-2811 (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1102)))) (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) +((-2836 (-12 (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-2836 (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1102)))) (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-596 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 @@ -2319,7 +2319,7 @@ NIL (-597 |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}."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-567)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-567)) (|devaluate| |#1|)))) (|HasCategory| (-567) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-567)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-567)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-567)) (|devaluate| |#1|)))) (|HasCategory| (-567) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -2504) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-567)))))) (-598 |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.}"))) (((-4424 "*") |has| |#1| (-559)) (-4415 |has| |#1| (-559)) (-4416 . T) (-4417 . T) (-4419 . T)) @@ -2332,7 +2332,7 @@ 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 -(-601 R -3888 FG) +(-601 R -1676 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 @@ -2343,7 +2343,7 @@ NIL (-603 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#1| (QUOTE (-1051))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-1051)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#1| (QUOTE (-1051))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-1051)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-604 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2362,12 +2362,12 @@ NIL NIL (-608 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4419 -2811 (-1686 (|has| |#2| (-369 |#1|)) (|has| |#1| (-559))) (-12 (|has| |#2| (-420 |#1|)) (|has| |#1| (-559)))) (-4417 . T) (-4416 . T)) -((-2811 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) +((-4419 -2836 (-1750 (|has| |#2| (-369 |#1|)) (|has| |#1| (-559))) (-12 (|has| |#2| (-420 |#1|)) (|has| |#1| (-559)))) (-4417 . T) (-4416 . T)) +((-2836 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-609 |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."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 |#1|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1809) (QUOTE (-1161))) (LIST (QUOTE |:|) (QUOTE -4236) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 |#1|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| (-1161) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 |#1|)) (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 |#1|)) (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 |#1|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2025) (QUOTE (-1161))) (LIST (QUOTE |:|) (QUOTE -2265) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 |#1|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| (-1161) (QUOTE (-851))) (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 |#1|)) (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 |#1|)) (LIST (QUOTE -614) (QUOTE (-863))))) (-610 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 @@ -2392,7 +2392,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-616 -3888 UP) +(-616 -1676 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2420,7 +2420,7 @@ 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}."))) ((-4416 . T) (-4417 . T) (-4419 . T)) ((|HasCategory| |#1| (QUOTE (-849)))) -(-623 R -3888) +(-623 R -1676) ((|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 @@ -2452,18 +2452,18 @@ 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 -(-631 R -3888) +(-631 R -1676) ((|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 -(-632 |lv| -3888) +(-632 |lv| -1676) ((|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 (-633) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4423 . T)) -((-12 (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1809) (QUOTE (-1161))) (LIST (QUOTE |:|) (QUOTE -4236) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 (-52))) (QUOTE (-1102))) (|HasCategory| (-52) (QUOTE (-1102)))) (-2811 (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1161) (QUOTE (-851))) (-2811 (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 (-1161)) (|:| -4236 (-52))) (QUOTE (-1102)))) +((-12 (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2025) (QUOTE (-1161))) (LIST (QUOTE |:|) (QUOTE -2265) (QUOTE (-52))))))) (-2836 (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 (-52))) (QUOTE (-1102))) (|HasCategory| (-52) (QUOTE (-1102)))) (-2836 (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1161) (QUOTE (-851))) (-2836 (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 (-1161)) (|:| -2265 (-52))) (QUOTE (-1102)))) (-634 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2474,8 +2474,8 @@ NIL NIL (-636 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4419 -2811 (-1686 (|has| |#2| (-369 |#1|)) (|has| |#1| (-559))) (-12 (|has| |#2| (-420 |#1|)) (|has| |#1| (-559)))) (-4417 . T) (-4416 . T)) -((-2811 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) +((-4419 -2836 (-1750 (|has| |#2| (-369 |#1|)) (|has| |#1| (-559))) (-12 (|has| |#2| (-420 |#1|)) (|has| |#1| (-559)))) (-4417 . T) (-4416 . T)) +((-2836 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-637 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 @@ -2487,7 +2487,7 @@ NIL (-639 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 -((-1673 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) +((-1736 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) (-640 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4419 . T)) @@ -2511,7 +2511,7 @@ NIL (-645 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-829))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-829))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-646 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2523,7 +2523,7 @@ NIL (-648 S) ((|substitute| (($ |#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."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-649 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 @@ -2540,7 +2540,7 @@ 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,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-653 R -3888 L) +(-653 R -1676 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 @@ -2560,11 +2560,11 @@ 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}."))) ((-4416 . T) (-4417 . T) (-4419 . T)) NIL -(-658 -3888 UP) +(-658 -1676 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)))) -(-659 A -3225) +(-659 A -2078) ((|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}}"))) ((-4416 . T) (-4417 . T) (-4419 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-365)))) @@ -2600,11 +2600,11 @@ 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}."))) ((-4423 . T) (-4422 . T)) NIL -(-668 -3888) +(-668 -1676) ((|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 -(-669 -3888 |Row| |Col| M) +(-669 -1676 |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 @@ -2615,7 +2615,7 @@ NIL (-671 |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."))) ((-4419 . T) (-4422 . T) (-4416 . T) (-4417 . T)) -((|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4424 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2811 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-559))) (-2811 (|HasAttribute| |#2| (QUOTE (-4424 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4424 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2836 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-559))) (-2836 (|HasAttribute| |#2| (QUOTE (-4424 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-672) ((|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 @@ -2635,7 +2635,7 @@ NIL (-676 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 -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-677) ((|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 @@ -2691,7 +2691,7 @@ NIL (-690 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."))) ((-4422 . T) (-4423 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-559))) (|HasAttribute| |#1| (QUOTE (-4424 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-559))) (|HasAttribute| |#1| (QUOTE (-4424 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-691 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 @@ -2700,7 +2700,7 @@ 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 -(-693 S -3888 FLAF FLAS) +(-693 S -1676 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 @@ -2710,8 +2710,8 @@ NIL NIL (-695) ((|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"))) -((-4415 . T) (-4420 |has| (-700) (-365)) (-4414 |has| (-700) (-365)) (-3065 . T) (-4421 |has| (-700) (-6 -4421)) (-4418 |has| (-700) (-6 -4418)) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| (-700) (QUOTE (-147))) (|HasCategory| (-700) (QUOTE (-145))) (|HasCategory| (-700) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-700) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-700) (QUOTE (-370))) (|HasCategory| (-700) (QUOTE (-365))) (-2811 (|HasCategory| (-700) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-700) (QUOTE (-365)))) (|HasCategory| (-700) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-700) (QUOTE (-233))) (-2811 (|HasCategory| (-700) (QUOTE (-365))) (|HasCategory| (-700) (QUOTE (-351)))) (|HasCategory| (-700) (QUOTE (-351))) (|HasCategory| (-700) (LIST (QUOTE -287) (QUOTE (-700)) (QUOTE (-700)))) (|HasCategory| (-700) (LIST (QUOTE -310) (QUOTE (-700)))) (|HasCategory| (-700) (LIST (QUOTE -517) (QUOTE (-1179)) (QUOTE (-700)))) (|HasCategory| (-700) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-700) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-700) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-700) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (-2811 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-365))) (|HasCategory| (-700) (QUOTE (-351)))) (|HasCategory| (-700) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-700) (QUOTE (-1024))) (|HasCategory| (-700) (QUOTE (-1204))) (-12 (|HasCategory| (-700) (QUOTE (-1004))) (|HasCategory| (-700) (QUOTE (-1204)))) (-2811 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-365))) (-12 (|HasCategory| (-700) (QUOTE (-351))) (|HasCategory| (-700) (QUOTE (-911))))) (-2811 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (-12 (|HasCategory| (-700) (QUOTE (-365))) (|HasCategory| (-700) (QUOTE (-911)))) (-12 (|HasCategory| (-700) (QUOTE (-351))) (|HasCategory| (-700) (QUOTE (-911))))) (|HasCategory| (-700) (QUOTE (-548))) (-12 (|HasCategory| (-700) (QUOTE (-1062))) (|HasCategory| (-700) (QUOTE (-1204)))) (|HasCategory| (-700) (QUOTE (-1062))) (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911))) (-2811 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-365)))) (-2811 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-559)))) (-12 (|HasCategory| (-700) (QUOTE (-233))) (|HasCategory| (-700) (QUOTE (-365)))) (-12 (|HasCategory| (-700) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-700) (QUOTE (-365)))) (|HasCategory| (-700) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-700) (QUOTE (-559))) (|HasAttribute| (-700) (QUOTE -4421)) (|HasAttribute| (-700) (QUOTE -4418)) (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-145)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-351))))) +((-4415 . T) (-4420 |has| (-700) (-365)) (-4414 |has| (-700) (-365)) (-3100 . T) (-4421 |has| (-700) (-6 -4421)) (-4418 |has| (-700) (-6 -4418)) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) +((|HasCategory| (-700) (QUOTE (-147))) (|HasCategory| (-700) (QUOTE (-145))) (|HasCategory| (-700) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-700) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-700) (QUOTE (-370))) (|HasCategory| (-700) (QUOTE (-365))) (-2836 (|HasCategory| (-700) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-700) (QUOTE (-365)))) (|HasCategory| (-700) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-700) (QUOTE (-233))) (-2836 (|HasCategory| (-700) (QUOTE (-365))) (|HasCategory| (-700) (QUOTE (-351)))) (|HasCategory| (-700) (QUOTE (-351))) (|HasCategory| (-700) (LIST (QUOTE -287) (QUOTE (-700)) (QUOTE (-700)))) (|HasCategory| (-700) (LIST (QUOTE -310) (QUOTE (-700)))) (|HasCategory| (-700) (LIST (QUOTE -517) (QUOTE (-1179)) (QUOTE (-700)))) (|HasCategory| (-700) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-700) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-700) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-700) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (-2836 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-365))) (|HasCategory| (-700) (QUOTE (-351)))) (|HasCategory| (-700) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-700) (QUOTE (-1024))) (|HasCategory| (-700) (QUOTE (-1204))) (-12 (|HasCategory| (-700) (QUOTE (-1004))) (|HasCategory| (-700) (QUOTE (-1204)))) (-2836 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-365))) (-12 (|HasCategory| (-700) (QUOTE (-351))) (|HasCategory| (-700) (QUOTE (-911))))) (-2836 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (-12 (|HasCategory| (-700) (QUOTE (-365))) (|HasCategory| (-700) (QUOTE (-911)))) (-12 (|HasCategory| (-700) (QUOTE (-351))) (|HasCategory| (-700) (QUOTE (-911))))) (|HasCategory| (-700) (QUOTE (-548))) (-12 (|HasCategory| (-700) (QUOTE (-1062))) (|HasCategory| (-700) (QUOTE (-1204)))) (|HasCategory| (-700) (QUOTE (-1062))) (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911))) (-2836 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-365)))) (-2836 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-559)))) (-12 (|HasCategory| (-700) (QUOTE (-233))) (|HasCategory| (-700) (QUOTE (-365)))) (-12 (|HasCategory| (-700) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-700) (QUOTE (-365)))) (|HasCategory| (-700) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-700) (QUOTE (-559))) (|HasAttribute| (-700) (QUOTE -4421)) (|HasAttribute| (-700) (QUOTE -4418)) (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-145)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-351))))) (-696 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}."))) ((-4423 . T)) @@ -2724,13 +2724,13 @@ 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 -(-699 OV E -3888 PG) +(-699 OV E -1676 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 (-700) ((|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}"))) -((-3058 . T) (-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) +((-3092 . T) (-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL (-701 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."))) @@ -2756,7 +2756,7 @@ 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 -(-707 S -2647 I) +(-707 S -2856 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 @@ -2776,14 +2776,14 @@ 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 -(-712 R |Mod| -3438 -2473 |exactQuo|) +(-712 R |Mod| -3461 -1315 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL (-713 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4418 |has| |#1| (-365)) (-4420 |has| |#1| (-6 -4420)) (-4417 . T) (-4416 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-911))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1154))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-911))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1154))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) (-714 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2792,7 +2792,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4417 |has| |#1| (-172)) (-4416 |has| |#1| (-172)) (-4419 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-716 R |Mod| -3438 -2473 |exactQuo|) +(-716 R |Mod| -3461 -1315 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4419 . T)) NIL @@ -2804,7 +2804,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4417 . T) (-4416 . T)) NIL -(-719 -3888) +(-719 -1676) ((|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]]}."))) ((-4419 . T)) NIL @@ -2840,7 +2840,7 @@ 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 -(-728 -3888 UP) +(-728 -1676 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 @@ -2859,7 +2859,7 @@ NIL (-732 |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."))) (((-4424 "*") |has| |#2| (-172)) (-4415 |has| |#2| (-559)) (-4420 |has| |#2| (-6 -4420)) (-4417 . T) (-4416 . T) (-4419 . T)) -((|HasCategory| |#2| (QUOTE (-911))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2811 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2811 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4420)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-911))) (-2836 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2836 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2836 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2836 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2836 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4420)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) (-733 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 @@ -2992,11 +2992,11 @@ 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 -(-766 -3888) +(-766 -1676) ((|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 -(-767 P -3888) +(-767 P -1676) ((|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 @@ -3004,7 +3004,7 @@ NIL NIL NIL NIL -(-769 UP -3888) +(-769 UP -1676) ((|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 @@ -3020,7 +3020,7 @@ 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."))) (((-4424 "*") . T)) NIL -(-773 R -3888) +(-773 R -1676) ((|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 @@ -3040,7 +3040,7 @@ 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 -(-778 -3888 |ExtF| |SUEx| |ExtP| |n|) +(-778 -1676 |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 @@ -3055,7 +3055,7 @@ NIL (-781 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."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-6 -4420)) (-4417 . T) (-4416 . T) (-4419 . 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|#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-1179))))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-1179))))) (-2836 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-1179)))) (-1736 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-1179)))))) (-2836 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-1179)))) (-1736 (|HasCategory| |#1| (QUOTE (-548)))) (-1736 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-1179)))) (-1736 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-567))))) (-1736 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-1179)))) (-1736 (|HasCategory| |#1| (LIST (QUOTE -994) (QUOTE (-567))))))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) (-782 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 @@ -3063,7 +3063,7 @@ NIL (-783 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)}"))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4418 |has| |#1| (-365)) (-4420 |has| |#1| (-6 -4420)) (-4417 . T) (-4416 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-911))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1154))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-911))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1154))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) (-784 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL @@ -3124,23 +3124,23 @@ 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4416 . T) (-4417 . T) (-4419 . T)) NIL -(-799 -2811 R OS S) +(-799 -2836 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-800 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1179)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-2811 (|HasCategory| (-1001 |#1|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2811 (|HasCategory| (-1001 |#1|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| (-1001 |#1|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1001 |#1|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1179)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-2836 (|HasCategory| (-1001 |#1|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2836 (|HasCategory| (-1001 |#1|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| (-1001 |#1|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1001 |#1|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (-801) ((|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 -(-802 R -3888 L) +(-802 R -1676 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 -(-803 R -3888) +(-803 R -1676) ((|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 @@ -3148,7 +3148,7 @@ 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 -(-805 R -3888) +(-805 R -1676) ((|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 @@ -3156,11 +3156,11 @@ 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 -(-807 -3888 UP UPUP R) +(-807 -1676 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 -(-808 -3888 UP L LQ) +(-808 -1676 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 @@ -3168,38 +3168,38 @@ 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 -(-810 -3888 UP L LQ) +(-810 -1676 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 -(-811 -3888 UP) +(-811 -1676 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 -(-812 -3888 L UP A LO) +(-812 -1676 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 -(-813 -3888 UP) +(-813 -1676 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)))) -(-814 -3888 LO) +(-814 -1676 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-815 -3888 LODO) +(-815 -1676 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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(QUOTE (-567))))) (-12 (|HasCategory| |#2| (QUOTE (-794))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (QUOTE (-849))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))))) (|HasCategory| (-567) (QUOTE (-851))) (-12 (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1051)))) (-12 (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179))))) (-2836 (|HasCategory| |#2| (QUOTE (-1051))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-1102)))) (|HasAttribute| |#2| (QUOTE -4419)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))))) (-817 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-6 -4420)) (-4417 . T) (-4416 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-911))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-819 (-1179)) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-819 (-1179)) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-819 (-1179)) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-819 (-1179)) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-819 (-1179)) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-911))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-819 (-1179)) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-819 (-1179)) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-819 (-1179)) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-819 (-1179)) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-819 (-1179)) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) (-818 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4424 "*") |has| |#2| (-365)) (-4415 |has| |#2| (-365)) (-4420 |has| |#2| (-365)) (-4414 |has| |#2| (-365)) (-4419 . T) (-4417 . T) (-4416 . T)) @@ -3267,7 +3267,7 @@ NIL (-834 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."))) ((-4419 |has| |#1| (-849))) -((|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (QUOTE (-21))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-849)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2811 (|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-548)))) +((|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (QUOTE (-21))) (-2836 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-849)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2836 (|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-548)))) (-835 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 @@ -3307,12 +3307,12 @@ NIL (-844 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4419 |has| |#1| (-849))) -((|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (QUOTE (-21))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-849)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2811 (|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-548)))) +((|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (QUOTE (-21))) (-2836 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-849)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2836 (|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-548)))) (-845) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-846 -2622 S) +(-846 -2424 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 @@ -3348,11 +3348,11 @@ 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 (-365))) (|HasCategory| |#1| (QUOTE (-559)))) -(-855 R |sigma| -3116) +(-855 R |sigma| -2582) ((|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."))) ((-4416 . T) (-4417 . T) (-4419 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-365)))) -(-856 |x| R |sigma| -3116) +(-856 |x| R |sigma| -2582) ((|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}."))) ((-4416 . T) (-4417 . T) (-4419 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-365)))) @@ -3419,15 +3419,15 @@ NIL (-872 |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)."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| (-871 |#1|) (QUOTE (-911))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-871 |#1|) (QUOTE (-145))) (|HasCategory| (-871 |#1|) (QUOTE (-147))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-871 |#1|) (QUOTE (-1024))) (|HasCategory| (-871 |#1|) (QUOTE (-821))) (-2811 (|HasCategory| (-871 |#1|) (QUOTE (-821))) (|HasCategory| (-871 |#1|) (QUOTE (-851)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-871 |#1|) (QUOTE (-1154))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-871 |#1|) (QUOTE (-233))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -517) (QUOTE (-1179)) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -871) (|devaluate| |#1|)) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| (-871 |#1|) (QUOTE (-308))) (|HasCategory| (-871 |#1|) (QUOTE (-548))) (|HasCategory| (-871 |#1|) (QUOTE (-851))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-871 |#1|) (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-871 |#1|) (QUOTE (-911)))) (|HasCategory| (-871 |#1|) (QUOTE (-145))))) +((|HasCategory| (-871 |#1|) (QUOTE (-911))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-871 |#1|) (QUOTE (-145))) (|HasCategory| (-871 |#1|) (QUOTE (-147))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-871 |#1|) (QUOTE (-1024))) (|HasCategory| (-871 |#1|) (QUOTE (-821))) (-2836 (|HasCategory| (-871 |#1|) (QUOTE (-821))) (|HasCategory| (-871 |#1|) (QUOTE (-851)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-871 |#1|) (QUOTE (-1154))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-871 |#1|) (QUOTE (-233))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -517) (QUOTE (-1179)) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -871) (|devaluate| |#1|)) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| (-871 |#1|) (QUOTE (-308))) (|HasCategory| (-871 |#1|) (QUOTE (-548))) (|HasCategory| (-871 |#1|) (QUOTE (-851))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-871 |#1|) (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-871 |#1|) (QUOTE (-911)))) (|HasCategory| (-871 |#1|) (QUOTE (-145))))) (-873 |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)}."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#2| (QUOTE (-911))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-1024))) (|HasCategory| |#2| (QUOTE (-821))) (-2811 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-851)))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-1154))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#2| (LIST (QUOTE -517) (QUOTE (-1179)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -287) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-548))) (|HasCategory| |#2| (QUOTE (-851))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-911))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-1024))) (|HasCategory| |#2| (QUOTE (-821))) (-2836 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-851)))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-1154))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#2| (LIST (QUOTE -517) (QUOTE (-1179)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -287) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-548))) (|HasCategory| |#2| (QUOTE (-851))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) (-874 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 (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))))) (-875) ((|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 @@ -3487,7 +3487,7 @@ NIL (-889 |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 (-1673 (|HasCategory| |#2| (QUOTE (-1051)))) (-1673 (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1179)))))) (-12 (|HasCategory| |#2| (QUOTE (-1051))) (-1673 (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1179)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1179))))) +((-12 (-1736 (|HasCategory| |#2| (QUOTE (-1051)))) (-1736 (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1179)))))) (-12 (|HasCategory| |#2| (QUOTE (-1051))) (-1736 (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1179)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1179))))) (-890 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 @@ -3496,7 +3496,7 @@ 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 -(-892 R -2647) +(-892 R -2856) ((|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 @@ -3520,7 +3520,7 @@ 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 -(-898 UP -3888) +(-898 UP -1676) ((|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 @@ -3543,7 +3543,7 @@ NIL (-903 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 (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-904 |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 @@ -3559,7 +3559,7 @@ NIL (-907 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."))) ((-4419 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-851)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-851)))) +((-2836 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-851)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-851)))) (-908 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 @@ -3580,7 +3580,7 @@ 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."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-370)))) -(-913 R0 -3888 UP UPUP R) +(-913 R0 -1676 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 @@ -3608,7 +3608,7 @@ 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 -(-920 -3888) +(-920 -1676) ((|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 @@ -3624,11 +3624,11 @@ 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}."))) (((-4424 "*") . T)) NIL -(-924 -3888 P) +(-924 -1676 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-925 |xx| -3888) +(-925 |xx| -1676) ((|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 @@ -3652,7 +3652,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-931 R -3888) +(-931 R -1676) ((|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 @@ -3664,7 +3664,7 @@ 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 -(-934 S R -3888) +(-934 S R -1676) ((|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 @@ -3684,11 +3684,11 @@ 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 -888) (|devaluate| |#1|)))) -(-939 R -3888 -2647) +(-939 R -1676 -2856) ((|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 -(-940 -2647) +(-940 -2856) ((|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 @@ -3711,7 +3711,7 @@ NIL (-945 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#1| (QUOTE (-1051))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-1051)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#1| (QUOTE (-1051))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-1051)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-946 |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 @@ -3736,7 +3736,7 @@ 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}."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-6 -4420)) (-4417 . T) (-4416 . T) (-4419 . T)) NIL -(-952 E V R P -3888) +(-952 E V R P -1676) ((|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 @@ -3747,8 +3747,8 @@ NIL (-954 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}."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-6 -4420)) (-4417 . T) (-4416 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-911))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1179) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1179) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1179) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1179) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1179) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-955 E V R P -3888) +((|HasCategory| |#1| (QUOTE (-911))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1179) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1179) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1179) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1179) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1179) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-955 E V R P -1676) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-455)))) @@ -3771,12 +3771,12 @@ NIL (-960 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-961) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-962 -3888) +(-962 -1676) ((|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 @@ -3791,11 +3791,11 @@ NIL (-965 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}"))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-6 -4420)) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4420))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4420))) (-966 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"))) ((-4419 -12 (|has| |#2| (-476)) (|has| |#1| (-476)))) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794)))) (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-851))))) (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794))))) (-12 (|HasCategory| |#1| (QUOTE (-476))) (|HasCategory| |#2| (QUOTE (-476)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-476))) (|HasCategory| |#2| (QUOTE (-476)))) (-12 (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#2| (QUOTE (-727))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-370)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-476))) (|HasCategory| |#2| (QUOTE (-476)))) (-12 (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#2| (QUOTE (-727)))) (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794))))) (-12 (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#2| (QUOTE (-727)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-851))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794)))) (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-851))))) (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794)))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794))))) (-12 (|HasCategory| |#1| (QUOTE (-476))) (|HasCategory| |#2| (QUOTE (-476)))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-476))) (|HasCategory| |#2| (QUOTE (-476)))) (-12 (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#2| (QUOTE (-727))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-370)))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-476))) (|HasCategory| |#2| (QUOTE (-476)))) (-12 (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#2| (QUOTE (-727)))) (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794))))) (-12 (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#2| (QUOTE (-727)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-851))))) (-967) ((|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 @@ -3876,7 +3876,7 @@ 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 -(-987 K R UP -3888) +(-987 K R UP -1676) ((|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 @@ -3935,11 +3935,11 @@ NIL (-1001 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.}"))) ((-4415 |has| |#1| (-291)) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-365))) (-2811 (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1179)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (QUOTE (-548)))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-365))) (-2836 (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1179)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (QUOTE (-548)))) (-1002 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}."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-1003 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3948,14 +3948,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1005 -3888 UP UPUP |radicnd| |n|) +(-1005 -1676 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4415 |has| (-410 |#2|) (-365)) (-4420 |has| (-410 |#2|) (-365)) (-4414 |has| (-410 |#2|) (-365)) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| (-410 |#2|) (QUOTE (-145))) (|HasCategory| (-410 |#2|) (QUOTE (-147))) (|HasCategory| (-410 |#2|) (QUOTE (-351))) (-2811 (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-370))) (-2811 (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (-2811 (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-410 |#2|) (QUOTE (-351))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -640) (QUOTE (-567)))) (-2811 (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365))))) +((|HasCategory| (-410 |#2|) (QUOTE (-145))) (|HasCategory| (-410 |#2|) (QUOTE (-147))) (|HasCategory| (-410 |#2|) (QUOTE (-351))) (-2836 (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-370))) (-2836 (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (-2836 (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-410 |#2|) (QUOTE (-351))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -640) (QUOTE (-567)))) (-2836 (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365))))) (-1006 |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."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| (-567) (QUOTE (-911))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1024))) (|HasCategory| (-567) (QUOTE (-821))) (-2811 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1154))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1179)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (|HasCategory| (-567) (QUOTE (-145))))) +((|HasCategory| (-567) (QUOTE (-911))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-1179)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1024))) (|HasCategory| (-567) (QUOTE (-821))) (-2836 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1154))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1179)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (|HasCategory| (-567) (QUOTE (-145))))) (-1007) ((|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 @@ -3988,19 +3988,19 @@ 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}}"))) ((-4415 . T) (-4420 . T) (-4414 . T) (-4417 . T) (-4416 . T) ((-4424 "*") . T) (-4419 . T)) NIL -(-1015 R -3888) +(-1015 R -1676) ((|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 -(-1016 R -3888) +(-1016 R -1676) ((|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 -(-1017 -3888 UP) +(-1017 -1676 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 -(-1018 -3888 UP) +(-1018 -1676 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 @@ -4035,8 +4035,8 @@ NIL (-1026 |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"))) ((-4415 . T) (-4420 . T) (-4414 . T) (-4417 . T) (-4416 . T) ((-4424 "*") . T) (-4419 . T)) -((-2811 (|HasCategory| (-410 (-567)) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-410 (-567)) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 (-567)) (LIST (QUOTE -1040) (QUOTE (-567))))) -(-1027 -3888 L) +((-2836 (|HasCategory| (-410 (-567)) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-410 (-567)) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 (-567)) (LIST (QUOTE -1040) (QUOTE (-567))))) +(-1027 -1676 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 @@ -4072,14 +4072,14 @@ 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 -(-1036 -3888 |Expon| |VarSet| |FPol| |LFPol|) +(-1036 -1676 |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"))) (((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL (-1037) ((|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.}"))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1809) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -4236) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (QUOTE (-1102))) (|HasCategory| (-52) (QUOTE (-1102)))) (-2811 (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (QUOTE (-1102))) (|HasCategory| (-1179) (QUOTE (-851))) (|HasCategory| (-52) (QUOTE (-1102))) (-2811 (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2025) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -2265) (QUOTE (-52))))))) (-2836 (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (QUOTE (-1102))) (|HasCategory| (-52) (QUOTE (-1102)))) (-2836 (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (QUOTE (-1102))) (|HasCategory| (-1179) (QUOTE (-851))) (|HasCategory| (-52) (QUOTE (-1102))) (-2836 (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (LIST (QUOTE -614) (QUOTE (-863))))) (-1038) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4136,7 +4136,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4419 . T)) NIL -(-1052 |xx| -3888) +(-1052 |xx| -1676) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4155,7 +4155,7 @@ NIL (-1056 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4422 . T) (-4417 . T) (-4416 . T)) -((|HasCategory| |#3| (QUOTE (-172))) (-2811 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-365)))) (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (QUOTE (-308))) (|HasCategory| |#3| (QUOTE (-559))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-863))))) +((|HasCategory| |#3| (QUOTE (-172))) (-2836 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-365)))) (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (QUOTE (-308))) (|HasCategory| |#3| (QUOTE (-559))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-863))))) (-1057 |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 @@ -4191,7 +4191,7 @@ NIL (-1065) ((|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}"))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1809) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -4236) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (QUOTE (-1102))) (|HasCategory| (-52) (QUOTE (-1102)))) (-2811 (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (QUOTE (-1102))) (|HasCategory| (-1179) (QUOTE (-851))) (|HasCategory| (-52) (QUOTE (-1102))) (-2811 (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2025) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -2265) (QUOTE (-52))))))) (-2836 (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (QUOTE (-1102))) (|HasCategory| (-52) (QUOTE (-1102)))) (-2836 (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (QUOTE (-1102))) (|HasCategory| (-1179) (QUOTE (-851))) (|HasCategory| (-52) (QUOTE (-1102))) (-2836 (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (LIST (QUOTE -614) (QUOTE (-863))))) (-1066 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 @@ -4240,11 +4240,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1078 |Base| R -3888) +(-1078 |Base| R -1676) ((|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 -(-1079 |Base| R -3888) +(-1079 |Base| R -1676) ((|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 @@ -4259,7 +4259,7 @@ NIL (-1082 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."))) ((-4415 |has| |#1| (-365)) (-4420 |has| |#1| (-365)) (-4414 |has| |#1| (-365)) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2811 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-351)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2836 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-351)))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365))))) (-1083 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 @@ -4287,7 +4287,7 @@ NIL (-1089 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"))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-6 -4420)) (-4417 . T) (-4416 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-911))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1090 (-1179)) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1090 (-1179)) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1090 (-1179)) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1090 (-1179)) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1090 (-1179)) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-911))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1090 (-1179)) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1090 (-1179)) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1090 (-1179)) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1090 (-1179)) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1090 (-1179)) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1090 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 @@ -4347,7 +4347,7 @@ NIL (-1104 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)}}"))) ((-4422 . T) (-4412 . T) (-4423 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-1105 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,...,an), [i1,...,im])} returns \\spad{(a_i1,...,a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,...,an), i)} returns \\spad{ai}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4391,7 +4391,7 @@ NIL (-1115 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4416 |has| |#3| (-1051)) (-4417 |has| |#3| (-1051)) (-4419 |has| |#3| (-6 -4419)) ((-4424 "*") |has| |#3| (-172)) (-4422 . 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(QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-794))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-849))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567)))))) (|HasCategory| (-567) (QUOTE (-851))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1051)))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -902) (QUOTE (-1179))))) (-2836 (|HasCategory| |#3| (QUOTE (-1051))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567)))))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#3| (QUOTE (-1102)))) (|HasAttribute| |#3| (QUOTE -4419)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (-1116 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 @@ -4400,7 +4400,7 @@ 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 -(-1118 R -3888) +(-1118 R -1676) ((|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 @@ -4439,16 +4439,16 @@ NIL (-1127 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."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-6 -4420)) (-4417 . T) (-4416 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-911))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-911))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1128 |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}."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4417 . T) (-4416 . T) (-4419 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-365)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-365)))) (-1129 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}"))) ((-4423 . T) (-4422 . T)) NIL -(-1130 UP -3888) +(-1130 UP -1676) ((|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 @@ -4485,7 +4485,7 @@ NIL NIL NIL (-1139) -((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) +((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) NIL NIL (-1140) @@ -4503,11 +4503,11 @@ NIL (-1143 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| (-1142 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1142) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1142 |#1| |#2|) (QUOTE (-1102)))) (|HasCategory| (-1142 |#1| |#2|) (QUOTE (-1102))) (-2811 (|HasCategory| (-1142 |#1| |#2|) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-1142 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1142) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1142 |#1| |#2|) (QUOTE (-1102))))) (|HasCategory| (-1142 |#1| |#2|) (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| (-1142 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1142) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1142 |#1| |#2|) (QUOTE (-1102)))) (|HasCategory| (-1142 |#1| |#2|) (QUOTE (-1102))) (-2836 (|HasCategory| (-1142 |#1| |#2|) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-1142 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1142) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1142 |#1| |#2|) (QUOTE (-1102))))) (|HasCategory| (-1142 |#1| |#2|) (LIST (QUOTE -614) (QUOTE (-863))))) (-1144 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) ((-4419 . T) (-4411 |has| |#2| (-6 (-4424 "*"))) (-4422 . T) (-4416 . T) (-4417 . T)) -((|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4424 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2811 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-365))) (-2811 (|HasAttribute| |#2| (QUOTE (-4424 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4424 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2836 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-365))) (-2836 (|HasAttribute| |#2| (QUOTE (-4424 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-1145 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4527,7 +4527,7 @@ NIL (-1149 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-1150 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 @@ -4539,7 +4539,7 @@ NIL (-1152 |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."))) ((-4423 . T)) -((-12 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1809) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4236) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-851))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102)))) +((-12 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2025) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2265) (|devaluate| |#2|)))))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-851))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102)))) (-1153) ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4567,7 +4567,7 @@ NIL (-1159 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) ((-4423 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-1160) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4423 . T) (-4422 . T)) @@ -4575,11 +4575,11 @@ NIL (-1161) NIL ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) +((-2836 (-12 (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-1162 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4422 . T) (-4423 . 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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 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,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 @@ -4610,9 +4610,9 @@ NIL NIL (-1170 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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(|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1154))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4420)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1176 |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}."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-365)) (-4414 |has| |#1| (-365)) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2811 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -4083) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -2859) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2836 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -2504) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2836 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -3670) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -3783) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|))))))) (-1177 |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}."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|)))) (|HasCategory| (-772) (QUOTE (-1114))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasCategory| |#1| (QUOTE (-365))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -4083) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -2859) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|)))) (|HasCategory| (-772) (QUOTE (-1114))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasSignature| |#1| (LIST (QUOTE -2504) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasCategory| |#1| (QUOTE (-365))) (-2836 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -3670) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -3783) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|))))))) (-1178) ((|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 @@ -4655,7 +4655,7 @@ NIL (-1181 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-6 -4420)) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| (-973) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasAttribute| |#1| (QUOTE -4420))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2836 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| (-973) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasAttribute| |#1| (QUOTE -4420))) (-1182) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4699,7 +4699,7 @@ NIL (-1192 |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}"))) ((-4422 . T) (-4423 . T)) -((-12 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1809) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4236) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (-2811 (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2025) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2265) (|devaluate| |#2|)))))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (-2836 (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) (-1193 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) NIL @@ -4751,7 +4751,7 @@ NIL (-1205 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4423 . T) (-4422 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-1206 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4760,7 +4760,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1208 R -3888) +(-1208 R -1676) ((|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 @@ -4768,7 +4768,7 @@ 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 -(-1210 R -3888) +(-1210 R -1676) ((|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 -615) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -888) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -888) (|devaluate| |#1|))))) @@ -4783,7 +4783,7 @@ NIL (-1213 |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}."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4417 . T) (-4416 . T) (-4419 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-365)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-365)))) (-1214 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4796,7 +4796,7 @@ 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 (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) -(-1217 -3888) +(-1217 -1676) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) 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the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4899,7 +4899,7 @@ NIL (-1242 |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}"))) (((-4424 "*") |has| |#2| (-172)) (-4415 |has| |#2| (-559)) (-4418 |has| |#2| (-365)) (-4420 |has| |#2| (-6 -4420)) (-4417 . T) (-4416 . T) (-4419 . T)) -((|HasCategory| |#2| (QUOTE (-911))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2811 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2811 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1154))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4420)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-911))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2836 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2836 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2836 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2836 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2836 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1154))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4420)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2836 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) (-1243 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 @@ -4915,7 +4915,7 @@ NIL (-1246 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1114))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4129) (LIST (|devaluate| |#2|) (QUOTE (-1179)))))) +((|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1114))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2504) (LIST (|devaluate| |#2|) (QUOTE (-1179)))))) (-1247 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4416 . T) (-4417 . T) (-4419 . T)) @@ -4943,15 +4943,15 @@ NIL (-1253 |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)}."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-365)) (-4414 |has| |#1| (-365)) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2811 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -4083) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -2859) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) +((|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2836 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -2504) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2836 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -3670) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -3783) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-1254 |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}."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4420 |has| |#1| (-365)) (-4414 |has| |#1| (-365)) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2811 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -4083) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -2859) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2836 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -2504) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2836 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -3670) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -3783) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|))))))) (-1255 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))}."))) (((-4424 "*") |has| (-1254 |#2| |#3| |#4|) (-172)) (-4415 |has| (-1254 |#2| |#3| |#4|) (-559)) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| (-1254 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1254 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1254 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1254 |#2| |#3| |#4|) (QUOTE (-172))) (-2811 (|HasCategory| (-1254 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1254 |#2| |#3| |#4|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| (-1254 |#2| |#3| |#4|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1254 |#2| |#3| |#4|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-1254 |#2| |#3| |#4|) (QUOTE (-365))) (|HasCategory| (-1254 |#2| |#3| |#4|) (QUOTE (-455))) (|HasCategory| (-1254 |#2| |#3| |#4|) (QUOTE (-559)))) +((|HasCategory| (-1254 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1254 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1254 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1254 |#2| |#3| |#4|) (QUOTE (-172))) (-2836 (|HasCategory| (-1254 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1254 |#2| |#3| |#4|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| (-1254 |#2| |#3| |#4|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1254 |#2| |#3| |#4|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-1254 |#2| |#3| |#4|) (QUOTE (-365))) (|HasCategory| (-1254 |#2| |#3| |#4|) (QUOTE (-455))) (|HasCategory| (-1254 |#2| |#3| |#4|) (QUOTE (-559)))) (-1256 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4967,7 +4967,7 @@ NIL (-1259 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-567)))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-1204))) (|HasSignature| |#2| (LIST (QUOTE -2859) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4083) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1179))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-1204))) (|HasSignature| |#2| (LIST (QUOTE -3783) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3670) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1179))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365)))) (-1260 |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."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4416 . T) (-4417 . T) (-4419 . T)) @@ -4975,12 +4975,12 @@ NIL (-1261 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4424 "*") |has| |#1| (-172)) (-4415 |has| |#1| (-559)) (-4416 . T) (-4417 . T) (-4419 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|)))) (|HasCategory| (-772) (QUOTE (-1114))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasCategory| |#1| (QUOTE (-365))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -4083) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -2859) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2836 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1179)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|)))) (|HasCategory| (-772) (QUOTE (-1114))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasSignature| |#1| (LIST (QUOTE -2504) (LIST (|devaluate| |#1|) (QUOTE (-1179)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasCategory| |#1| (QUOTE (-365))) (-2836 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1204))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -3670) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1179))))) (|HasSignature| |#1| (LIST (QUOTE -3783) (LIST (LIST (QUOTE -645) (QUOTE (-1179))) (|devaluate| |#1|))))))) (-1262 |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 -(-1263 -3888 UP L UTS) +(-1263 -1676 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 (-559)))) @@ -5007,7 +5007,7 @@ NIL (-1269 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."))) ((-4423 . T) (-4422 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2811 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#1| (QUOTE (-1051))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-1051)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2836 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2836 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2836 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#1| (QUOTE (-1051))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-1051)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-1270) ((|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 @@ -5040,7 +5040,7 @@ 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 -(-1278 K R UP -3888) +(-1278 K R UP -1676) ((|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 @@ -5076,11 +5076,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4415 |has| |#2| (-6 -4415)) (-4417 . T) (-4416 . T) (-4419 . T)) NIL -(-1287 S -3888) +(-1287 S -1676) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1288 -3888) +(-1288 -1676) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4414 . T) (-4420 . T) (-4415 . T) ((-4424 "*") . T) (-4416 . T) (-4417 . T) (-4419 . T)) NIL @@ -5136,4 +5136,4 @@ NIL NIL NIL NIL -((-3 NIL 2264550 2264555 2264560 2264565) (-2 NIL 2264530 2264535 2264540 2264545) (-1 NIL 2264510 2264515 2264520 2264525) (0 NIL 2264490 2264495 2264500 2264505) (-1297 "ZMOD.spad" 2264299 2264312 2264428 2264485) (-1296 "ZLINDEP.spad" 2263365 2263376 2264289 2264294) (-1295 "ZDSOLVE.spad" 2253310 2253332 2263355 2263360) (-1294 "YSTREAM.spad" 2252805 2252816 2253300 2253305) (-1293 "XRPOLY.spad" 2252025 2252045 2252661 2252730) (-1292 "XPR.spad" 2249820 2249833 2251743 2251842) (-1291 "XPOLY.spad" 2249375 2249386 2249676 2249745) (-1290 "XPOLYC.spad" 2248694 2248710 2249301 2249370) (-1289 "XPBWPOLY.spad" 2247131 2247151 2248474 2248543) (-1288 "XF.spad" 2245594 2245609 2247033 2247126) (-1287 "XF.spad" 2244037 2244054 2245478 2245483) (-1286 "XFALG.spad" 2241085 2241101 2243963 2244032) (-1285 "XEXPPKG.spad" 2240336 2240362 2241075 2241080) (-1284 "XDPOLY.spad" 2239950 2239966 2240192 2240261) (-1283 "XALG.spad" 2239610 2239621 2239906 2239945) (-1282 "WUTSET.spad" 2235449 2235466 2239256 2239283) (-1281 "WP.spad" 2234648 2234692 2235307 2235374) (-1280 "WHILEAST.spad" 2234446 2234455 2234638 2234643) (-1279 "WHEREAST.spad" 2234117 2234126 2234436 2234441) (-1278 "WFFINTBS.spad" 2231780 2231802 2234107 2234112) (-1277 "WEIER.spad" 2230002 2230013 2231770 2231775) (-1276 "VSPACE.spad" 2229675 2229686 2229970 2229997) (-1275 "VSPACE.spad" 2229368 2229381 2229665 2229670) (-1274 "VOID.spad" 2229045 2229054 2229358 2229363) (-1273 "VIEW.spad" 2226725 2226734 2229035 2229040) (-1272 "VIEWDEF.spad" 2221926 2221935 2226715 2226720) (-1271 "VIEW3D.spad" 2205887 2205896 2221916 2221921) (-1270 "VIEW2D.spad" 2193778 2193787 2205877 2205882) (-1269 "VECTOR.spad" 2192452 2192463 2192703 2192730) (-1268 "VECTOR2.spad" 2191091 2191104 2192442 2192447) (-1267 "VECTCAT.spad" 2188995 2189006 2191059 2191086) (-1266 "VECTCAT.spad" 2186706 2186719 2188772 2188777) (-1265 "VARIABLE.spad" 2186486 2186501 2186696 2186701) (-1264 "UTYPE.spad" 2186130 2186139 2186476 2186481) (-1263 "UTSODETL.spad" 2185425 2185449 2186086 2186091) (-1262 "UTSODE.spad" 2183641 2183661 2185415 2185420) (-1261 "UTS.spad" 2178454 2178482 2182108 2182205) (-1260 "UTSCAT.spad" 2175933 2175949 2178352 2178449) (-1259 "UTSCAT.spad" 2173056 2173074 2175477 2175482) (-1258 "UTS2.spad" 2172651 2172686 2173046 2173051) (-1257 "URAGG.spad" 2167324 2167335 2172641 2172646) (-1256 "URAGG.spad" 2161961 2161974 2167280 2167285) (-1255 "UPXSSING.spad" 2159606 2159632 2161042 2161175) (-1254 "UPXS.spad" 2156760 2156788 2157738 2157887) (-1253 "UPXSCONS.spad" 2154519 2154539 2154892 2155041) (-1252 "UPXSCCA.spad" 2153090 2153110 2154365 2154514) (-1251 "UPXSCCA.spad" 2151803 2151825 2153080 2153085) (-1250 "UPXSCAT.spad" 2150392 2150408 2151649 2151798) (-1249 "UPXS2.spad" 2149935 2149988 2150382 2150387) (-1248 "UPSQFREE.spad" 2148349 2148363 2149925 2149930) (-1247 "UPSCAT.spad" 2145960 2145984 2148247 2148344) (-1246 "UPSCAT.spad" 2143277 2143303 2145566 2145571) (-1245 "UPOLYC.spad" 2138317 2138328 2143119 2143272) (-1244 "UPOLYC.spad" 2133249 2133262 2138053 2138058) (-1243 "UPOLYC2.spad" 2132720 2132739 2133239 2133244) (-1242 "UP.spad" 2129919 2129934 2130306 2130459) (-1241 "UPMP.spad" 2128819 2128832 2129909 2129914) (-1240 "UPDIVP.spad" 2128384 2128398 2128809 2128814) (-1239 "UPDECOMP.spad" 2126629 2126643 2128374 2128379) (-1238 "UPCDEN.spad" 2125838 2125854 2126619 2126624) (-1237 "UP2.spad" 2125202 2125223 2125828 2125833) (-1236 "UNISEG.spad" 2124555 2124566 2125121 2125126) (-1235 "UNISEG2.spad" 2124052 2124065 2124511 2124516) (-1234 "UNIFACT.spad" 2123155 2123167 2124042 2124047) (-1233 "ULS.spad" 2113713 2113741 2114800 2115229) (-1232 "ULSCONS.spad" 2106109 2106129 2106479 2106628) (-1231 "ULSCCAT.spad" 2103846 2103866 2105955 2106104) (-1230 "ULSCCAT.spad" 2101691 2101713 2103802 2103807) (-1229 "ULSCAT.spad" 2099923 2099939 2101537 2101686) (-1228 "ULS2.spad" 2099437 2099490 2099913 2099918) (-1227 "UINT8.spad" 2099314 2099323 2099427 2099432) (-1226 "UINT64.spad" 2099190 2099199 2099304 2099309) (-1225 "UINT32.spad" 2099066 2099075 2099180 2099185) (-1224 "UINT16.spad" 2098942 2098951 2099056 2099061) (-1223 "UFD.spad" 2098007 2098016 2098868 2098937) (-1222 "UFD.spad" 2097134 2097145 2097997 2098002) (-1221 "UDVO.spad" 2096015 2096024 2097124 2097129) (-1220 "UDPO.spad" 2093508 2093519 2095971 2095976) (-1219 "TYPE.spad" 2093440 2093449 2093498 2093503) (-1218 "TYPEAST.spad" 2093359 2093368 2093430 2093435) (-1217 "TWOFACT.spad" 2092011 2092026 2093349 2093354) (-1216 "TUPLE.spad" 2091497 2091508 2091910 2091915) (-1215 "TUBETOOL.spad" 2088364 2088373 2091487 2091492) (-1214 "TUBE.spad" 2087011 2087028 2088354 2088359) (-1213 "TS.spad" 2085610 2085626 2086576 2086673) (-1212 "TSETCAT.spad" 2072737 2072754 2085578 2085605) (-1211 "TSETCAT.spad" 2059850 2059869 2072693 2072698) (-1210 "TRMANIP.spad" 2054216 2054233 2059556 2059561) (-1209 "TRIMAT.spad" 2053179 2053204 2054206 2054211) (-1208 "TRIGMNIP.spad" 2051706 2051723 2053169 2053174) (-1207 "TRIGCAT.spad" 2051218 2051227 2051696 2051701) (-1206 "TRIGCAT.spad" 2050728 2050739 2051208 2051213) (-1205 "TREE.spad" 2049303 2049314 2050335 2050362) (-1204 "TRANFUN.spad" 2049142 2049151 2049293 2049298) (-1203 "TRANFUN.spad" 2048979 2048990 2049132 2049137) (-1202 "TOPSP.spad" 2048653 2048662 2048969 2048974) (-1201 "TOOLSIGN.spad" 2048316 2048327 2048643 2048648) (-1200 "TEXTFILE.spad" 2046877 2046886 2048306 2048311) (-1199 "TEX.spad" 2044023 2044032 2046867 2046872) (-1198 "TEX1.spad" 2043579 2043590 2044013 2044018) (-1197 "TEMUTL.spad" 2043134 2043143 2043569 2043574) (-1196 "TBCMPPK.spad" 2041227 2041250 2043124 2043129) (-1195 "TBAGG.spad" 2040277 2040300 2041207 2041222) (-1194 "TBAGG.spad" 2039335 2039360 2040267 2040272) (-1193 "TANEXP.spad" 2038743 2038754 2039325 2039330) (-1192 "TABLE.spad" 2037154 2037177 2037424 2037451) (-1191 "TABLEAU.spad" 2036635 2036646 2037144 2037149) (-1190 "TABLBUMP.spad" 2033438 2033449 2036625 2036630) (-1189 "SYSTEM.spad" 2032666 2032675 2033428 2033433) (-1188 "SYSSOLP.spad" 2030149 2030160 2032656 2032661) (-1187 "SYSPTR.spad" 2030048 2030057 2030139 2030144) (-1186 "SYSNNI.spad" 2029230 2029241 2030038 2030043) (-1185 "SYSINT.spad" 2028634 2028645 2029220 2029225) (-1184 "SYNTAX.spad" 2024840 2024849 2028624 2028629) (-1183 "SYMTAB.spad" 2022908 2022917 2024830 2024835) (-1182 "SYMS.spad" 2018931 2018940 2022898 2022903) (-1181 "SYMPOLY.spad" 2017938 2017949 2018020 2018147) (-1180 "SYMFUNC.spad" 2017439 2017450 2017928 2017933) (-1179 "SYMBOL.spad" 2014942 2014951 2017429 2017434) (-1178 "SWITCH.spad" 2011713 2011722 2014932 2014937) (-1177 "SUTS.spad" 2008618 2008646 2010180 2010277) (-1176 "SUPXS.spad" 2005759 2005787 2006750 2006899) (-1175 "SUP.spad" 2002572 2002583 2003345 2003498) (-1174 "SUPFRACF.spad" 2001677 2001695 2002562 2002567) (-1173 "SUP2.spad" 2001069 2001082 2001667 2001672) (-1172 "SUMRF.spad" 2000043 2000054 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1833290 1833568 1833573) (-1097 "SEGXCAT.spad" 1832437 1832450 1833271 1833276) (-1096 "SEG.spad" 1832250 1832261 1832356 1832361) (-1095 "SEGCAT.spad" 1831175 1831186 1832240 1832245) (-1094 "SEGBIND.spad" 1830933 1830944 1831122 1831127) (-1093 "SEGBIND2.spad" 1830631 1830644 1830923 1830928) (-1092 "SEGAST.spad" 1830345 1830354 1830621 1830626) (-1091 "SEG2.spad" 1829780 1829793 1830301 1830306) (-1090 "SDVAR.spad" 1829056 1829067 1829770 1829775) (-1089 "SDPOL.spad" 1826482 1826493 1826773 1826900) (-1088 "SCPKG.spad" 1824571 1824582 1826472 1826477) (-1087 "SCOPE.spad" 1823724 1823733 1824561 1824566) (-1086 "SCACHE.spad" 1822420 1822431 1823714 1823719) (-1085 "SASTCAT.spad" 1822329 1822338 1822410 1822415) (-1084 "SAOS.spad" 1822201 1822210 1822319 1822324) (-1083 "SAERFFC.spad" 1821914 1821934 1822191 1822196) (-1082 "SAE.spad" 1820089 1820105 1820700 1820835) (-1081 "SAEFACT.spad" 1819790 1819810 1820079 1820084) (-1080 "RURPK.spad" 1817449 1817465 1819780 1819785) (-1079 "RULESET.spad" 1816902 1816926 1817439 1817444) (-1078 "RULE.spad" 1815142 1815166 1816892 1816897) (-1077 "RULECOLD.spad" 1814994 1815007 1815132 1815137) (-1076 "RTVALUE.spad" 1814729 1814738 1814984 1814989) (-1075 "RSTRCAST.spad" 1814446 1814455 1814719 1814724) (-1074 "RSETGCD.spad" 1810824 1810844 1814436 1814441) (-1073 "RSETCAT.spad" 1800760 1800777 1810792 1810819) (-1072 "RSETCAT.spad" 1790716 1790735 1800750 1800755) (-1071 "RSDCMPK.spad" 1789168 1789188 1790706 1790711) (-1070 "RRCC.spad" 1787552 1787582 1789158 1789163) (-1069 "RRCC.spad" 1785934 1785966 1787542 1787547) (-1068 "RPTAST.spad" 1785636 1785645 1785924 1785929) (-1067 "RPOLCAT.spad" 1764996 1765011 1785504 1785631) (-1066 "RPOLCAT.spad" 1744070 1744087 1764580 1764585) (-1065 "ROUTINE.spad" 1739953 1739962 1742717 1742744) (-1064 "ROMAN.spad" 1739281 1739290 1739819 1739948) (-1063 "ROIRC.spad" 1738361 1738393 1739271 1739276) (-1062 "RNS.spad" 1737264 1737273 1738263 1738356) (-1061 "RNS.spad" 1736253 1736264 1737254 1737259) (-1060 "RNG.spad" 1735988 1735997 1736243 1736248) (-1059 "RNGBIND.spad" 1735148 1735162 1735943 1735948) (-1058 "RMODULE.spad" 1734913 1734924 1735138 1735143) (-1057 "RMCAT2.spad" 1734333 1734390 1734903 1734908) (-1056 "RMATRIX.spad" 1733157 1733176 1733500 1733539) (-1055 "RMATCAT.spad" 1728736 1728767 1733113 1733152) (-1054 "RMATCAT.spad" 1724205 1724238 1728584 1728589) (-1053 "RLINSET.spad" 1723599 1723610 1724195 1724200) (-1052 "RINTERP.spad" 1723487 1723507 1723589 1723594) (-1051 "RING.spad" 1722957 1722966 1723467 1723482) (-1050 "RING.spad" 1722435 1722446 1722947 1722952) (-1049 "RIDIST.spad" 1721827 1721836 1722425 1722430) (-1048 "RGCHAIN.spad" 1720410 1720426 1721312 1721339) (-1047 "RGBCSPC.spad" 1720191 1720203 1720400 1720405) (-1046 "RGBCMDL.spad" 1719721 1719733 1720181 1720186) (-1045 "RF.spad" 1717363 1717374 1719711 1719716) (-1044 "RFFACTOR.spad" 1716825 1716836 1717353 1717358) (-1043 "RFFACT.spad" 1716560 1716572 1716815 1716820) (-1042 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1685469 1685474) (-1023 "REAL0Q.spad" 1682649 1682664 1685341 1685346) (-1022 "REAL0.spad" 1679493 1679508 1682639 1682644) (-1021 "RDUCEAST.spad" 1679214 1679223 1679483 1679488) (-1020 "RDIV.spad" 1678869 1678894 1679204 1679209) (-1019 "RDIST.spad" 1678436 1678447 1678859 1678864) (-1018 "RDETRS.spad" 1677300 1677318 1678426 1678431) (-1017 "RDETR.spad" 1675439 1675457 1677290 1677295) (-1016 "RDEEFS.spad" 1674538 1674555 1675429 1675434) (-1015 "RDEEF.spad" 1673548 1673565 1674528 1674533) (-1014 "RCFIELD.spad" 1670734 1670743 1673450 1673543) (-1013 "RCFIELD.spad" 1668006 1668017 1670724 1670729) (-1012 "RCAGG.spad" 1665934 1665945 1667996 1668001) (-1011 "RCAGG.spad" 1663789 1663802 1665853 1665858) (-1010 "RATRET.spad" 1663149 1663160 1663779 1663784) (-1009 "RATFACT.spad" 1662841 1662853 1663139 1663144) (-1008 "RANDSRC.spad" 1662160 1662169 1662831 1662836) (-1007 "RADUTIL.spad" 1661916 1661925 1662150 1662155) (-1006 "RADIX.spad" 1658837 1658851 1660383 1660476) (-1005 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1633208) (-986 "PUSHVAR.spad" 1629968 1629987 1630619 1630624) (-985 "PTRANFN.spad" 1626096 1626106 1629958 1629963) (-984 "PTPACK.spad" 1623184 1623194 1626086 1626091) (-983 "PTFUNC2.spad" 1623007 1623021 1623174 1623179) (-982 "PTCAT.spad" 1622262 1622272 1622975 1623002) (-981 "PSQFR.spad" 1621569 1621593 1622252 1622257) (-980 "PSEUDLIN.spad" 1620455 1620465 1621559 1621564) (-979 "PSETPK.spad" 1605888 1605904 1620333 1620338) (-978 "PSETCAT.spad" 1599808 1599831 1605868 1605883) (-977 "PSETCAT.spad" 1593702 1593727 1599764 1599769) (-976 "PSCURVE.spad" 1592685 1592693 1593692 1593697) (-975 "PSCAT.spad" 1591468 1591497 1592583 1592680) (-974 "PSCAT.spad" 1590341 1590372 1591458 1591463) (-973 "PRTITION.spad" 1589302 1589310 1590331 1590336) (-972 "PRTDAST.spad" 1589021 1589029 1589292 1589297) (-971 "PRS.spad" 1578583 1578600 1588977 1588982) (-970 "PRQAGG.spad" 1578018 1578028 1578551 1578578) (-969 "PROPLOG.spad" 1577317 1577325 1578008 1578013) (-968 "PROPFRML.spad" 1576133 1576144 1577307 1577312) (-967 "PROPERTY.spad" 1575621 1575629 1576123 1576128) (-966 "PRODUCT.spad" 1573303 1573315 1573587 1573642) (-965 "PR.spad" 1571695 1571707 1572394 1572521) (-964 "PRINT.spad" 1571447 1571455 1571685 1571690) (-963 "PRIMES.spad" 1569700 1569710 1571437 1571442) (-962 "PRIMELT.spad" 1567781 1567795 1569690 1569695) (-961 "PRIMCAT.spad" 1567408 1567416 1567771 1567776) (-960 "PRIMARR.spad" 1566413 1566423 1566591 1566618) (-959 "PRIMARR2.spad" 1565180 1565192 1566403 1566408) (-958 "PREASSOC.spad" 1564562 1564574 1565170 1565175) (-957 "PPCURVE.spad" 1563699 1563707 1564552 1564557) (-956 "PORTNUM.spad" 1563474 1563482 1563689 1563694) (-955 "POLYROOT.spad" 1562323 1562345 1563430 1563435) (-954 "POLY.spad" 1559658 1559668 1560173 1560300) (-953 "POLYLIFT.spad" 1558923 1558946 1559648 1559653) (-952 "POLYCATQ.spad" 1557041 1557063 1558913 1558918) (-951 "POLYCAT.spad" 1550511 1550532 1556909 1557036) (-950 "POLYCAT.spad" 1543319 1543342 1549719 1549724) (-949 "POLY2UP.spad" 1542771 1542785 1543309 1543314) (-948 "POLY2.spad" 1542368 1542380 1542761 1542766) (-947 "POLUTIL.spad" 1541309 1541338 1542324 1542329) (-946 "POLTOPOL.spad" 1540057 1540072 1541299 1541304) (-945 "POINT.spad" 1538895 1538905 1538982 1539009) (-944 "PNTHEORY.spad" 1535597 1535605 1538885 1538890) (-943 "PMTOOLS.spad" 1534372 1534386 1535587 1535592) (-942 "PMSYM.spad" 1533921 1533931 1534362 1534367) (-941 "PMQFCAT.spad" 1533512 1533526 1533911 1533916) (-940 "PMPRED.spad" 1532991 1533005 1533502 1533507) (-939 "PMPREDFS.spad" 1532445 1532467 1532981 1532986) (-938 "PMPLCAT.spad" 1531525 1531543 1532377 1532382) (-937 "PMLSAGG.spad" 1531110 1531124 1531515 1531520) (-936 "PMKERNEL.spad" 1530689 1530701 1531100 1531105) (-935 "PMINS.spad" 1530269 1530279 1530679 1530684) (-934 "PMFS.spad" 1529846 1529864 1530259 1530264) (-933 "PMDOWN.spad" 1529136 1529150 1529836 1529841) (-932 "PMASS.spad" 1528146 1528154 1529126 1529131) (-931 "PMASSFS.spad" 1527113 1527129 1528136 1528141) (-930 "PLOTTOOL.spad" 1526893 1526901 1527103 1527108) (-929 "PLOT.spad" 1521816 1521824 1526883 1526888) (-928 "PLOT3D.spad" 1518280 1518288 1521806 1521811) (-927 "PLOT1.spad" 1517437 1517447 1518270 1518275) (-926 "PLEQN.spad" 1504727 1504754 1517427 1517432) (-925 "PINTERP.spad" 1504349 1504368 1504717 1504722) (-924 "PINTERPA.spad" 1504133 1504149 1504339 1504344) (-923 "PI.spad" 1503742 1503750 1504107 1504128) (-922 "PID.spad" 1502712 1502720 1503668 1503737) (-921 "PICOERCE.spad" 1502369 1502379 1502702 1502707) (-920 "PGROEB.spad" 1500970 1500984 1502359 1502364) (-919 "PGE.spad" 1492587 1492595 1500960 1500965) (-918 "PGCD.spad" 1491477 1491494 1492577 1492582) (-917 "PFRPAC.spad" 1490626 1490636 1491467 1491472) (-916 "PFR.spad" 1487289 1487299 1490528 1490621) (-915 "PFOTOOLS.spad" 1486547 1486563 1487279 1487284) (-914 "PFOQ.spad" 1485917 1485935 1486537 1486542) (-913 "PFO.spad" 1485336 1485363 1485907 1485912) (-912 "PF.spad" 1484910 1484922 1485141 1485234) 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1443594) (-892 "PATTERN1.spad" 1441673 1441689 1443327 1443332) (-891 "PATRES.spad" 1439248 1439260 1441663 1441668) (-890 "PATRES2.spad" 1438920 1438934 1439238 1439243) (-889 "PATMATCH.spad" 1437117 1437148 1438628 1438633) (-888 "PATMAB.spad" 1436546 1436556 1437107 1437112) (-887 "PATLRES.spad" 1435632 1435646 1436536 1436541) (-886 "PATAB.spad" 1435396 1435406 1435622 1435627) (-885 "PARTPERM.spad" 1432796 1432804 1435386 1435391) (-884 "PARSURF.spad" 1432230 1432258 1432786 1432791) (-883 "PARSU2.spad" 1432027 1432043 1432220 1432225) (-882 "script-parser.spad" 1431547 1431555 1432017 1432022) (-881 "PARSCURV.spad" 1430981 1431009 1431537 1431542) (-880 "PARSC2.spad" 1430772 1430788 1430971 1430976) (-879 "PARPCURV.spad" 1430234 1430262 1430762 1430767) (-878 "PARPC2.spad" 1430025 1430041 1430224 1430229) (-877 "PARAMAST.spad" 1429153 1429161 1430015 1430020) (-876 "PAN2EXPR.spad" 1428565 1428573 1429143 1429148) (-875 "PALETTE.spad" 1427535 1427543 1428555 1428560) (-874 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1018161) (-648 "LMDICT.spad" 1017221 1017231 1017485 1017512) (-647 "LLINSET.spad" 1016618 1016628 1017211 1017216) (-646 "LITERAL.spad" 1016524 1016535 1016608 1016613) (-645 "LIST.spad" 1014259 1014269 1015671 1015698) (-644 "LIST3.spad" 1013570 1013584 1014249 1014254) (-643 "LIST2.spad" 1012272 1012284 1013560 1013565) (-642 "LIST2MAP.spad" 1009175 1009187 1012262 1012267) (-641 "LINSET.spad" 1008797 1008807 1009165 1009170) (-640 "LINEXP.spad" 1008231 1008241 1008777 1008792) (-639 "LINDEP.spad" 1007040 1007052 1008143 1008148) (-638 "LIMITRF.spad" 1004968 1004978 1007030 1007035) (-637 "LIMITPS.spad" 1003871 1003884 1004958 1004963) (-636 "LIE.spad" 1001887 1001899 1003161 1003306) (-635 "LIECAT.spad" 1001363 1001373 1001813 1001882) (-634 "LIECAT.spad" 1000867 1000879 1001319 1001324) (-633 "LIB.spad" 998917 998925 999526 999541) (-632 "LGROBP.spad" 996270 996289 998907 998912) (-631 "LF.spad" 995225 995241 996260 996265) (-630 "LFCAT.spad" 994284 994292 995215 995220) (-629 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290622 292414 292419) (-240 "DIRPROD.spad" 280194 280210 280834 280965) (-239 "DIRPROD2.spad" 279012 279030 280184 280189) (-238 "DIRPCAT.spad" 277956 277972 278876 279007) (-237 "DIRPCAT.spad" 276629 276647 277551 277556) (-236 "DIOSP.spad" 275454 275462 276619 276624) (-235 "DIOPS.spad" 274450 274460 275434 275449) (-234 "DIOPS.spad" 273420 273432 274406 274411) (-233 "DIFRING.spad" 272716 272724 273400 273415) (-232 "DIFRING.spad" 272020 272030 272706 272711) (-231 "DIFEXT.spad" 271191 271201 272000 272015) (-230 "DIFEXT.spad" 270279 270291 271090 271095) (-229 "DIAGG.spad" 269909 269919 270259 270274) (-228 "DIAGG.spad" 269547 269559 269899 269904) (-227 "DHMATRIX.spad" 267859 267869 269004 269031) (-226 "DFSFUN.spad" 261499 261507 267849 267854) (-225 "DFLOAT.spad" 258230 258238 261389 261494) (-224 "DFINTTLS.spad" 256461 256477 258220 258225) (-223 "DERHAM.spad" 254375 254407 256441 256456) (-222 "DEQUEUE.spad" 253699 253709 253982 254009) (-221 "DEGRED.spad" 253316 253330 253689 253694) (-220 "DEFINTRF.spad" 250853 250863 253306 253311) (-219 "DEFINTEF.spad" 249363 249379 250843 250848) (-218 "DEFAST.spad" 248731 248739 249353 249358) (-217 "DECIMAL.spad" 246837 246845 247198 247291) (-216 "DDFACT.spad" 244650 244667 246827 246832) (-215 "DBLRESP.spad" 244250 244274 244640 244645) (-214 "DBASE.spad" 242914 242924 244240 244245) (-213 "DATAARY.spad" 242376 242389 242904 242909) (-212 "D03FAFA.spad" 242204 242212 242366 242371) (-211 "D03EEFA.spad" 242024 242032 242194 242199) (-210 "D03AGNT.spad" 241110 241118 242014 242019) (-209 "D02EJFA.spad" 240572 240580 241100 241105) (-208 "D02CJFA.spad" 240050 240058 240562 240567) (-207 "D02BHFA.spad" 239540 239548 240040 240045) (-206 "D02BBFA.spad" 239030 239038 239530 239535) (-205 "D02AGNT.spad" 233844 233852 239020 239025) (-204 "D01WGTS.spad" 232163 232171 233834 233839) (-203 "D01TRNS.spad" 232140 232148 232153 232158) (-202 "D01GBFA.spad" 231662 231670 232130 232135) (-201 "D01FCFA.spad" 231184 231192 231652 231657) (-200 "D01ASFA.spad" 230652 230660 231174 231179) (-199 "D01AQFA.spad" 230098 230106 230642 230647) (-198 "D01APFA.spad" 229522 229530 230088 230093) (-197 "D01ANFA.spad" 229016 229024 229512 229517) (-196 "D01AMFA.spad" 228526 228534 229006 229011) (-195 "D01ALFA.spad" 228066 228074 228516 228521) (-194 "D01AKFA.spad" 227592 227600 228056 228061) (-193 "D01AJFA.spad" 227115 227123 227582 227587) (-192 "D01AGNT.spad" 223182 223190 227105 227110) (-191 "CYCLOTOM.spad" 222688 222696 223172 223177) (-190 "CYCLES.spad" 219544 219552 222678 222683) (-189 "CVMP.spad" 218961 218971 219534 219539) (-188 "CTRIGMNP.spad" 217461 217477 218951 218956) (-187 "CTOR.spad" 217152 217160 217451 217456) (-186 "CTORKIND.spad" 216755 216763 217142 217147) (-185 "CTORCAT.spad" 216004 216012 216745 216750) (-184 "CTORCAT.spad" 215251 215261 215994 215999) (-183 "CTORCALL.spad" 214840 214850 215241 215246) (-182 "CSTTOOLS.spad" 214085 214098 214830 214835) (-181 "CRFP.spad" 207809 207822 214075 214080) (-180 "CRCEAST.spad" 207529 207537 207799 207804) (-179 "CRAPACK.spad" 206580 206590 207519 207524) (-178 "CPMATCH.spad" 206084 206099 206505 206510) (-177 "CPIMA.spad" 205789 205808 206074 206079) (-176 "COORDSYS.spad" 200798 200808 205779 205784) (-175 "CONTOUR.spad" 200209 200217 200788 200793) (-174 "CONTFRAC.spad" 195959 195969 200111 200204) (-173 "CONDUIT.spad" 195717 195725 195949 195954) (-172 "COMRING.spad" 195391 195399 195655 195712) (-171 "COMPPROP.spad" 194909 194917 195381 195386) (-170 "COMPLPAT.spad" 194676 194691 194899 194904) (-169 "COMPLEX.spad" 188813 188823 189057 189318) (-168 "COMPLEX2.spad" 188528 188540 188803 188808) (-167 "COMPFACT.spad" 188130 188144 188518 188523) (-166 "COMPCAT.spad" 186202 186212 187864 188125) (-165 "COMPCAT.spad" 184002 184014 185666 185671) (-164 "COMMUPC.spad" 183750 183768 183992 183997) (-163 "COMMONOP.spad" 183283 183291 183740 183745) (-162 "COMM.spad" 183094 183102 183273 183278) (-161 "COMMAAST.spad" 182857 182865 183084 183089) (-160 "COMBOPC.spad" 181772 181780 182847 182852) (-159 "COMBINAT.spad" 180539 180549 181762 181767) (-158 "COMBF.spad" 177921 177937 180529 180534) (-157 "COLOR.spad" 176758 176766 177911 177916) (-156 "COLONAST.spad" 176424 176432 176748 176753) (-155 "CMPLXRT.spad" 176135 176152 176414 176419) (-154 "CLLCTAST.spad" 175797 175805 176125 176130) (-153 "CLIP.spad" 171905 171913 175787 175792) (-152 "CLIF.spad" 170560 170576 171861 171900) (-151 "CLAGG.spad" 167065 167075 170550 170555) (-150 "CLAGG.spad" 163441 163453 166928 166933) (-149 "CINTSLPE.spad" 162772 162785 163431 163436) (-148 "CHVAR.spad" 160910 160932 162762 162767) (-147 "CHARZ.spad" 160825 160833 160890 160905) (-146 "CHARPOL.spad" 160335 160345 160815 160820) (-145 "CHARNZ.spad" 160088 160096 160315 160330) (-144 "CHAR.spad" 157962 157970 160078 160083) (-143 "CFCAT.spad" 157290 157298 157952 157957) (-142 "CDEN.spad" 156486 156500 157280 157285) (-141 "CCLASS.spad" 154635 154643 155897 155936) (-140 "CATEGORY.spad" 153677 153685 154625 154630) (-139 "CATCTOR.spad" 153568 153576 153667 153672) (-138 "CATAST.spad" 153186 153194 153558 153563) (-137 "CASEAST.spad" 152900 152908 153176 153181) (-136 "CARTEN.spad" 148187 148211 152890 152895) (-135 "CARTEN2.spad" 147577 147604 148177 148182) (-134 "CARD.spad" 144872 144880 147551 147572) (-133 "CAPSLAST.spad" 144646 144654 144862 144867) (-132 "CACHSET.spad" 144270 144278 144636 144641) (-131 "CABMON.spad" 143825 143833 144260 144265) (-130 "BYTEORD.spad" 143500 143508 143815 143820) (-129 "BYTE.spad" 142927 142935 143490 143495) (-128 "BYTEBUF.spad" 140786 140794 142096 142123) (-127 "BTREE.spad" 139859 139869 140393 140420) (-126 "BTOURN.spad" 138864 138874 139466 139493) (-125 "BTCAT.spad" 138256 138266 138832 138859) (-124 "BTCAT.spad" 137668 137680 138246 138251) (-123 "BTAGG.spad" 136796 136804 137636 137663) (-122 "BTAGG.spad" 135944 135954 136786 136791) (-121 "BSTREE.spad" 134685 134695 135551 135578) (-120 "BRILL.spad" 132882 132893 134675 134680) (-119 "BRAGG.spad" 131822 131832 132872 132877) (-118 "BRAGG.spad" 130726 130738 131778 131783) (-117 "BPADICRT.spad" 128707 128719 128962 129055) (-116 "BPADIC.spad" 128371 128383 128633 128702) (-115 "BOUNDZRO.spad" 128027 128044 128361 128366) (-114 "BOP.spad" 123209 123217 128017 128022) (-113 "BOP1.spad" 120675 120685 123199 123204) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2264843 2264848 2264853 2264858) (-2 NIL 2264823 2264828 2264833 2264838) (-1 NIL 2264803 2264808 2264813 2264818) (0 NIL 2264783 2264788 2264793 2264798) (-1297 "ZMOD.spad" 2264592 2264605 2264721 2264778) (-1296 "ZLINDEP.spad" 2263658 2263669 2264582 2264587) (-1295 "ZDSOLVE.spad" 2253603 2253625 2263648 2263653) (-1294 "YSTREAM.spad" 2253098 2253109 2253593 2253598) (-1293 "XRPOLY.spad" 2252318 2252338 2252954 2253023) (-1292 "XPR.spad" 2250113 2250126 2252036 2252135) (-1291 "XPOLY.spad" 2249668 2249679 2249969 2250038) (-1290 "XPOLYC.spad" 2248987 2249003 2249594 2249663) (-1289 "XPBWPOLY.spad" 2247424 2247444 2248767 2248836) (-1288 "XF.spad" 2245887 2245902 2247326 2247419) (-1287 "XF.spad" 2244330 2244347 2245771 2245776) (-1286 "XFALG.spad" 2241378 2241394 2244256 2244325) (-1285 "XEXPPKG.spad" 2240629 2240655 2241368 2241373) (-1284 "XDPOLY.spad" 2240243 2240259 2240485 2240554) (-1283 "XALG.spad" 2239903 2239914 2240199 2240238) (-1282 "WUTSET.spad" 2235742 2235759 2239549 2239576) (-1281 "WP.spad" 2234941 2234985 2235600 2235667) (-1280 "WHILEAST.spad" 2234739 2234748 2234931 2234936) (-1279 "WHEREAST.spad" 2234410 2234419 2234729 2234734) (-1278 "WFFINTBS.spad" 2232073 2232095 2234400 2234405) (-1277 "WEIER.spad" 2230295 2230306 2232063 2232068) (-1276 "VSPACE.spad" 2229968 2229979 2230263 2230290) (-1275 "VSPACE.spad" 2229661 2229674 2229958 2229963) (-1274 "VOID.spad" 2229338 2229347 2229651 2229656) (-1273 "VIEW.spad" 2227018 2227027 2229328 2229333) (-1272 "VIEWDEF.spad" 2222219 2222228 2227008 2227013) (-1271 "VIEW3D.spad" 2206180 2206189 2222209 2222214) (-1270 "VIEW2D.spad" 2194071 2194080 2206170 2206175) (-1269 "VECTOR.spad" 2192745 2192756 2192996 2193023) (-1268 "VECTOR2.spad" 2191384 2191397 2192735 2192740) (-1267 "VECTCAT.spad" 2189288 2189299 2191352 2191379) (-1266 "VECTCAT.spad" 2186999 2187012 2189065 2189070) (-1265 "VARIABLE.spad" 2186779 2186794 2186989 2186994) (-1264 "UTYPE.spad" 2186423 2186432 2186769 2186774) (-1263 "UTSODETL.spad" 2185718 2185742 2186379 2186384) (-1262 "UTSODE.spad" 2183934 2183954 2185708 2185713) (-1261 "UTS.spad" 2178747 2178775 2182401 2182498) (-1260 "UTSCAT.spad" 2176226 2176242 2178645 2178742) (-1259 "UTSCAT.spad" 2173349 2173367 2175770 2175775) (-1258 "UTS2.spad" 2172944 2172979 2173339 2173344) (-1257 "URAGG.spad" 2167617 2167628 2172934 2172939) (-1256 "URAGG.spad" 2162254 2162267 2167573 2167578) (-1255 "UPXSSING.spad" 2159899 2159925 2161335 2161468) (-1254 "UPXS.spad" 2157053 2157081 2158031 2158180) (-1253 "UPXSCONS.spad" 2154812 2154832 2155185 2155334) (-1252 "UPXSCCA.spad" 2153383 2153403 2154658 2154807) (-1251 "UPXSCCA.spad" 2152096 2152118 2153373 2153378) (-1250 "UPXSCAT.spad" 2150685 2150701 2151942 2152091) (-1249 "UPXS2.spad" 2150228 2150281 2150675 2150680) (-1248 "UPSQFREE.spad" 2148642 2148656 2150218 2150223) (-1247 "UPSCAT.spad" 2146253 2146277 2148540 2148637) (-1246 "UPSCAT.spad" 2143570 2143596 2145859 2145864) (-1245 "UPOLYC.spad" 2138610 2138621 2143412 2143565) (-1244 "UPOLYC.spad" 2133542 2133555 2138346 2138351) (-1243 "UPOLYC2.spad" 2133013 2133032 2133532 2133537) (-1242 "UP.spad" 2130212 2130227 2130599 2130752) (-1241 "UPMP.spad" 2129112 2129125 2130202 2130207) (-1240 "UPDIVP.spad" 2128677 2128691 2129102 2129107) (-1239 "UPDECOMP.spad" 2126922 2126936 2128667 2128672) (-1238 "UPCDEN.spad" 2126131 2126147 2126912 2126917) (-1237 "UP2.spad" 2125495 2125516 2126121 2126126) (-1236 "UNISEG.spad" 2124848 2124859 2125414 2125419) (-1235 "UNISEG2.spad" 2124345 2124358 2124804 2124809) (-1234 "UNIFACT.spad" 2123448 2123460 2124335 2124340) (-1233 "ULS.spad" 2114006 2114034 2115093 2115522) (-1232 "ULSCONS.spad" 2106402 2106422 2106772 2106921) (-1231 "ULSCCAT.spad" 2104139 2104159 2106248 2106397) (-1230 "ULSCCAT.spad" 2101984 2102006 2104095 2104100) (-1229 "ULSCAT.spad" 2100216 2100232 2101830 2101979) (-1228 "ULS2.spad" 2099730 2099783 2100206 2100211) (-1227 "UINT8.spad" 2099607 2099616 2099720 2099725) (-1226 "UINT64.spad" 2099483 2099492 2099597 2099602) (-1225 "UINT32.spad" 2099359 2099368 2099473 2099478) (-1224 "UINT16.spad" 2099235 2099244 2099349 2099354) (-1223 "UFD.spad" 2098300 2098309 2099161 2099230) (-1222 "UFD.spad" 2097427 2097438 2098290 2098295) (-1221 "UDVO.spad" 2096308 2096317 2097417 2097422) (-1220 "UDPO.spad" 2093801 2093812 2096264 2096269) (-1219 "TYPE.spad" 2093733 2093742 2093791 2093796) (-1218 "TYPEAST.spad" 2093652 2093661 2093723 2093728) (-1217 "TWOFACT.spad" 2092304 2092319 2093642 2093647) (-1216 "TUPLE.spad" 2091790 2091801 2092203 2092208) (-1215 "TUBETOOL.spad" 2088657 2088666 2091780 2091785) (-1214 "TUBE.spad" 2087304 2087321 2088647 2088652) (-1213 "TS.spad" 2085903 2085919 2086869 2086966) (-1212 "TSETCAT.spad" 2073030 2073047 2085871 2085898) (-1211 "TSETCAT.spad" 2060143 2060162 2072986 2072991) (-1210 "TRMANIP.spad" 2054509 2054526 2059849 2059854) (-1209 "TRIMAT.spad" 2053472 2053497 2054499 2054504) (-1208 "TRIGMNIP.spad" 2051999 2052016 2053462 2053467) (-1207 "TRIGCAT.spad" 2051511 2051520 2051989 2051994) (-1206 "TRIGCAT.spad" 2051021 2051032 2051501 2051506) (-1205 "TREE.spad" 2049596 2049607 2050628 2050655) (-1204 "TRANFUN.spad" 2049435 2049444 2049586 2049591) (-1203 "TRANFUN.spad" 2049272 2049283 2049425 2049430) (-1202 "TOPSP.spad" 2048946 2048955 2049262 2049267) (-1201 "TOOLSIGN.spad" 2048609 2048620 2048936 2048941) (-1200 "TEXTFILE.spad" 2047170 2047179 2048599 2048604) (-1199 "TEX.spad" 2044316 2044325 2047160 2047165) (-1198 "TEX1.spad" 2043872 2043883 2044306 2044311) (-1197 "TEMUTL.spad" 2043427 2043436 2043862 2043867) (-1196 "TBCMPPK.spad" 2041520 2041543 2043417 2043422) (-1195 "TBAGG.spad" 2040570 2040593 2041500 2041515) (-1194 "TBAGG.spad" 2039628 2039653 2040560 2040565) (-1193 "TANEXP.spad" 2039036 2039047 2039618 2039623) (-1192 "TABLE.spad" 2037447 2037470 2037717 2037744) (-1191 "TABLEAU.spad" 2036928 2036939 2037437 2037442) (-1190 "TABLBUMP.spad" 2033731 2033742 2036918 2036923) (-1189 "SYSTEM.spad" 2032959 2032968 2033721 2033726) (-1188 "SYSSOLP.spad" 2030442 2030453 2032949 2032954) (-1187 "SYSPTR.spad" 2030341 2030350 2030432 2030437) (-1186 "SYSNNI.spad" 2029523 2029534 2030331 2030336) (-1185 "SYSINT.spad" 2028927 2028938 2029513 2029518) (-1184 "SYNTAX.spad" 2025133 2025142 2028917 2028922) (-1183 "SYMTAB.spad" 2023201 2023210 2025123 2025128) (-1182 "SYMS.spad" 2019224 2019233 2023191 2023196) (-1181 "SYMPOLY.spad" 2018231 2018242 2018313 2018440) (-1180 "SYMFUNC.spad" 2017732 2017743 2018221 2018226) (-1179 "SYMBOL.spad" 2015235 2015244 2017722 2017727) (-1178 "SWITCH.spad" 2012006 2012015 2015225 2015230) (-1177 "SUTS.spad" 2008911 2008939 2010473 2010570) (-1176 "SUPXS.spad" 2006052 2006080 2007043 2007192) (-1175 "SUP.spad" 2002865 2002876 2003638 2003791) (-1174 "SUPFRACF.spad" 2001970 2001988 2002855 2002860) (-1173 "SUP2.spad" 2001362 2001375 2001960 2001965) (-1172 "SUMRF.spad" 2000336 2000347 2001352 2001357) (-1171 "SUMFS.spad" 1999973 1999990 2000326 2000331) (-1170 "SULS.spad" 1990518 1990546 1991618 1992047) (-1169 "SUCHTAST.spad" 1990287 1990296 1990508 1990513) (-1168 "SUCH.spad" 1989969 1989984 1990277 1990282) (-1167 "SUBSPACE.spad" 1982084 1982099 1989959 1989964) (-1166 "SUBRESP.spad" 1981254 1981268 1982040 1982045) (-1165 "STTF.spad" 1977353 1977369 1981244 1981249) (-1164 "STTFNC.spad" 1973821 1973837 1977343 1977348) (-1163 "STTAYLOR.spad" 1966475 1966486 1973702 1973707) (-1162 "STRTBL.spad" 1964980 1964997 1965129 1965156) (-1161 "STRING.spad" 1964389 1964398 1964403 1964430) (-1160 "STRICAT.spad" 1964177 1964186 1964357 1964384) (-1159 "STREAM.spad" 1961095 1961106 1963702 1963717) (-1158 "STREAM3.spad" 1960668 1960683 1961085 1961090) (-1157 "STREAM2.spad" 1959796 1959809 1960658 1960663) (-1156 "STREAM1.spad" 1959502 1959513 1959786 1959791) (-1155 "STINPROD.spad" 1958438 1958454 1959492 1959497) (-1154 "STEP.spad" 1957639 1957648 1958428 1958433) (-1153 "STEPAST.spad" 1956873 1956882 1957629 1957634) (-1152 "STBL.spad" 1955399 1955427 1955566 1955581) (-1151 "STAGG.spad" 1954474 1954485 1955389 1955394) (-1150 "STAGG.spad" 1953547 1953560 1954464 1954469) (-1149 "STACK.spad" 1952904 1952915 1953154 1953181) (-1148 "SREGSET.spad" 1950608 1950625 1952550 1952577) (-1147 "SRDCMPK.spad" 1949169 1949189 1950598 1950603) (-1146 "SRAGG.spad" 1944312 1944321 1949137 1949164) (-1145 "SRAGG.spad" 1939475 1939486 1944302 1944307) (-1144 "SQMATRIX.spad" 1937091 1937109 1938007 1938094) (-1143 "SPLTREE.spad" 1931643 1931656 1936527 1936554) (-1142 "SPLNODE.spad" 1928231 1928244 1931633 1931638) (-1141 "SPFCAT.spad" 1927040 1927049 1928221 1928226) (-1140 "SPECOUT.spad" 1925592 1925601 1927030 1927035) (-1139 "SPADXPT.spad" 1917187 1917196 1925582 1925587) (-1138 "spad-parser.spad" 1916652 1916661 1917177 1917182) (-1137 "SPADAST.spad" 1916353 1916362 1916642 1916647) (-1136 "SPACEC.spad" 1900552 1900563 1916343 1916348) (-1135 "SPACE3.spad" 1900328 1900339 1900542 1900547) (-1134 "SORTPAK.spad" 1899877 1899890 1900284 1900289) (-1133 "SOLVETRA.spad" 1897640 1897651 1899867 1899872) (-1132 "SOLVESER.spad" 1896168 1896179 1897630 1897635) (-1131 "SOLVERAD.spad" 1892194 1892205 1896158 1896163) (-1130 "SOLVEFOR.spad" 1890656 1890674 1892184 1892189) (-1129 "SNTSCAT.spad" 1890256 1890273 1890624 1890651) (-1128 "SMTS.spad" 1888528 1888554 1889821 1889918) (-1127 "SMP.spad" 1886003 1886023 1886393 1886520) (-1126 "SMITH.spad" 1884848 1884873 1885993 1885998) (-1125 "SMATCAT.spad" 1882958 1882988 1884792 1884843) (-1124 "SMATCAT.spad" 1881000 1881032 1882836 1882841) (-1123 "SKAGG.spad" 1879963 1879974 1880968 1880995) (-1122 "SINT.spad" 1878795 1878804 1879829 1879958) (-1121 "SIMPAN.spad" 1878523 1878532 1878785 1878790) (-1120 "SIG.spad" 1877853 1877862 1878513 1878518) (-1119 "SIGNRF.spad" 1876971 1876982 1877843 1877848) (-1118 "SIGNEF.spad" 1876250 1876267 1876961 1876966) (-1117 "SIGAST.spad" 1875635 1875644 1876240 1876245) (-1116 "SHP.spad" 1873563 1873578 1875591 1875596) (-1115 "SHDP.spad" 1863274 1863301 1863783 1863914) (-1114 "SGROUP.spad" 1862882 1862891 1863264 1863269) (-1113 "SGROUP.spad" 1862488 1862499 1862872 1862877) (-1112 "SGCF.spad" 1855651 1855660 1862478 1862483) (-1111 "SFRTCAT.spad" 1854581 1854598 1855619 1855646) (-1110 "SFRGCD.spad" 1853644 1853664 1854571 1854576) (-1109 "SFQCMPK.spad" 1848281 1848301 1853634 1853639) (-1108 "SFORT.spad" 1847720 1847734 1848271 1848276) (-1107 "SEXOF.spad" 1847563 1847603 1847710 1847715) (-1106 "SEX.spad" 1847455 1847464 1847553 1847558) (-1105 "SEXCAT.spad" 1845056 1845096 1847445 1847450) (-1104 "SET.spad" 1843380 1843391 1844477 1844516) (-1103 "SETMN.spad" 1841830 1841847 1843370 1843375) (-1102 "SETCAT.spad" 1841152 1841161 1841820 1841825) (-1101 "SETCAT.spad" 1840472 1840483 1841142 1841147) (-1100 "SETAGG.spad" 1837021 1837032 1840452 1840467) (-1099 "SETAGG.spad" 1833578 1833591 1837011 1837016) (-1098 "SEQAST.spad" 1833281 1833290 1833568 1833573) (-1097 "SEGXCAT.spad" 1832437 1832450 1833271 1833276) (-1096 "SEG.spad" 1832250 1832261 1832356 1832361) (-1095 "SEGCAT.spad" 1831175 1831186 1832240 1832245) (-1094 "SEGBIND.spad" 1830933 1830944 1831122 1831127) (-1093 "SEGBIND2.spad" 1830631 1830644 1830923 1830928) (-1092 "SEGAST.spad" 1830345 1830354 1830621 1830626) (-1091 "SEG2.spad" 1829780 1829793 1830301 1830306) (-1090 "SDVAR.spad" 1829056 1829067 1829770 1829775) (-1089 "SDPOL.spad" 1826482 1826493 1826773 1826900) (-1088 "SCPKG.spad" 1824571 1824582 1826472 1826477) (-1087 "SCOPE.spad" 1823724 1823733 1824561 1824566) (-1086 "SCACHE.spad" 1822420 1822431 1823714 1823719) (-1085 "SASTCAT.spad" 1822329 1822338 1822410 1822415) (-1084 "SAOS.spad" 1822201 1822210 1822319 1822324) (-1083 "SAERFFC.spad" 1821914 1821934 1822191 1822196) (-1082 "SAE.spad" 1820089 1820105 1820700 1820835) (-1081 "SAEFACT.spad" 1819790 1819810 1820079 1820084) (-1080 "RURPK.spad" 1817449 1817465 1819780 1819785) (-1079 "RULESET.spad" 1816902 1816926 1817439 1817444) (-1078 "RULE.spad" 1815142 1815166 1816892 1816897) (-1077 "RULECOLD.spad" 1814994 1815007 1815132 1815137) (-1076 "RTVALUE.spad" 1814729 1814738 1814984 1814989) (-1075 "RSTRCAST.spad" 1814446 1814455 1814719 1814724) (-1074 "RSETGCD.spad" 1810824 1810844 1814436 1814441) (-1073 "RSETCAT.spad" 1800760 1800777 1810792 1810819) (-1072 "RSETCAT.spad" 1790716 1790735 1800750 1800755) (-1071 "RSDCMPK.spad" 1789168 1789188 1790706 1790711) (-1070 "RRCC.spad" 1787552 1787582 1789158 1789163) (-1069 "RRCC.spad" 1785934 1785966 1787542 1787547) (-1068 "RPTAST.spad" 1785636 1785645 1785924 1785929) (-1067 "RPOLCAT.spad" 1764996 1765011 1785504 1785631) (-1066 "RPOLCAT.spad" 1744070 1744087 1764580 1764585) (-1065 "ROUTINE.spad" 1739953 1739962 1742717 1742744) (-1064 "ROMAN.spad" 1739281 1739290 1739819 1739948) (-1063 "ROIRC.spad" 1738361 1738393 1739271 1739276) (-1062 "RNS.spad" 1737264 1737273 1738263 1738356) (-1061 "RNS.spad" 1736253 1736264 1737254 1737259) (-1060 "RNG.spad" 1735988 1735997 1736243 1736248) (-1059 "RNGBIND.spad" 1735148 1735162 1735943 1735948) (-1058 "RMODULE.spad" 1734913 1734924 1735138 1735143) (-1057 "RMCAT2.spad" 1734333 1734390 1734903 1734908) (-1056 "RMATRIX.spad" 1733157 1733176 1733500 1733539) (-1055 "RMATCAT.spad" 1728736 1728767 1733113 1733152) (-1054 "RMATCAT.spad" 1724205 1724238 1728584 1728589) (-1053 "RLINSET.spad" 1723599 1723610 1724195 1724200) (-1052 "RINTERP.spad" 1723487 1723507 1723589 1723594) (-1051 "RING.spad" 1722957 1722966 1723467 1723482) (-1050 "RING.spad" 1722435 1722446 1722947 1722952) (-1049 "RIDIST.spad" 1721827 1721836 1722425 1722430) (-1048 "RGCHAIN.spad" 1720410 1720426 1721312 1721339) (-1047 "RGBCSPC.spad" 1720191 1720203 1720400 1720405) (-1046 "RGBCMDL.spad" 1719721 1719733 1720181 1720186) (-1045 "RF.spad" 1717363 1717374 1719711 1719716) (-1044 "RFFACTOR.spad" 1716825 1716836 1717353 1717358) (-1043 "RFFACT.spad" 1716560 1716572 1716815 1716820) (-1042 "RFDIST.spad" 1715556 1715565 1716550 1716555) (-1041 "RETSOL.spad" 1714975 1714988 1715546 1715551) (-1040 "RETRACT.spad" 1714403 1714414 1714965 1714970) (-1039 "RETRACT.spad" 1713829 1713842 1714393 1714398) (-1038 "RETAST.spad" 1713641 1713650 1713819 1713824) (-1037 "RESULT.spad" 1711701 1711710 1712288 1712315) (-1036 "RESRING.spad" 1711048 1711095 1711639 1711696) (-1035 "RESLATC.spad" 1710372 1710383 1711038 1711043) (-1034 "REPSQ.spad" 1710103 1710114 1710362 1710367) (-1033 "REP.spad" 1707657 1707666 1710093 1710098) (-1032 "REPDB.spad" 1707364 1707375 1707647 1707652) (-1031 "REP2.spad" 1697022 1697033 1707206 1707211) (-1030 "REP1.spad" 1691218 1691229 1696972 1696977) (-1029 "REGSET.spad" 1689015 1689032 1690864 1690891) (-1028 "REF.spad" 1688350 1688361 1688970 1688975) (-1027 "REDORDER.spad" 1687556 1687573 1688340 1688345) (-1026 "RECLOS.spad" 1686339 1686359 1687043 1687136) (-1025 "REALSOLV.spad" 1685479 1685488 1686329 1686334) (-1024 "REAL.spad" 1685351 1685360 1685469 1685474) (-1023 "REAL0Q.spad" 1682649 1682664 1685341 1685346) (-1022 "REAL0.spad" 1679493 1679508 1682639 1682644) (-1021 "RDUCEAST.spad" 1679214 1679223 1679483 1679488) (-1020 "RDIV.spad" 1678869 1678894 1679204 1679209) (-1019 "RDIST.spad" 1678436 1678447 1678859 1678864) (-1018 "RDETRS.spad" 1677300 1677318 1678426 1678431) (-1017 "RDETR.spad" 1675439 1675457 1677290 1677295) (-1016 "RDEEFS.spad" 1674538 1674555 1675429 1675434) (-1015 "RDEEF.spad" 1673548 1673565 1674528 1674533) (-1014 "RCFIELD.spad" 1670734 1670743 1673450 1673543) (-1013 "RCFIELD.spad" 1668006 1668017 1670724 1670729) (-1012 "RCAGG.spad" 1665934 1665945 1667996 1668001) (-1011 "RCAGG.spad" 1663789 1663802 1665853 1665858) (-1010 "RATRET.spad" 1663149 1663160 1663779 1663784) (-1009 "RATFACT.spad" 1662841 1662853 1663139 1663144) (-1008 "RANDSRC.spad" 1662160 1662169 1662831 1662836) (-1007 "RADUTIL.spad" 1661916 1661925 1662150 1662155) (-1006 "RADIX.spad" 1658837 1658851 1660383 1660476) (-1005 "RADFF.spad" 1657250 1657287 1657369 1657525) (-1004 "RADCAT.spad" 1656845 1656854 1657240 1657245) (-1003 "RADCAT.spad" 1656438 1656449 1656835 1656840) (-1002 "QUEUE.spad" 1655786 1655797 1656045 1656072) (-1001 "QUAT.spad" 1654367 1654378 1654710 1654775) (-1000 "QUATCT2.spad" 1653987 1654006 1654357 1654362) (-999 "QUATCAT.spad" 1652158 1652168 1653917 1653982) (-998 "QUATCAT.spad" 1650080 1650092 1651841 1651846) (-997 "QUAGG.spad" 1648908 1648918 1650048 1650075) (-996 "QQUTAST.spad" 1648677 1648685 1648898 1648903) (-995 "QFORM.spad" 1648142 1648156 1648667 1648672) (-994 "QFCAT.spad" 1646845 1646855 1648044 1648137) (-993 "QFCAT.spad" 1645139 1645151 1646340 1646345) (-992 "QFCAT2.spad" 1644832 1644848 1645129 1645134) (-991 "QEQUAT.spad" 1644391 1644399 1644822 1644827) (-990 "QCMPACK.spad" 1639138 1639157 1644381 1644386) (-989 "QALGSET.spad" 1635217 1635249 1639052 1639057) (-988 "QALGSET2.spad" 1633213 1633231 1635207 1635212) (-987 "PWFFINTB.spad" 1630629 1630650 1633203 1633208) (-986 "PUSHVAR.spad" 1629968 1629987 1630619 1630624) (-985 "PTRANFN.spad" 1626096 1626106 1629958 1629963) (-984 "PTPACK.spad" 1623184 1623194 1626086 1626091) (-983 "PTFUNC2.spad" 1623007 1623021 1623174 1623179) (-982 "PTCAT.spad" 1622262 1622272 1622975 1623002) (-981 "PSQFR.spad" 1621569 1621593 1622252 1622257) (-980 "PSEUDLIN.spad" 1620455 1620465 1621559 1621564) (-979 "PSETPK.spad" 1605888 1605904 1620333 1620338) (-978 "PSETCAT.spad" 1599808 1599831 1605868 1605883) (-977 "PSETCAT.spad" 1593702 1593727 1599764 1599769) (-976 "PSCURVE.spad" 1592685 1592693 1593692 1593697) (-975 "PSCAT.spad" 1591468 1591497 1592583 1592680) (-974 "PSCAT.spad" 1590341 1590372 1591458 1591463) (-973 "PRTITION.spad" 1589302 1589310 1590331 1590336) (-972 "PRTDAST.spad" 1589021 1589029 1589292 1589297) (-971 "PRS.spad" 1578583 1578600 1588977 1588982) (-970 "PRQAGG.spad" 1578018 1578028 1578551 1578578) (-969 "PROPLOG.spad" 1577317 1577325 1578008 1578013) (-968 "PROPFRML.spad" 1576133 1576144 1577307 1577312) (-967 "PROPERTY.spad" 1575621 1575629 1576123 1576128) (-966 "PRODUCT.spad" 1573303 1573315 1573587 1573642) (-965 "PR.spad" 1571695 1571707 1572394 1572521) (-964 "PRINT.spad" 1571447 1571455 1571685 1571690) (-963 "PRIMES.spad" 1569700 1569710 1571437 1571442) (-962 "PRIMELT.spad" 1567781 1567795 1569690 1569695) (-961 "PRIMCAT.spad" 1567408 1567416 1567771 1567776) (-960 "PRIMARR.spad" 1566413 1566423 1566591 1566618) (-959 "PRIMARR2.spad" 1565180 1565192 1566403 1566408) (-958 "PREASSOC.spad" 1564562 1564574 1565170 1565175) (-957 "PPCURVE.spad" 1563699 1563707 1564552 1564557) (-956 "PORTNUM.spad" 1563474 1563482 1563689 1563694) (-955 "POLYROOT.spad" 1562323 1562345 1563430 1563435) (-954 "POLY.spad" 1559658 1559668 1560173 1560300) (-953 "POLYLIFT.spad" 1558923 1558946 1559648 1559653) (-952 "POLYCATQ.spad" 1557041 1557063 1558913 1558918) (-951 "POLYCAT.spad" 1550511 1550532 1556909 1557036) (-950 "POLYCAT.spad" 1543319 1543342 1549719 1549724) (-949 "POLY2UP.spad" 1542771 1542785 1543309 1543314) (-948 "POLY2.spad" 1542368 1542380 1542761 1542766) (-947 "POLUTIL.spad" 1541309 1541338 1542324 1542329) (-946 "POLTOPOL.spad" 1540057 1540072 1541299 1541304) (-945 "POINT.spad" 1538895 1538905 1538982 1539009) (-944 "PNTHEORY.spad" 1535597 1535605 1538885 1538890) (-943 "PMTOOLS.spad" 1534372 1534386 1535587 1535592) (-942 "PMSYM.spad" 1533921 1533931 1534362 1534367) (-941 "PMQFCAT.spad" 1533512 1533526 1533911 1533916) (-940 "PMPRED.spad" 1532991 1533005 1533502 1533507) (-939 "PMPREDFS.spad" 1532445 1532467 1532981 1532986) (-938 "PMPLCAT.spad" 1531525 1531543 1532377 1532382) (-937 "PMLSAGG.spad" 1531110 1531124 1531515 1531520) (-936 "PMKERNEL.spad" 1530689 1530701 1531100 1531105) (-935 "PMINS.spad" 1530269 1530279 1530679 1530684) (-934 "PMFS.spad" 1529846 1529864 1530259 1530264) (-933 "PMDOWN.spad" 1529136 1529150 1529836 1529841) (-932 "PMASS.spad" 1528146 1528154 1529126 1529131) (-931 "PMASSFS.spad" 1527113 1527129 1528136 1528141) (-930 "PLOTTOOL.spad" 1526893 1526901 1527103 1527108) (-929 "PLOT.spad" 1521816 1521824 1526883 1526888) (-928 "PLOT3D.spad" 1518280 1518288 1521806 1521811) (-927 "PLOT1.spad" 1517437 1517447 1518270 1518275) (-926 "PLEQN.spad" 1504727 1504754 1517427 1517432) (-925 "PINTERP.spad" 1504349 1504368 1504717 1504722) (-924 "PINTERPA.spad" 1504133 1504149 1504339 1504344) (-923 "PI.spad" 1503742 1503750 1504107 1504128) (-922 "PID.spad" 1502712 1502720 1503668 1503737) (-921 "PICOERCE.spad" 1502369 1502379 1502702 1502707) (-920 "PGROEB.spad" 1500970 1500984 1502359 1502364) (-919 "PGE.spad" 1492587 1492595 1500960 1500965) (-918 "PGCD.spad" 1491477 1491494 1492577 1492582) (-917 "PFRPAC.spad" 1490626 1490636 1491467 1491472) (-916 "PFR.spad" 1487289 1487299 1490528 1490621) (-915 "PFOTOOLS.spad" 1486547 1486563 1487279 1487284) (-914 "PFOQ.spad" 1485917 1485935 1486537 1486542) (-913 "PFO.spad" 1485336 1485363 1485907 1485912) (-912 "PF.spad" 1484910 1484922 1485141 1485234) (-911 "PFECAT.spad" 1482592 1482600 1484836 1484905) (-910 "PFECAT.spad" 1480302 1480312 1482548 1482553) (-909 "PFBRU.spad" 1478190 1478202 1480292 1480297) (-908 "PFBR.spad" 1475750 1475773 1478180 1478185) (-907 "PERM.spad" 1471435 1471445 1475580 1475595) (-906 "PERMGRP.spad" 1466197 1466207 1471425 1471430) (-905 "PERMCAT.spad" 1464755 1464765 1466177 1466192) (-904 "PERMAN.spad" 1463287 1463301 1464745 1464750) (-903 "PENDTREE.spad" 1462628 1462638 1462916 1462921) (-902 "PDRING.spad" 1461179 1461189 1462608 1462623) (-901 "PDRING.spad" 1459738 1459750 1461169 1461174) (-900 "PDEPROB.spad" 1458753 1458761 1459728 1459733) (-899 "PDEPACK.spad" 1452793 1452801 1458743 1458748) (-898 "PDECOMP.spad" 1452263 1452280 1452783 1452788) (-897 "PDECAT.spad" 1450619 1450627 1452253 1452258) (-896 "PCOMP.spad" 1450472 1450485 1450609 1450614) (-895 "PBWLB.spad" 1449060 1449077 1450462 1450467) (-894 "PATTERN.spad" 1443599 1443609 1449050 1449055) (-893 "PATTERN2.spad" 1443337 1443349 1443589 1443594) (-892 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"OPERCAT.spad" 1365561 1365571 1366085 1366090) (-835 "OPERCAT.spad" 1365025 1365037 1365551 1365556) (-834 "ONECOMP.spad" 1363770 1363780 1364572 1364601) (-833 "ONECOMP2.spad" 1363194 1363206 1363760 1363765) (-832 "OMSERVER.spad" 1362200 1362208 1363184 1363189) (-831 "OMSAGG.spad" 1361988 1361998 1362156 1362195) (-830 "OMPKG.spad" 1360604 1360612 1361978 1361983) (-829 "OM.spad" 1359577 1359585 1360594 1360599) (-828 "OMLO.spad" 1359002 1359014 1359463 1359502) (-827 "OMEXPR.spad" 1358836 1358846 1358992 1358997) (-826 "OMERR.spad" 1358381 1358389 1358826 1358831) (-825 "OMERRK.spad" 1357415 1357423 1358371 1358376) (-824 "OMENC.spad" 1356759 1356767 1357405 1357410) (-823 "OMDEV.spad" 1351068 1351076 1356749 1356754) (-822 "OMCONN.spad" 1350477 1350485 1351058 1351063) (-821 "OINTDOM.spad" 1350240 1350248 1350403 1350472) (-820 "OFMONOID.spad" 1348363 1348373 1350196 1350201) (-819 "ODVAR.spad" 1347624 1347634 1348353 1348358) (-818 "ODR.spad" 1347268 1347294 1347436 1347585) (-817 "ODPOL.spad" 1344650 1344660 1344990 1345117) (-816 "ODP.spad" 1334497 1334517 1334870 1335001) (-815 "ODETOOLS.spad" 1333146 1333165 1334487 1334492) (-814 "ODESYS.spad" 1330840 1330857 1333136 1333141) (-813 "ODERTRIC.spad" 1326849 1326866 1330797 1330802) (-812 "ODERED.spad" 1326248 1326272 1326839 1326844) (-811 "ODERAT.spad" 1323863 1323880 1326238 1326243) (-810 "ODEPRRIC.spad" 1320900 1320922 1323853 1323858) (-809 "ODEPROB.spad" 1320157 1320165 1320890 1320895) (-808 "ODEPRIM.spad" 1317491 1317513 1320147 1320152) (-807 "ODEPAL.spad" 1316877 1316901 1317481 1317486) (-806 "ODEPACK.spad" 1303543 1303551 1316867 1316872) (-805 "ODEINT.spad" 1302978 1302994 1303533 1303538) (-804 "ODEIFTBL.spad" 1300373 1300381 1302968 1302973) (-803 "ODEEF.spad" 1295864 1295880 1300363 1300368) (-802 "ODECONST.spad" 1295401 1295419 1295854 1295859) (-801 "ODECAT.spad" 1293999 1294007 1295391 1295396) (-800 "OCT.spad" 1292135 1292145 1292849 1292888) (-799 "OCTCT2.spad" 1291781 1291802 1292125 1292130) (-798 "OC.spad" 1289577 1289587 1291737 1291776) (-797 "OC.spad" 1287098 1287110 1289260 1289265) (-796 "OCAMON.spad" 1286946 1286954 1287088 1287093) (-795 "OASGP.spad" 1286761 1286769 1286936 1286941) (-794 "OAMONS.spad" 1286283 1286291 1286751 1286756) (-793 "OAMON.spad" 1286144 1286152 1286273 1286278) (-792 "OAGROUP.spad" 1286006 1286014 1286134 1286139) (-791 "NUMTUBE.spad" 1285597 1285613 1285996 1286001) (-790 "NUMQUAD.spad" 1273573 1273581 1285587 1285592) (-789 "NUMODE.spad" 1264927 1264935 1273563 1273568) (-788 "NUMINT.spad" 1262493 1262501 1264917 1264922) (-787 "NUMFMT.spad" 1261333 1261341 1262483 1262488) (-786 "NUMERIC.spad" 1253447 1253457 1261138 1261143) (-785 "NTSCAT.spad" 1251955 1251971 1253415 1253442) (-784 "NTPOLFN.spad" 1251506 1251516 1251872 1251877) (-783 "NSUP.spad" 1244552 1244562 1249092 1249245) (-782 "NSUP2.spad" 1243944 1243956 1244542 1244547) (-781 "NSMP.spad" 1240175 1240194 1240483 1240610) (-780 "NREP.spad" 1238553 1238567 1240165 1240170) (-779 "NPCOEF.spad" 1237799 1237819 1238543 1238548) (-778 "NORMRETR.spad" 1237397 1237436 1237789 1237794) (-777 "NORMPK.spad" 1235299 1235318 1237387 1237392) (-776 "NORMMA.spad" 1234987 1235013 1235289 1235294) (-775 "NONE.spad" 1234728 1234736 1234977 1234982) (-774 "NONE1.spad" 1234404 1234414 1234718 1234723) (-773 "NODE1.spad" 1233891 1233907 1234394 1234399) (-772 "NNI.spad" 1232786 1232794 1233865 1233886) (-771 "NLINSOL.spad" 1231412 1231422 1232776 1232781) (-770 "NIPROB.spad" 1229953 1229961 1231402 1231407) (-769 "NFINTBAS.spad" 1227513 1227530 1229943 1229948) (-768 "NETCLT.spad" 1227487 1227498 1227503 1227508) (-767 "NCODIV.spad" 1225703 1225719 1227477 1227482) (-766 "NCNTFRAC.spad" 1225345 1225359 1225693 1225698) (-765 "NCEP.spad" 1223511 1223525 1225335 1225340) (-764 "NASRING.spad" 1223107 1223115 1223501 1223506) (-763 "NASRING.spad" 1222701 1222711 1223097 1223102) (-762 "NARNG.spad" 1222053 1222061 1222691 1222696) (-761 "NARNG.spad" 1221403 1221413 1222043 1222048) (-760 "NAGSP.spad" 1220480 1220488 1221393 1221398) (-759 "NAGS.spad" 1210141 1210149 1220470 1220475) (-758 "NAGF07.spad" 1208572 1208580 1210131 1210136) (-757 "NAGF04.spad" 1202974 1202982 1208562 1208567) (-756 "NAGF02.spad" 1197043 1197051 1202964 1202969) (-755 "NAGF01.spad" 1192804 1192812 1197033 1197038) (-754 "NAGE04.spad" 1186504 1186512 1192794 1192799) (-753 "NAGE02.spad" 1177164 1177172 1186494 1186499) (-752 "NAGE01.spad" 1173166 1173174 1177154 1177159) (-751 "NAGD03.spad" 1171170 1171178 1173156 1173161) (-750 "NAGD02.spad" 1163917 1163925 1171160 1171165) (-749 "NAGD01.spad" 1158210 1158218 1163907 1163912) (-748 "NAGC06.spad" 1154085 1154093 1158200 1158205) (-747 "NAGC05.spad" 1152586 1152594 1154075 1154080) (-746 "NAGC02.spad" 1151853 1151861 1152576 1152581) (-745 "NAALG.spad" 1151394 1151404 1151821 1151848) (-744 "NAALG.spad" 1150955 1150967 1151384 1151389) (-743 "MULTSQFR.spad" 1147913 1147930 1150945 1150950) (-742 "MULTFACT.spad" 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"MONADWU.spad" 1125152 1125160 1127112 1127117) (-722 "MONADWU.spad" 1123180 1123190 1125142 1125147) (-721 "MONAD.spad" 1122340 1122348 1123170 1123175) (-720 "MONAD.spad" 1121498 1121508 1122330 1122335) (-719 "MOEBIUS.spad" 1120234 1120248 1121478 1121493) (-718 "MODULE.spad" 1120104 1120114 1120202 1120229) (-717 "MODULE.spad" 1119994 1120006 1120094 1120099) (-716 "MODRING.spad" 1119329 1119368 1119974 1119989) (-715 "MODOP.spad" 1117994 1118006 1119151 1119218) (-714 "MODMONOM.spad" 1117725 1117743 1117984 1117989) (-713 "MODMON.spad" 1114520 1114536 1115239 1115392) (-712 "MODFIELD.spad" 1113882 1113921 1114422 1114515) (-711 "MMLFORM.spad" 1112742 1112750 1113872 1113877) (-710 "MMAP.spad" 1112484 1112518 1112732 1112737) (-709 "MLO.spad" 1110943 1110953 1112440 1112479) (-708 "MLIFT.spad" 1109555 1109572 1110933 1110938) (-707 "MKUCFUNC.spad" 1109090 1109108 1109545 1109550) (-706 "MKRECORD.spad" 1108694 1108707 1109080 1109085) (-705 "MKFUNC.spad" 1108101 1108111 1108684 1108689) (-704 "MKFLCFN.spad" 1107069 1107079 1108091 1108096) (-703 "MKBCFUNC.spad" 1106564 1106582 1107059 1107064) (-702 "MINT.spad" 1106003 1106011 1106466 1106559) (-701 "MHROWRED.spad" 1104514 1104524 1105993 1105998) (-700 "MFLOAT.spad" 1103034 1103042 1104404 1104509) (-699 "MFINFACT.spad" 1102434 1102456 1103024 1103029) (-698 "MESH.spad" 1100216 1100224 1102424 1102429) (-697 "MDDFACT.spad" 1098427 1098437 1100206 1100211) (-696 "MDAGG.spad" 1097718 1097728 1098407 1098422) (-695 "MCMPLX.spad" 1093729 1093737 1094343 1094544) (-694 "MCDEN.spad" 1092939 1092951 1093719 1093724) (-693 "MCALCFN.spad" 1090061 1090087 1092929 1092934) (-692 "MAYBE.spad" 1089345 1089356 1090051 1090056) (-691 "MATSTOR.spad" 1086653 1086663 1089335 1089340) (-690 "MATRIX.spad" 1085357 1085367 1085841 1085868) (-689 "MATLIN.spad" 1082701 1082725 1085241 1085246) (-688 "MATCAT.spad" 1074430 1074452 1082669 1082696) (-687 "MATCAT.spad" 1066031 1066055 1074272 1074277) (-686 "MATCAT2.spad" 1065313 1065361 1066021 1066026) (-685 "MAPPKG3.spad" 1064228 1064242 1065303 1065308) (-684 "MAPPKG2.spad" 1063566 1063578 1064218 1064223) (-683 "MAPPKG1.spad" 1062394 1062404 1063556 1063561) (-682 "MAPPAST.spad" 1061709 1061717 1062384 1062389) (-681 "MAPHACK3.spad" 1061521 1061535 1061699 1061704) (-680 "MAPHACK2.spad" 1061290 1061302 1061511 1061516) (-679 "MAPHACK1.spad" 1060934 1060944 1061280 1061285) (-678 "MAGMA.spad" 1058724 1058741 1060924 1060929) (-677 "MACROAST.spad" 1058303 1058311 1058714 1058719) (-676 "M3D.spad" 1056023 1056033 1057681 1057686) (-675 "LZSTAGG.spad" 1053261 1053271 1056013 1056018) (-674 "LZSTAGG.spad" 1050497 1050509 1053251 1053256) (-673 "LWORD.spad" 1047202 1047219 1050487 1050492) (-672 "LSTAST.spad" 1046986 1046994 1047192 1047197) (-671 "LSQM.spad" 1045216 1045230 1045610 1045661) (-670 "LSPP.spad" 1044751 1044768 1045206 1045211) (-669 "LSMP.spad" 1043601 1043629 1044741 1044746) (-668 "LSMP1.spad" 1041419 1041433 1043591 1043596) (-667 "LSAGG.spad" 1041088 1041098 1041387 1041414) (-666 "LSAGG.spad" 1040777 1040789 1041078 1041083) (-665 "LPOLY.spad" 1039731 1039750 1040633 1040702) (-664 "LPEFRAC.spad" 1039002 1039012 1039721 1039726) (-663 "LO.spad" 1038403 1038417 1038936 1038963) (-662 "LOGIC.spad" 1038005 1038013 1038393 1038398) (-661 "LOGIC.spad" 1037605 1037615 1037995 1038000) (-660 "LODOOPS.spad" 1036535 1036547 1037595 1037600) (-659 "LODO.spad" 1035919 1035935 1036215 1036254) (-658 "LODOF.spad" 1034965 1034982 1035876 1035881) (-657 "LODOCAT.spad" 1033631 1033641 1034921 1034960) (-656 "LODOCAT.spad" 1032295 1032307 1033587 1033592) (-655 "LODO2.spad" 1031568 1031580 1031975 1032014) (-654 "LODO1.spad" 1030968 1030978 1031248 1031287) (-653 "LODEEF.spad" 1029770 1029788 1030958 1030963) (-652 "LNAGG.spad" 1025602 1025612 1029760 1029765) (-651 "LNAGG.spad" 1021398 1021410 1025558 1025563) (-650 "LMOPS.spad" 1018166 1018183 1021388 1021393) (-649 "LMODULE.spad" 1017934 1017944 1018156 1018161) (-648 "LMDICT.spad" 1017221 1017231 1017485 1017512) (-647 "LLINSET.spad" 1016618 1016628 1017211 1017216) (-646 "LITERAL.spad" 1016524 1016535 1016608 1016613) (-645 "LIST.spad" 1014259 1014269 1015671 1015698) (-644 "LIST3.spad" 1013570 1013584 1014249 1014254) (-643 "LIST2.spad" 1012272 1012284 1013560 1013565) (-642 "LIST2MAP.spad" 1009175 1009187 1012262 1012267) (-641 "LINSET.spad" 1008797 1008807 1009165 1009170) (-640 "LINEXP.spad" 1008231 1008241 1008777 1008792) (-639 "LINDEP.spad" 1007040 1007052 1008143 1008148) (-638 "LIMITRF.spad" 1004968 1004978 1007030 1007035) (-637 "LIMITPS.spad" 1003871 1003884 1004958 1004963) (-636 "LIE.spad" 1001887 1001899 1003161 1003306) (-635 "LIECAT.spad" 1001363 1001373 1001813 1001882) (-634 "LIECAT.spad" 1000867 1000879 1001319 1001324) (-633 "LIB.spad" 998917 998925 999526 999541) (-632 "LGROBP.spad" 996270 996289 998907 998912) (-631 "LF.spad" 995225 995241 996260 996265) (-630 "LFCAT.spad" 994284 994292 995215 995220) (-629 "LEXTRIPK.spad" 989787 989802 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index a8b81b21..c80d41db 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(188400 . 3467417897) -(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) ((#0=(-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) #0#) |has| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (-310 (-2 (|:| -1809 |#1|) (|:| -4236 |#2|))))) -((((-567)) . T) (($) -2811 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-559))) (((-410 (-567))) -2811 (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-1040 (-410 (-567))))) ((|#1|) . T)) +(188400 . 3474699327) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) ((#0=(-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) #0#) |has| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (-310 (-2 (|:| -2025 |#1|) (|:| -2265 |#2|))))) +((((-567)) . T) (($) -2836 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-559))) (((-410 (-567))) -2836 (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-1040 (-410 (-567))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-567)) . T)) -((($ $) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) ((|#2| |#2|) . T) ((#0=(-410 (-567)) #0#) |has| |#2| (-38 (-410 (-567))))) +((($ $) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) ((|#2| |#2|) . T) ((#0=(-410 (-567)) #0#) |has| |#2| (-38 (-410 (-567))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) (((|#2|) . T)) -((($) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) ((|#2|) . T) (((-410 (-567))) |has| |#2| (-38 (-410 (-567))))) +((($) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) ((|#2|) . T) (((-410 (-567))) |has| |#2| (-38 (-410 (-567))))) (|has| |#1| (-911)) ((((-863)) . T)) ((((-863)) . T)) @@ -24,19 +24,19 @@ ((((-225)) . T) (((-863)) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (((|#1|) . T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-849))) -((($ $) . T) ((#0=(-410 (-567)) #0#) -2811 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1| |#1|) . T)) -(-2811 (|has| |#1| (-821)) (|has| |#1| (-851))) +(-2836 (|has| |#1| (-21)) (|has| |#1| (-849))) +((($ $) . T) ((#0=(-410 (-567)) #0#) -2836 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1| |#1|) . T)) +(-2836 (|has| |#1| (-821)) (|has| |#1| (-851))) ((((-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) (((-567)) |has| |#1| (-1040 (-567))) ((|#1|) . T)) ((((-863)) . T)) ((((-863)) . T)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-559))) (|has| |#1| (-849)) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) ((((-317 |#1|)) . T) (((-567)) . T) (($) . T)) (((|#1| |#2| |#3|) . T)) ((((-567)) . T) (((-871 |#1|)) . T) (($) . T) (((-410 (-567))) . T)) -((($) . T) (((-410 (-567))) -2811 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) +((($) . T) (((-410 (-567))) -2836 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) ((((-410 (-567))) . T) (((-700)) . T) (($) . T)) ((((-863)) . T)) ((((-1184)) . T)) @@ -49,14 +49,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1184)) . T)) (((|#1|) . T) (((-567)) |has| |#1| (-1040 (-567))) (((-410 (-567))) |has| |#1| (-1040 (-410 (-567))))) -(-2811 (|has| |#2| (-172)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) -(-2811 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) -(((|#2| (-485 (-2423 |#1|) (-772))) . T)) +(-2836 (|has| |#2| (-172)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) +(-2836 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) +(((|#2| (-485 (-2498 |#1|) (-772))) . T)) (((|#1| (-534 (-1179))) . T)) (((#0=(-871 |#1|) #0#) . T) ((#1=(-410 (-567)) #1#) . T) (($ $) . T)) ((((-1161)) . T) (((-960 (-129))) . T) (((-863)) . T)) ((((-863)) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) (|has| |#4| (-370)) (|has| |#3| (-370)) (((|#1|) . T)) @@ -71,13 +71,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-559)) -((((-567)) . T) (((-410 (-567))) -2811 (|has| |#2| (-38 (-410 (-567)))) (|has| |#2| (-1040 (-410 (-567))))) ((|#2|) . T) (($) -2811 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) (((-865 |#1|)) . T)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-559))) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-559))) -((((-2 (|:| -3779 |#1|) (|:| -3468 |#2|))) . 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T)) -((((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) |has| |#2| (-172)) (($) -2811 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911)))) -((($) -2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) |has| |#2| (-172)) (($) -2836 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911)))) +((($) -2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) (((|#1|) . T) (((-410 (-567))) . T) (($) . T)) ((((-116 |#1|)) . T) (((-410 (-567))) . T) (($) . T)) (((|#1|) . T) (((-410 (-567))) . T) (($) . T)) @@ -110,14 +110,14 @@ ((((-410 (-567))) . T) (($) . T) (((-567)) . T)) ((($) . T) (((-567)) . T) (((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) . T)) (((|#2|) . T) (((-567)) . T) ((|#6|) . 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T) (($ $) -2836 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911)))) +((((-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((|#1|) . T) (($) -2836 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911)))) ((($ $) . T)) ((($) . T)) ((((-567)) . T) (($) . T) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) @@ -126,30 +126,30 @@ (((|#1|) . T)) (|has| |#1| (-370)) (((|#1|) . T)) -((((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (((-1261 |#1| |#2| |#3|)) |has| |#1| (-365)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) . T)) +((((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (((-1261 |#1| |#2| |#3|)) |has| |#1| (-365)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) . T)) (((|#1|) . 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T)) ((((-410 |#2|)) . T) (((-410 (-567))) . T) (($) . T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-849))) +(-2836 (|has| |#1| (-21)) (|has| |#1| (-849))) ((($ $) . T) ((#0=(-410 (-567)) #0#) . T)) -(-2811 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-559))) -(-2811 (|has| |#1| (-851)) (|has| |#1| (-1102))) +(-2836 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-851)) (|has| |#1| (-1102))) (|has| |#1| (-1102)) -(-2811 (|has| |#1| (-851)) (|has| |#1| (-1102))) +(-2836 (|has| |#1| (-851)) (|has| |#1| (-1102))) (|has| |#1| (-1102)) -(-2811 (|has| |#1| (-851)) (|has| |#1| (-1102))) +(-2836 (|has| |#1| (-851)) (|has| |#1| (-1102))) (|has| |#1| (-849)) ((($) . T) (((-410 (-567))) . T)) ((((-863)) . T)) @@ -158,12 +158,12 @@ ((((-567) (-129)) . T)) ((($) . T) (((-410 (-567))) . T)) ((((-129)) . T)) -(-2811 (|has| |#4| (-794)) (|has| |#4| (-849))) -(-2811 (|has| |#4| (-794)) (|has| |#4| (-849))) -(-2811 (|has| |#3| (-794)) (|has| |#3| (-849))) -(-2811 (|has| |#3| (-794)) (|has| |#3| (-849))) +(-2836 (|has| |#4| (-794)) (|has| |#4| (-849))) +(-2836 (|has| |#4| (-794)) (|has| |#4| (-849))) +(-2836 (|has| |#3| (-794)) (|has| |#3| (-849))) +(-2836 (|has| |#3| (-794)) (|has| |#3| (-849))) (((|#1| |#2|) . T)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-351))) ((((-1184)) . T)) (((|#2| |#2|) -12 (|has| |#1| (-365)) (|has| |#2| (-310 |#2|))) (((-1179) |#2|) -12 (|has| |#1| (-365)) (|has| |#2| (-517 (-1179) |#2|)))) (((|#1| |#2|) . T)) @@ -179,39 +179,39 @@ ((((-567)) . T)) ((((-567)) . T)) (((|#1|) . T)) -(-2811 (|has| |#2| (-172)) (|has| |#2| (-727)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (|has| |#2| (-172)) (|has| |#2| (-727)) (|has| |#2| (-849)) (|has| |#2| (-1051))) (((|#1| (-772)) . 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T) ((#0=(-410 (-567)) #0#) |has| |#1| (-38 (-410 (-567))))) +(((#0=(-410 (-567)) #0#) |has| |#1| (-38 (-410 (-567)))) ((|#1| |#1|) . T) (($ $) -2836 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911)))) +((($ $) -2836 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1| |#1|) . T) ((#0=(-410 (-567)) #0#) |has| |#1| (-38 (-410 (-567))))) (((|#1|) . T)) (((|#1|) . T)) -((((-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((|#1|) . T) (($) -2811 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911)))) -((($) -2811 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) -((($) -2811 (|has| |#2| (-172)) (|has| |#2| (-849)) (|has| |#2| (-1051))) ((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051)))) +((((-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((|#1|) . T) (($) -2836 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911)))) +((($) -2836 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#2| (-172)) (|has| |#2| (-849)) (|has| |#2| (-1051))) ((|#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051)))) ((((-863)) . T)) ((((-863)) . T)) ((((-863)) . T)) @@ -249,10 +249,10 @@ ((((-169 (-225))) |has| |#1| (-1024)) (((-169 (-381))) |has| |#1| (-1024)) (((-539)) |has| |#1| (-615 (-539))) (((-1175 |#1|)) . T) (((-894 (-567))) |has| |#1| (-615 (-894 (-567)))) (((-894 (-381))) |has| |#1| (-615 (-894 (-381))))) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (((|#1|) . T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-849))) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-849))) -((((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2811 (|has| |#1| (-365)) (|has| |#1| (-559))) ((|#2|) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2811 (|has| |#1| (-365)) (|has| |#1| (-559)))) +(-2836 (|has| |#1| (-21)) (|has| |#1| (-849))) +(-2836 (|has| |#1| (-21)) (|has| |#1| (-849))) +((((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2836 (|has| |#1| (-365)) (|has| |#1| (-559))) ((|#2|) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2836 (|has| |#1| (-365)) (|has| |#1| (-559)))) (|has| |#1| (-365)) ((((-863)) . T)) ((($) . T)) @@ -260,8 +260,8 @@ ((((-129)) . T)) (-12 (|has| |#4| (-233)) (|has| |#4| (-1051))) (-12 (|has| |#3| (-233)) (|has| |#3| (-1051))) -(-2811 (|has| |#4| (-172)) (|has| |#4| (-849)) (|has| |#4| (-1051))) -(-2811 (|has| |#3| (-172)) (|has| |#3| (-849)) (|has| |#3| (-1051))) +(-2836 (|has| |#4| (-172)) (|has| |#4| (-849)) (|has| |#4| (-1051))) +(-2836 (|has| |#3| (-172)) (|has| |#3| (-849)) (|has| |#3| (-1051))) ((((-863)) . T) (((-1184)) . T)) ((((-863)) . T) (((-1184)) . T)) ((((-1184)) . T)) @@ -270,14 +270,14 @@ (((|#1|) . T)) ((((-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) (((-567)) |has| |#1| (-1040 (-567))) ((|#1|) . T)) (((|#1|) . T) (((-567)) |has| |#1| (-640 (-567)))) -(((|#2|) . T) (((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -1809 (-1161)) (|:| -4236 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2025 (-1161)) (|:| -2265 |#1|))) . T)) (|has| |#1| (-559)) -((((-567)) -2811 (|has| |#4| (-172)) (|has| |#4| (-849)) (-12 (|has| |#4| (-1040 (-567))) (|has| |#4| (-1102))) (|has| |#4| (-1051))) ((|#4|) -2811 (|has| |#4| (-172)) (|has| |#4| (-1102))) (((-410 (-567))) -12 (|has| |#4| (-1040 (-410 (-567)))) (|has| |#4| (-1102)))) -((((-567)) -2811 (|has| |#3| (-172)) (|has| |#3| (-849)) (-12 (|has| |#3| (-1040 (-567))) (|has| |#3| (-1102))) (|has| |#3| (-1051))) ((|#3|) -2811 (|has| |#3| (-172)) (|has| |#3| (-1102))) (((-410 (-567))) -12 (|has| |#3| (-1040 (-410 (-567)))) (|has| |#3| (-1102)))) +((((-567)) -2836 (|has| |#4| (-172)) (|has| |#4| (-849)) (-12 (|has| |#4| (-1040 (-567))) (|has| |#4| (-1102))) (|has| |#4| (-1051))) ((|#4|) -2836 (|has| |#4| (-172)) (|has| |#4| (-1102))) (((-410 (-567))) -12 (|has| |#4| (-1040 (-410 (-567)))) (|has| |#4| (-1102)))) +((((-567)) -2836 (|has| |#3| (-172)) (|has| |#3| (-849)) (-12 (|has| |#3| (-1040 (-567))) (|has| |#3| (-1102))) (|has| |#3| (-1051))) ((|#3|) -2836 (|has| |#3| (-172)) (|has| |#3| (-1102))) (((-410 (-567))) -12 (|has| |#3| (-1040 (-410 (-567)))) (|has| |#3| (-1102)))) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (|has| |#1| (-559)) -(-2811 (|has| |#1| (-851)) (|has| |#1| (-1102))) +(-2836 (|has| |#1| (-851)) (|has| |#1| (-1102))) (((|#1|) . T)) (|has| |#1| (-559)) (|has| |#1| (-559)) @@ -290,21 +290,21 @@ ((((-410 |#2|)) . T) (((-410 (-567))) . T) (($) . T)) (-12 (|has| |#1| (-1102)) (|has| |#2| (-1102))) ((($) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((|#1|) . T)) -((((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (((-1177 |#1| |#2| |#3|)) |has| |#1| (-365)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) . T)) +((((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (((-1177 |#1| |#2| |#3|)) |has| |#1| (-365)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) . T)) (((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567)))) (($) . T)) -(((|#4| |#4|) -2811 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1051))) (($ $) |has| |#4| (-172))) -(((|#3| |#3|) -2811 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051))) (($ $) |has| |#3| (-172))) +(((|#4| |#4|) -2836 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1051))) (($ $) |has| |#4| (-172))) +(((|#3| |#3|) -2836 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051))) (($ $) |has| |#3| (-172))) (((|#2|) . T)) (((|#1|) . T)) ((((-539)) |has| |#2| (-615 (-539))) (((-894 (-381))) |has| |#2| (-615 (-894 (-381)))) (((-894 (-567))) |has| |#2| (-615 (-894 (-567))))) ((((-863)) . T)) (((|#1| |#2| |#3| |#4|) . T)) -((((-2 (|:| -3779 |#1|) (|:| -3468 |#2|))) . T) (((-863)) . T)) +((((-2 (|:| -2188 |#1|) (|:| -2618 |#2|))) . T) (((-863)) . T)) ((((-539)) |has| |#1| (-615 (-539))) (((-894 (-381))) |has| |#1| (-615 (-894 (-381)))) (((-894 (-567))) |has| |#1| (-615 (-894 (-567))))) -(((|#4|) -2811 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1051))) (($) |has| |#4| (-172))) -(((|#3|) -2811 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051))) (($) |has| |#3| (-172))) -((((-2 (|:| -3779 |#1|) (|:| -3468 |#2|))) . T)) +(((|#4|) -2836 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1051))) (($) |has| |#4| (-172))) +(((|#3|) -2836 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051))) (($) |has| |#3| (-172))) +((((-2 (|:| -2188 |#1|) (|:| -2618 |#2|))) . T)) ((((-863)) . T)) ((((-863)) . T)) ((((-539)) . T) (((-567)) . T) (((-894 (-567))) . T) (((-381)) . T) (((-225)) . T)) @@ -312,14 +312,14 @@ (((|#1|) . T) (((-567)) |has| |#1| (-1040 (-567))) (((-410 (-567))) |has| |#1| (-1040 (-410 (-567))))) ((($) . T) (((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) . T)) ((((-410 $) (-410 $)) |has| |#2| (-559)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -1809 (-1161)) (|:| -4236 (-52)))) . T)) +((((-2 (|:| -2025 (-1161)) (|:| -2265 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-911)) ((((-1161) (-52)) . T)) ((((-567)) |has| #0=(-410 |#2|) (-640 (-567))) ((#0#) . T)) ((((-539)) . T) (((-225)) . T) (((-381)) . T) (((-894 (-381))) . T)) ((((-863)) . T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051))) +(-2836 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051))) (((|#1|) |has| |#1| (-172))) (((|#1| $) |has| |#1| (-287 |#1| |#1|))) ((((-863)) . T)) @@ -333,15 +333,15 @@ (|has| |#1| (-1102)) ((((-912 |#1|)) . T) (($) . T) (((-410 (-567))) . T)) (((|#1|) . T)) -((((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-851)) (|has| |#1| (-1102)))) +((((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-851)) (|has| |#1| (-1102)))) ((((-539)) |has| |#1| (-615 (-539)))) ((((-863)) . T) (((-1184)) . T)) -((((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) |has| |#2| (-172)) (($) -2811 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911)))) +((((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) |has| |#2| (-172)) (($) -2836 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911)))) ((((-1184)) . T)) -((($) -2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) -((($) -2811 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) (|has| |#1| (-233)) -((($) -2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) (((|#1| (-534 (-819 (-1179)))) . T)) (((|#1| (-973)) . T)) ((((-567)) . T) ((|#2|) . T)) @@ -351,7 +351,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1154)) -((((-2 (|:| -1809 (-1161)) (|:| -4236 |#1|))) . T)) +((((-2 (|:| -2025 (-1161)) (|:| -2265 |#1|))) . T)) (|has| (-1255 |#1| |#2| |#3| |#4|) (-145)) (|has| (-1255 |#1| |#2| |#3| |#4|) (-147)) (|has| |#1| (-145)) @@ -363,27 +363,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-567)) |has| |#2| (-640 (-567)))) -((((-1127 |#1| (-1179))) . T) (((-567)) . T) (((-819 (-1179))) . T) (($) -2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-1040 (-410 (-567))))) (((-1179)) . T)) +((((-1127 |#1| (-1179))) . T) (((-567)) . T) (((-819 (-1179))) . T) (($) -2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-1040 (-410 (-567))))) (((-1179)) . T)) (|has| |#2| (-370)) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-1051))) ((((-863)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) ((#0=(-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) #0#) |has| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (-310 (-2 (|:| -1809 |#1|) (|:| -4236 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) ((#0=(-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) #0#) |has| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (-310 (-2 (|:| -2025 |#1|) (|:| -2265 |#2|))))) (((|#1|) . T)) -((((-1269 (-341 (-4145) (-4145 (QUOTE X)) (-700)))) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102))) ((#0=(-2 (|:| -1809 (-1161)) (|:| -4236 |#1|)) #0#) |has| (-2 (|:| -1809 (-1161)) (|:| -4236 |#1|)) (-310 (-2 (|:| -1809 (-1161)) (|:| -4236 |#1|))))) +((((-1269 (-341 (-2516) (-2516 (QUOTE X)) (-700)))) . T)) +(((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102))) ((#0=(-2 (|:| -2025 (-1161)) (|:| -2265 |#1|)) #0#) |has| (-2 (|:| -2025 (-1161)) (|:| -2265 |#1|)) (-310 (-2 (|:| -2025 (-1161)) (|:| -2265 |#1|))))) ((((-863)) . T)) ((((-567) |#1|) . T)) ((((-539)) -12 (|has| |#1| (-615 (-539))) (|has| |#2| (-615 (-539)))) (((-894 (-381))) -12 (|has| |#1| (-615 (-894 (-381)))) (|has| |#2| (-615 (-894 (-381))))) (((-894 (-567))) -12 (|has| |#1| (-615 (-894 (-567)))) (|has| |#2| (-615 (-894 (-567)))))) ((($) . T)) ((((-863)) . T)) -((($ $) -2811 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1| |#1|) . T) ((#0=(-410 (-567)) #0#) |has| |#1| (-38 (-410 (-567))))) +((($ $) -2836 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1| |#1|) . T) ((#0=(-410 (-567)) #0#) |has| |#1| (-38 (-410 (-567))))) ((((-863)) . T)) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -2811 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) ((((-863)) . T)) ((((-863)) . T)) (|has| (-1254 |#2| |#3| |#4|) (-147)) @@ -394,16 +394,16 @@ ((((-863)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051))) +(-2836 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051))) (((|#1|) . T)) ((((-567) |#1|) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-849))) +(-2836 (|has| |#1| (-21)) (|has| |#1| (-849))) ((((-863)) |has| |#1| (-1102))) -(-2811 (|has| |#1| (-476)) (|has| |#1| (-727)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051)) (|has| |#1| (-1114))) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-476)) (|has| |#1| (-727)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051)) (|has| |#1| (-1114))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-351))) ((((-912 |#1|)) . T)) ((((-410 |#2|) |#3|) . T)) (|has| |#1| (-15 * (|#1| (-567) |#1|))) @@ -414,7 +414,7 @@ ((((-863)) . T)) ((((-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((|#1|) |has| |#1| (-172)) (($) |has| |#1| (-559))) (|has| |#1| (-365)) -(-2811 (-12 (|has| (-1261 |#1| |#2| |#3|) (-233)) (|has| |#1| (-365))) (|has| |#1| (-15 * (|#1| (-567) |#1|)))) +(-2836 (-12 (|has| (-1261 |#1| |#2| |#3|) (-233)) (|has| |#1| (-365))) (|has| |#1| (-15 * (|#1| (-567) |#1|)))) (|has| |#1| (-15 * (|#1| (-410 (-567)) |#1|))) (|has| |#1| (-365)) (|has| |#1| (-15 * (|#1| (-772) |#1|))) @@ -428,20 +428,20 @@ ((((-567) |#1|) . T)) ((((-863)) . T)) (((|#2|) . T)) -(-2811 (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) +(-2836 (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) ((((-567)) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((|#1|) |has| |#1| (-172)) (($) |has| |#1| (-559))) ((($) |has| |#1| (-559)) (((-567)) . T)) -(-2811 (|has| |#2| (-794)) (|has| |#2| (-849))) -(-2811 (|has| |#2| (-794)) (|has| |#2| (-849))) -((((-1261 |#1| |#2| |#3|)) . 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T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($ $) -2836 (|has| |#1| (-172)) (|has| |#1| (-559))) ((|#1| |#1|) . T) ((#0=(-410 (-567)) #0#) |has| |#1| (-38 (-410 (-567))))) (|has| (-1096 |#1|) (-1102)) (((|#2| (-820 |#1|)) . T)) ((($) . T) (((-567)) . T) (((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) . T)) @@ -469,20 +469,20 @@ (((|#1|) . T) (((-410 (-567))) . T) (((-567)) . T) (($) . T)) (((|#1|) . T) (((-410 (-567))) . T) (((-567)) . T) (($) . T)) (((|#1|) . T) (((-410 (-567))) . T) (((-567)) . T) (($) . T)) -((((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) |has| |#2| (-172)) (($) -2811 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911)))) +((((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) |has| |#2| (-172)) (($) -2836 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911)))) (((|#2|) . T) ((|#6|) . T)) (|has| |#1| (-365)) ((((-567)) . T) ((|#2|) . T)) -((((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) . 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T)) -(-2811 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) +(-2836 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) ((((-410 (-567))) . T)) (|has| |#1| (-370)) -(-2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) +(-2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((((-567)) . T)) ((((-567)) . T)) (((|#1|) . T) (((-567)) . T)) -(-2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) +(-2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) ((((-863)) . T)) ((((-863)) . T)) (((|#1|) . T) (((-410 (-567))) . T) (((-567)) . T) (($) . T)) @@ -537,10 +537,10 @@ ((((-567) |#4|) . T)) ((((-567) |#3|) . T)) (((|#1|) . T) (((-567)) |has| |#1| (-640 (-567)))) -(-2811 (|has| |#2| (-172)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (|has| |#2| (-172)) (|has| |#2| (-849)) (|has| |#2| (-1051))) ((((-1255 |#1| |#2| |#3| |#4|)) . T)) ((((-410 (-567))) . T) (((-567)) . T)) -((((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) +((((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) @@ -549,9 +549,9 @@ ((($) . T) (((-567)) . T) (((-410 (-567))) . T)) ((((-567)) . T)) ((((-567)) . T)) -((($) . T) (((-567)) . T) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) ((|#1|) . T)) +((($) . T) (((-567)) . T) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) ((|#1|) . T)) ((($) . T) (((-567)) . T) (((-410 (-567))) . 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T)) -(-2811 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-559))) -(-2811 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-559))) -(-2811 (|has| |#1| (-172)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-172)) (|has| |#1| (-559))) ((((-863)) . T)) ((((-863)) . T)) ((((-863)) . T)) (((|#1| (-1269 |#1|) (-1269 |#1|)) . T)) ((((-567) (-144)) . T)) ((($) . T)) -(-2811 (|has| |#4| (-172)) (|has| |#4| (-849)) (|has| |#4| (-1051))) -(-2811 (|has| |#3| (-172)) (|has| |#3| (-849)) (|has| |#3| (-1051))) +(-2836 (|has| |#4| (-172)) (|has| |#4| (-849)) (|has| |#4| (-1051))) +(-2836 (|has| |#3| (-172)) (|has| |#3| (-849)) (|has| |#3| (-1051))) ((((-1184)) . T) (((-863)) . T)) ((((-1184)) . T)) ((((-863)) . T)) @@ -982,20 +982,20 @@ (((|#1| (-973)) . T)) (((|#1| |#1|) . T)) ((($) . T)) -(-2811 (|has| |#2| (-794)) (|has| |#2| (-849))) -(-2811 (|has| |#2| (-794)) (|has| |#2| (-849))) +(-2836 (|has| |#2| (-794)) (|has| |#2| (-849))) +(-2836 (|has| |#2| (-794)) (|has| |#2| (-849))) (-12 (|has| |#1| (-476)) (|has| |#2| (-476))) -(-2811 (|has| |#2| (-172)) (|has| |#2| (-727)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (|has| |#2| (-172)) (|has| |#2| (-727)) (|has| |#2| (-849)) (|has| |#2| (-1051))) ((($) . T) (((-567)) . T) (((-871 |#1|)) . T) (((-410 (-567))) . T)) (((|#1|) . T)) (|has| |#2| (-794)) -(-2811 (|has| |#2| (-794)) (|has| |#2| (-849))) +(-2836 (|has| |#2| (-794)) (|has| |#2| (-849))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (|has| |#2| (-849)) (-12 (|has| |#1| (-794)) (|has| |#2| (-794))) (-12 (|has| |#1| (-794)) (|has| |#2| (-794))) -(-2811 (-12 (|has| |#1| (-476)) (|has| |#2| (-476))) (-12 (|has| |#1| (-727)) (|has| |#2| (-727)))) +(-2836 (-12 (|has| |#1| (-476)) (|has| |#2| (-476))) (-12 (|has| |#1| (-727)) (|has| |#2| (-727)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-172)) ((|#4|) . T) (((-567)) . T)) (((|#2|) |has| |#2| (-172))) @@ -1007,7 +1007,7 @@ (((|#1|) . T)) ((((-410 (-567))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-410 (-567))) . T)) -((($) . T) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) ((|#1|) . T)) +((($) . T) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) ((|#1|) . T)) (|has| |#1| (-829)) ((((-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) (((-567)) |has| |#1| (-1040 (-567))) ((|#1|) . T)) (|has| |#1| (-1102)) @@ -1018,13 +1018,13 @@ (((|#4|) |has| |#4| (-1102))) (((|#3|) |has| |#3| (-1102))) (|has| |#3| (-370)) -((($) |has| |#1| (-559)) ((|#1|) . T) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-1040 (-410 (-567))))) (((-567)) . T)) -((((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2811 (|has| |#1| (-365)) (|has| |#1| (-559))) (((-1261 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) +((($) |has| |#1| (-559)) ((|#1|) . T) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-1040 (-410 (-567))))) (((-567)) . T)) +((((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2836 (|has| |#1| (-365)) (|has| |#1| (-559))) (((-1261 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) ((((-863)) . T)) ((((-863)) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) -(((|#1|) |has| |#1| (-172)) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2811 (|has| |#1| (-365)) (|has| |#1| (-559)))) +(((|#1|) |has| |#1| (-172)) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2836 (|has| |#1| (-365)) (|has| |#1| (-559)))) ((($) |has| |#1| (-559)) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) (((|#1| |#1|) |has| |#1| (-172))) (|has| |#2| (-365)) @@ -1032,19 +1032,19 @@ (((|#1|) |has| |#1| (-172))) ((((-410 (-567))) . T) (((-567)) . T)) ((($) . T) (((-567)) . T) (((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) . T)) -((($ $) -2811 (|has| |#1| (-172)) (|has| |#1| (-559))) ((|#1| |#1|) . T) ((#0=(-410 (-567)) #0#) |has| |#1| (-38 (-410 (-567))))) +((($ $) -2836 (|has| |#1| (-172)) (|has| |#1| (-559))) ((|#1| |#1|) . T) ((#0=(-410 (-567)) #0#) |has| |#1| (-38 (-410 (-567))))) ((($) . T) (((-567)) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((|#1|) . T)) ((($) . T) (((-567)) . T)) -((($) -2811 (|has| |#1| (-172)) (|has| |#1| (-559))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#1| (-172)) (|has| |#1| (-559))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) (((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102)))) ((((-144)) . T)) (((|#1|) . T)) -((($) -2811 (|has| |#2| (-172)) (|has| |#2| (-849)) (|has| |#2| (-1051))) ((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051)))) +((($) -2836 (|has| |#2| (-172)) (|has| |#2| (-849)) (|has| |#2| (-1051))) ((|#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051)))) ((((-144)) . T)) ((((-144)) . T)) ((((-410 (-567))) . #0=(|has| |#2| (-365))) (($) . #0#) ((|#2|) . T) (((-567)) . T)) (((|#1| |#2| |#3|) . T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-559)) (|has| |#1| (-1051))) +(-2836 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-559)) (|has| |#1| (-1051))) (((|#1|) |has| |#1| (-172))) (|has| $ (-147)) (|has| $ (-147)) @@ -1054,15 +1054,15 @@ ((((-863)) . T)) (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567)))) -(-2811 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-476)) (|has| |#1| (-559)) (|has| |#1| (-1051)) (|has| |#1| (-1114))) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-476)) (|has| |#1| (-559)) (|has| |#1| (-1051)) (|has| |#1| (-1114))) ((($ $) |has| |#1| (-287 $ $)) ((|#1| $) |has| |#1| (-287 |#1| |#1|))) (((|#1| (-410 (-567))) . T)) (((|#1|) . T)) ((((-410 (-567))) . T) (((-567)) . T) (($) . T)) ((((-1179)) . T)) (|has| |#1| (-559)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-559))) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-559))) (|has| |#1| (-559)) (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567)))) @@ -1073,7 +1073,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-849)) -(((|#2| (-240 (-2423 |#1|) (-772)) (-865 |#1|)) . T)) +(((|#2| (-240 (-2498 |#1|) (-772)) (-865 |#1|)) . T)) (|has| |#3| (-849)) (((|#1| (-534 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -1088,20 +1088,20 @@ (|has| |#1| (-145)) ((((-410 (-567))) |has| |#2| (-365)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) -(-2811 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) -(-2811 (|has| |#1| (-351)) (|has| |#1| (-370))) +(-2836 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) +(-2836 (|has| |#1| (-351)) (|has| |#1| (-370))) ((((-1144 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1051))) -(((|#2|) . T) (((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) -(-2811 (|has| |#3| (-794)) (|has| |#3| (-849))) -(-2811 (|has| |#3| (-794)) (|has| |#3| (-849))) +(((|#2|) . T) (((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) +(-2836 (|has| |#3| (-794)) (|has| |#3| (-849))) +(-2836 (|has| |#3| (-794)) (|has| |#3| (-849))) ((((-863)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-700)) . T)) -(-2811 (|has| |#2| (-172)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (|has| |#2| (-172)) (|has| |#2| (-849)) (|has| |#2| (-1051))) (|has| |#1| (-559)) (((|#1|) . T)) (((|#1|) . T)) @@ -1125,11 +1125,11 @@ (((|#1| (-410 (-567))) . T)) (((|#3|) . T) (((-613 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) -((((-567)) -2811 (|has| |#2| (-172)) (|has| |#2| (-849)) (-12 (|has| |#2| (-1040 (-567))) (|has| |#2| (-1102))) (|has| |#2| (-1051))) ((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-1102))) (((-410 (-567))) -12 (|has| |#2| (-1040 (-410 (-567)))) (|has| |#2| (-1102)))) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) +((((-567)) -2836 (|has| |#2| (-172)) (|has| |#2| (-849)) (-12 (|has| |#2| (-1040 (-567))) (|has| |#2| (-1102))) (|has| |#2| (-1051))) ((|#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-1102))) (((-410 (-567))) -12 (|has| |#2| (-1040 (-410 (-567)))) (|has| |#2| (-1102)))) (((|#1|) . T) (((-410 (-567))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-567)) . T) (($) . T) (((-410 (-567))) . T)) @@ -1137,8 +1137,8 @@ ((((-863)) . T)) ((((-863)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) (((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) |has| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (-310 (-2 (|:| -1809 |#1|) (|:| -4236 |#2|))))) -(((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102))) (((-2 (|:| -1809 (-1161)) (|:| -4236 |#1|))) |has| (-2 (|:| -1809 (-1161)) (|:| -4236 |#1|)) (-310 (-2 (|:| -1809 (-1161)) (|:| -4236 |#1|))))) +(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) (((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) |has| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (-310 (-2 (|:| -2025 |#1|) (|:| -2265 |#2|))))) +(((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102))) (((-2 (|:| -2025 (-1161)) (|:| -2265 |#1|))) |has| (-2 (|:| -2025 (-1161)) (|:| -2265 |#1|)) (-310 (-2 (|:| -2025 (-1161)) (|:| -2265 |#1|))))) ((((-863)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1152,10 +1152,10 @@ ((($) . T) (((-567)) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((|#1|) . T)) ((((-567)) . T) (($) . 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T)) -(((|#3| |#3|) -2811 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051))) (($ $) |has| |#3| (-172))) +(((|#3| |#3|) -2836 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051))) (($ $) |has| |#3| (-172))) (|has| |#1| (-1024)) ((((-863)) . T)) -(((|#3|) -2811 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051))) (($) |has| |#3| (-172))) +(((|#3|) -2836 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051))) (($) |has| |#3| (-172))) ((((-567) (-112)) . T)) ((((-1184)) . T)) (((|#1|) |has| |#1| (-310 |#1|))) @@ -1257,11 +1257,11 @@ (|has| |#1| (-370)) ((((-1179) $) |has| |#1| (-517 (-1179) $)) (($ $) |has| |#1| (-310 $)) ((|#1| |#1|) |has| |#1| (-310 |#1|)) (((-1179) |#1|) |has| |#1| (-517 (-1179) |#1|))) ((((-1179)) |has| |#1| (-902 (-1179)))) -(-2811 (-12 (|has| |#1| (-233)) (|has| |#1| (-365))) (|has| |#1| (-351))) +(-2836 (-12 (|has| |#1| (-233)) (|has| |#1| (-365))) (|has| |#1| (-351))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-391) |#1|) . 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T)) ((((-645 |#4|)) . T) (((-863)) . T)) @@ -1409,34 +1409,34 @@ ((((-539)) |has| |#4| (-615 (-539)))) ((((-863)) . T) (((-645 |#4|)) . T)) ((($) |has| |#1| (-849))) -((((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (((-1261 |#1| |#2| |#3|)) |has| |#1| (-365)) (((-567)) . T) (($) . T) ((|#1|) . T)) -((((-567)) -2811 (|has| |#2| (-172)) (|has| |#2| (-849)) (-12 (|has| |#2| (-1040 (-567))) (|has| |#2| (-1102))) (|has| |#2| (-1051))) ((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-1102))) (((-410 (-567))) -12 (|has| |#2| (-1040 (-410 (-567)))) (|has| |#2| (-1102)))) +((((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (((-1261 |#1| |#2| |#3|)) |has| |#1| (-365)) (((-567)) . T) (($) . T) ((|#1|) . 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T)) -(-2811 (|has| |#1| (-851)) (|has| |#1| (-1102))) -(((|#2| |#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051))) (($ $) |has| |#2| (-172))) +(-2836 (|has| |#1| (-851)) (|has| |#1| (-1102))) +(((|#2| |#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051))) (($ $) |has| |#2| (-172))) (((|#2|) . T) (((-567)) . T)) ((((-863)) . T)) ((((-863)) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T) ((|#2|) . T)) ((((-863)) . T)) ((((-863)) . T)) ((((-1161) (-1179) (-567) (-225) (-863)) . T)) @@ -1472,9 +1472,9 @@ ((((-410 (-567))) . T) (($) . T)) ((((-863)) . T)) ((((-539)) |has| |#1| (-615 (-539)))) -((((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) +((((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) ((($) . T) (((-410 (-567))) . T)) -(((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051))) (($) |has| |#2| (-172))) +(((|#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051))) (($) |has| |#2| (-172))) (|has| $ (-147)) ((((-410 |#2|)) . T)) ((((-410 (-567))) |has| #0=(-410 |#2|) (-1040 (-410 (-567)))) (((-567)) |has| #0# (-1040 (-567))) ((#0#) . T)) @@ -1485,11 +1485,11 @@ (((|#3|) |has| |#3| (-172))) (|has| |#1| (-147)) (|has| |#1| (-145)) -(-2811 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-370))) (|has| |#1| (-147)) -(-2811 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-370))) (|has| |#1| (-147)) -(-2811 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-370))) (|has| |#1| (-147)) (((|#1|) . T)) (|has| |#2| (-233)) @@ -1527,7 +1527,7 @@ ((((-1001 |#1|)) . T) ((|#1|) . T)) ((((-863)) . T)) ((((-863)) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) ((((-410 (-567))) . T) (((-410 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1175 |#1|)) . T)) ((((-567)) . T) (($) . T) (((-410 (-567))) . T)) @@ -1536,8 +1536,8 @@ (((|#1|) . T) (((-567)) . T) (($) . T)) (((|#2|) . T)) ((((-567)) . T) (($) . T) (((-410 (-567))) . T)) -((((-2 (|:| -1809 (-1161)) (|:| -4236 |#1|))) . T)) -((((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) +((((-2 (|:| -2025 (-1161)) (|:| -2265 |#1|))) . T)) +((((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) ((((-567) |#2|) . T)) (((|#1|) . T) (((-410 (-567))) . T) (((-567)) . T) (($) . T)) ((($) . T) (((-567)) . T) (((-410 (-567))) . T)) @@ -1550,7 +1550,7 @@ (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567)))) ((((-1261 |#1| |#2| |#3|)) |has| |#1| (-365))) -(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) ((#0=(-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) #0#) |has| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (-310 (-2 (|:| -1809 |#1|) (|:| -4236 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) ((#0=(-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) #0#) |has| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (-310 (-2 (|:| -2025 |#1|) (|:| -2265 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-1102)) (|has| |#1| (-38 (-410 (-567)))) @@ -1561,15 +1561,15 @@ (|has| |#1| (-38 (-410 (-567)))) (((|#2|) . 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T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) (((|#2|) |has| |#2| (-172))) -((($) -2811 (|has| |#2| (-172)) (|has| |#2| (-849)) (|has| |#2| (-1051))) (((-567)) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-849)) (|has| |#2| (-1051))) ((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051)))) +((($) -2836 (|has| |#2| (-172)) (|has| |#2| (-849)) (|has| |#2| (-1051))) (((-567)) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-849)) (|has| |#2| (-1051))) ((|#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051)))) ((((-567) |#3|) . T)) ((((-567) (-144)) . T)) ((((-144)) . T)) @@ -1595,19 +1595,19 @@ (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (((|#1| |#2|) . T)) ((((-567) (-144)) . T)) -(((#0=(-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) #0#) |has| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (-310 (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102)))) -((($) -2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +(((#0=(-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) #0#) |has| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (-310 (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102)))) +((($) -2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) (|has| |#1| (-851)) (((|#2| (-772) (-1084)) . T)) (((|#1| |#2|) . T)) -(-2811 (|has| |#1| (-172)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-172)) (|has| |#1| (-559))) (|has| |#1| (-792)) (((|#1|) |has| |#1| (-172))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-2811 (|has| |#1| (-147)) (-12 (|has| |#1| (-365)) (|has| |#2| (-147)))) -(-2811 (|has| |#1| (-145)) (-12 (|has| |#1| (-365)) (|has| |#2| (-145)))) +(-2836 (|has| |#1| (-147)) (-12 (|has| |#1| (-365)) (|has| |#2| (-147)))) +(-2836 (|has| |#1| (-145)) (-12 (|has| |#1| (-365)) (|has| |#2| (-145)))) (((|#4|) . T)) (|has| |#1| (-145)) ((((-1161) |#1|) . T)) @@ -1621,24 +1621,24 @@ (((|#3|) . T)) ((((-1261 |#1| |#2| |#3|)) |has| |#1| (-365))) ((($) . T) (((-567)) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((|#1|) . T)) -((((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (((-1177 |#1| |#2| |#3|)) |has| |#1| (-365)) (((-567)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (((-567)) . T) (($) . T)) +((((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (((-1177 |#1| |#2| |#3|)) |has| |#1| (-365)) (((-567)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . 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T)) -(((|#4|) -2811 (|has| |#4| (-172)) (|has| |#4| (-365)))) -(((|#3|) -2811 (|has| |#3| (-172)) (|has| |#3| (-365)))) +(((|#4|) -2836 (|has| |#4| (-172)) (|has| |#4| (-365)))) +(((|#3|) -2836 (|has| |#3| (-172)) (|has| |#3| (-365)))) (|has| |#2| (-365)) (((|#1|) |has| |#1| (-172))) -(((|#4|) -2811 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1051))) (($) |has| |#4| (-172))) -(((|#3|) -2811 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051))) (($) |has| |#3| (-172))) +(((|#4|) -2836 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1051))) (($) |has| |#4| (-172))) +(((|#3|) -2836 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051))) (($) |has| |#3| (-172))) (((|#2|) |has| |#2| (-1051))) ((((-1161) |#1|) . T)) (((|#3| |#3|) -12 (|has| |#3| (-310 |#3|)) (|has| |#3| (-1102)))) @@ -1647,8 +1647,8 @@ ((($) . T) (((-567)) . T) (((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) . T)) ((((-391) (-1161)) . T)) ((($) |has| |#1| (-559)) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) -((((-863)) -2811 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-614 (-863))) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-727)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051)) (|has| |#2| (-1102))) (((-1269 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1809 (-1161)) (|:| -4236 #0#))) . T)) +((((-863)) -2836 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-614 (-863))) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-727)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051)) (|has| |#2| (-1102))) (((-1269 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2025 (-1161)) (|:| -2265 #0#))) . T)) (((|#1|) . T)) ((((-863)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102)))) @@ -1657,7 +1657,7 @@ ((((-567)) . T)) (|has| |#2| (-147)) (|has| |#1| (-476)) -(-2811 (|has| |#1| (-476)) (|has| |#1| (-727)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051))) +(-2836 (|has| |#1| (-476)) (|has| |#1| (-727)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051))) (|has| |#1| (-365)) ((((-863)) . T)) (|has| |#1| (-38 (-410 (-567)))) @@ -1668,8 +1668,8 @@ (|has| |#1| (-849)) ((((-863)) . T)) (((|#2|) . T)) -((((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2811 (|has| |#1| (-365)) (|has| |#1| (-559))) (((-1261 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2811 (|has| |#1| (-365)) (|has| |#1| (-559)))) +((((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2836 (|has| |#1| (-365)) (|has| |#1| (-559))) (((-1261 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2836 (|has| |#1| (-365)) (|has| |#1| (-559)))) ((($) |has| |#1| (-559)) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) (((|#2|) . T) (((-567)) . T) (((-820 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1678,7 +1678,7 @@ ((((-863)) . T)) ((((-863)) . T)) (|has| |#1| (-1102)) -(((|#2| (-485 (-2423 |#1|) (-772)) (-865 |#1|)) . T)) +(((|#2| (-485 (-2498 |#1|) (-772)) (-865 |#1|)) . T)) ((((-410 (-567))) . #0=(|has| |#2| (-365))) (($) . #0#)) (((|#1| (-534 (-1179)) (-1179)) . T)) (((|#1|) . T)) @@ -1699,17 +1699,17 @@ (((|#2|) |has| |#2| (-172))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -1809 (-1161)) (|:| -4236 |#1|))) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2025 (-1161)) (|:| -2265 |#1|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -1809 (-1179)) (|:| -4236 (-52)))) . T)) +((((-2 (|:| -2025 (-1179)) (|:| -2265 (-52)))) . T)) ((((-1177 |#1| |#2| |#3|)) |has| |#1| (-365))) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) ((((-1179) (-52)) . T)) ((($ $) . T)) (((|#1| (-567)) . T)) ((((-912 |#1|)) . T)) -(((|#1|) -2811 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1051))) (($) -2811 (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051)))) +(((|#1|) -2836 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1051))) (($) -2836 (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051)))) (((|#1|) . T) (((-567)) |has| |#1| (-1040 (-567))) (((-410 (-567))) |has| |#1| (-1040 (-410 (-567))))) (|has| |#1| (-851)) (|has| |#1| (-851)) @@ -1727,13 +1727,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1102)))) (((|#1|) |has| |#1| (-172))) (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1102)))) -(((|#3|) -2811 (|has| |#3| (-172)) (|has| |#3| (-365)))) -((($) -2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) -(-2811 (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-911))) -((($) -2811 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +(((|#3|) -2836 (|has| |#3| (-172)) (|has| |#3| (-365)))) +((($) -2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +(-2836 (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-911))) +((($) -2836 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) ((($ $) . T) ((#0=(-410 (-567)) #0#) . T)) ((((-567) |#2|) . T)) -(((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)))) (|has| |#1| (-351)) (((|#3| |#3|) -12 (|has| |#3| (-310 |#3|)) (|has| |#3| (-1102)))) (((|#2|) . T) (((-567)) . T)) @@ -1742,7 +1742,7 @@ (|has| |#1| (-821)) (|has| |#1| (-821)) (((|#1|) . T)) -(-2811 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) (|has| |#1| (-849)) (|has| |#1| (-849)) (|has| |#1| (-849)) @@ -1751,14 +1751,14 @@ ((((-567)) . T) (($) . T) (((-410 (-567))) . T)) (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567)))) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-351))) (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567)))) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) ((((-1179)) |has| |#1| (-902 (-1179))) (((-1084)) . T)) (((|#1|) . 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T)) (|has| |#1| (-1204)) (|has| |#1| (-1204)) -(-2811 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-727)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051)) (|has| |#2| (-1102))) +(-2836 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-727)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051)) (|has| |#2| (-1102))) (|has| |#1| (-1204)) (|has| |#1| (-1204)) ((((-567)) . T) (($) . T) (((-410 (-567))) . T)) @@ -1883,16 +1883,16 @@ ((((-1161) (-52)) . T)) (|has| |#1| (-1102)) (((|#1|) |has| |#1| (-172)) (($) . T)) -(-2811 (|has| |#2| (-821)) (|has| |#2| (-851))) +(-2836 (|has| |#2| (-821)) (|has| |#2| (-851))) (((|#1|) . T) (($) . T) (((-410 (-567))) . T)) (((|#1|) . T) (((-410 (-567))) . T) (($) . T)) (((|#1|) . T)) ((((-567)) . T) (($) . T) (((-410 (-567))) . T)) ((((-567)) . T) (((-410 (-567))) . T) (($) . 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T)) @@ -1900,35 +1900,35 @@ (|has| |#2| (-911)) (|has| |#1| (-365)) (((|#2|) |has| |#2| (-1102))) -(-2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) -(-2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) +(-2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) +(-2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((((-539)) . T) (((-410 (-1175 (-567)))) . T) (((-225)) . T) (((-381)) . T)) ((((-381)) . T) (((-225)) . T) (((-863)) . T)) (|has| |#1| (-911)) (|has| |#1| (-911)) (|has| |#1| (-911)) -(-2811 (|has| |#1| (-455)) (|has| |#1| (-911))) +(-2836 (|has| |#1| (-455)) (|has| |#1| (-911))) ((($) . T)) -(-2811 (|has| |#1| (-851)) (|has| |#1| (-1102))) +(-2836 (|has| |#1| (-851)) (|has| |#1| (-1102))) ((($) . T) ((|#2|) . T)) -(((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)))) ((((-1177 |#1| |#2| |#3|)) -12 (|has| (-1177 |#1| |#2| |#3|) (-310 (-1177 |#1| |#2| |#3|))) (|has| |#1| (-365)))) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-911))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-911))) (((|#1|) . T)) -(((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051))) (($) |has| |#2| (-172))) +(((|#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051))) (($) |has| |#2| (-172))) (((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102)))) ((((-863)) . T)) ((((-863)) . T)) ((($ $) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) ((($ $) . T)) ((((-567) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-567)) . T)) ((((-112)) . T)) -(-2811 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-559))) (|has| |#1| (-38 (-410 (-567)))) (((|#1| (-567)) . T)) ((($) . T)) @@ -1950,7 +1950,7 @@ (((|#1| (-1233 |#1| |#2| |#3|)) . T)) (((|#1| (-772)) . T)) (((|#1|) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) ((((-863)) . T)) (|has| |#1| (-1102)) ((((-1161) |#1|) . T)) @@ -1971,19 +1971,19 @@ (((|#1|) . T)) ((((-567)) . T)) ((((-863)) . T)) -(-2811 (|has| |#1| (-145)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-351))) ((((-863)) . T)) (|has| |#1| (-147)) (((|#3|) . T)) -(-2811 (|has| |#3| (-172)) (|has| |#3| (-849)) (|has| |#3| (-1051))) +(-2836 (|has| |#3| (-172)) (|has| |#3| (-849)) (|has| |#3| (-1051))) ((((-863)) . T)) ((((-1254 |#2| |#3| |#4|)) . T) (((-1255 |#1| |#2| |#3| |#4|)) . T)) ((((-863)) . T)) -((((-48)) -12 (|has| |#1| (-559)) (|has| |#1| (-1040 (-567)))) (((-613 $)) . T) ((|#1|) . T) (((-567)) |has| |#1| (-1040 (-567))) (((-410 (-567))) -2811 (-12 (|has| |#1| (-559)) (|has| |#1| (-1040 (-567)))) (|has| |#1| (-1040 (-410 (-567))))) (((-410 (-954 |#1|))) |has| |#1| (-559)) (((-954 |#1|)) |has| |#1| (-1051)) (((-1179)) . T)) +((((-48)) -12 (|has| |#1| (-559)) (|has| |#1| (-1040 (-567)))) (((-613 $)) . T) ((|#1|) . T) (((-567)) |has| |#1| (-1040 (-567))) (((-410 (-567))) -2836 (-12 (|has| |#1| (-559)) (|has| |#1| (-1040 (-567)))) (|has| |#1| (-1040 (-410 (-567))))) (((-410 (-954 |#1|))) |has| |#1| (-559)) (((-954 |#1|)) |has| |#1| (-1051)) (((-1179)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-772)) . T)) (((|#1|) . T)) -((($) -2811 (|has| |#1| (-365)) (|has| |#1| (-559))) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) ((|#1|) |has| |#1| (-172))) +((($) -2836 (|has| |#1| (-365)) (|has| |#1| (-559))) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) ((|#1|) |has| |#1| (-172))) (((|#1|) |has| |#1| (-310 |#1|))) ((((-1255 |#1| |#2| |#3| |#4|)) . T)) ((((-567)) |has| |#1| (-888 (-567))) (((-381)) |has| |#1| (-888 (-381)))) @@ -1992,14 +1992,14 @@ (|has| |#1| (-559)) ((((-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((|#1|) |has| |#1| (-172)) (($) |has| |#1| (-559))) (((|#1|) . 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T)) -(((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)))) ((((-1254 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-821)) @@ -2022,8 +2022,8 @@ (|has| |#1| (-849)) (|has| |#1| (-849)) (((|#1| (-567) (-1084)) . T)) -(-2811 (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051))) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +(-2836 (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051))) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) (((|#1| (-410 (-567)) (-1084)) . T)) (((|#1| (-772) (-1084)) . T)) (|has| |#1| (-851)) @@ -2037,41 +2037,41 @@ ((((-912 |#1|)) . T) (($) . T) (((-410 (-567))) . T)) (|has| |#1| (-1102)) ((((-410 (-567))) |has| |#2| (-365)) (($) . T) (((-567)) . T)) -((((-567)) -2811 (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051)))) +((((-567)) -2836 (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051)))) (((|#1|) . 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T) (((-567)) . T) (((-894 (-567))) . T) (((-381)) . T) (((-225)) . T)) ((((-863)) . T)) (|has| |#1| (-38 (-410 (-567)))) @@ -2104,28 +2104,28 @@ (|has| |#1| (-145)) ((($) |has| |#1| (-559)) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) (((|#1|) |has| |#1| (-172))) -((($) -2811 (|has| |#1| (-172)) (|has| |#1| (-559))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#1| (-172)) (|has| |#1| (-559))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) ((((-567)) . T) ((|#1|) . T) (($) . T) (((-410 (-567))) . T) (((-1179)) |has| |#1| (-1040 (-1179)))) (((|#1| |#2|) . T)) -((((-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) (((-567)) -2811 (|has| |#1| (-849)) (|has| |#1| (-1040 (-567)))) ((|#1|) . T)) +((((-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) (((-567)) -2836 (|has| |#1| (-849)) (|has| |#1| (-1040 (-567)))) ((|#1|) . T)) ((((-144)) . 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T)) (|has| |#1| (-911)) (((|#2|) |has| |#2| (-1051))) -(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) (((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) |has| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (-310 (-2 (|:| -1809 |#1|) (|:| -4236 |#2|))))) +(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) (((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) |has| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (-310 (-2 (|:| -2025 |#1|) (|:| -2265 |#2|))))) (|has| |#1| (-365)) (((|#1|) |has| |#1| (-172))) (((|#1| |#1|) . T)) @@ -2136,7 +2136,7 @@ (((|#1|) . T)) ((((-410 |#2|)) . T) (((-410 (-567))) . T) (($) . T) (((-567)) . T)) ((((-645 $)) . T) (((-1161)) . T) (((-1179)) . T) (((-567)) . T) (((-225)) . T) (((-863)) . T)) -((($) -2811 (|has| |#3| (-172)) (|has| |#3| (-849)) (|has| |#3| (-1051))) (((-567)) -2811 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-849)) (|has| |#3| (-1051))) ((|#3|) -2811 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051)))) +((($) -2836 (|has| |#3| (-172)) (|has| |#3| (-849)) (|has| |#3| (-1051))) (((-567)) -2836 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-849)) (|has| |#3| (-1051))) ((|#3|) -2836 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051)))) ((((-410 (-567))) . T) (((-567)) . T) (((-613 $)) . T)) (((|#1|) . T)) ((((-863)) . T)) @@ -2151,7 +2151,7 @@ (((|#1|) . T)) (((|#1| (-772) (-1084)) . T)) (((#0=(-410 |#2|) #0#) . T) ((#1=(-410 (-567)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-567)) -2811 (|has| (-410 (-567)) (-1040 (-567))) (|has| |#1| (-1040 (-567)))) (((-410 (-567))) . T)) +(((|#1|) . T) (((-567)) -2836 (|has| (-410 (-567)) (-1040 (-567))) (|has| |#1| (-1040 (-567)))) (((-410 (-567))) . T)) (((|#1| (-603 |#1| |#3|) (-603 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2172,12 +2172,12 @@ (((|#2|) |has| |#2| (-172))) (|has| |#2| (-849)) ((((-567)) . T) ((|#2|) . T) (((-410 (-567))) |has| |#2| (-1040 (-410 (-567))))) -((((-112)) |has| |#1| (-1102)) (((-863)) -2811 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-476)) (|has| |#1| (-727)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051)) (|has| |#1| (-1114)) (|has| |#1| (-1102)))) +((((-112)) |has| |#1| (-1102)) (((-863)) -2836 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-476)) (|has| |#1| (-727)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051)) (|has| |#1| (-1114)) (|has| |#1| (-1102)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-567)) . T) (((-410 (-567))) . T)) ((((-567)) . T) (($) . T) (((-410 (-567))) . T)) -((((-2 (|:| -1809 (-1161)) (|:| -4236 (-52)))) . T)) +((((-2 (|:| -2025 (-1161)) (|:| -2265 (-52)))) . T)) (((|#1|) . T) (((-410 (-567))) . T) (((-567)) . T) (($) . T)) (((|#1|) . T) (((-410 (-567))) . T) (((-567)) . T) (($) . T)) (((|#1|) . T) (((-410 (-567))) . T) (((-567)) . T) (($) . T)) @@ -2189,17 +2189,17 @@ ((((-700)) . T) (((-410 (-567))) . T) (((-567)) . T)) (((|#1| |#1|) |has| |#1| (-172))) (((|#2|) . T)) -((($) . T) (((-567)) . T) (((-410 (-567))) -2811 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) +((($) . T) (((-567)) . T) (((-410 (-567))) -2836 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) ((((-567) |#1|) . 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T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) ((((-410 (-567))) . T) (($) . T)) (|has| |#1| (-476)) (|has| |#1| (-370)) (|has| |#1| (-370)) (|has| |#1| (-370)) (|has| |#1| (-365)) -(-2811 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-476)) (|has| |#1| (-559)) (|has| |#1| (-1051)) (|has| |#1| (-1114))) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-476)) (|has| |#1| (-559)) (|has| |#1| (-1051)) (|has| |#1| (-1114))) (|has| |#1| (-38 (-410 (-567)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -2236,12 +2236,12 @@ (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-851)) -((((-2 (|:| -1809 (-1161)) (|:| -4236 |#1|))) . T)) +((((-2 (|:| -2025 (-1161)) (|:| -2265 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-567)) . T)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) |has| (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)) (-310 (-2 (|:| -1809 |#1|) (|:| -4236 |#2|)))) ((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102)))) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) |has| (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)) (-310 (-2 (|:| -2025 |#1|) (|:| -2265 |#2|)))) ((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2261,12 +2261,12 @@ ((((-539)) |has| |#1| (-615 (-539))) (((-894 (-567))) |has| |#1| (-615 (-894 (-567)))) (((-894 (-381))) |has| |#1| (-615 (-894 (-381)))) (((-381)) . #0=(|has| |#1| (-1024))) (((-225)) . #0#)) (((|#1|) |has| |#1| (-365))) ((((-863)) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) ((($ $) . T) (((-613 $) $) . T)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-559))) ((($) . 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T)) ((((-567) |#1|) . T)) ((((-1179)) |has| (-410 |#2|) (-902 (-1179)))) -(((|#1|) . T) (($) -2811 (|has| |#1| (-291)) (|has| |#1| (-365))) (((-410 (-567))) |has| |#1| (-365))) +(((|#1|) . T) (($) -2836 (|has| |#1| (-291)) (|has| |#1| (-365))) (((-410 (-567))) |has| |#1| (-365))) ((((-539)) |has| |#2| (-615 (-539)))) ((((-690 |#2|)) . T) (((-863)) . T)) (((|#1|) . T)) @@ -2347,22 +2347,22 @@ (((|#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1102)))) ((((-871 |#1|)) . T)) (((|#1|) |has| |#1| (-172))) -(-2811 (|has| |#4| (-794)) (|has| |#4| (-849))) -(-2811 (|has| |#3| (-794)) (|has| |#3| (-849))) +(-2836 (|has| |#4| (-794)) (|has| |#4| (-849))) +(-2836 (|has| |#3| (-794)) (|has| |#3| (-849))) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) ((((-863)) . T)) ((((-863)) . T)) (((|#1|) . T)) ((($) . T) (((-567)) . T) ((|#2|) . T)) (((|#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1102)))) -(((|#3|) -2811 (|has| |#3| (-172)) (|has| |#3| (-365)))) +(((|#3|) -2836 (|has| |#3| (-172)) (|has| |#3| (-365)))) (((|#2|) |has| |#2| (-1051))) (((|#3|) . T)) (((|#1|) . T)) ((((-410 |#2|)) . T)) -(((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)))) (((|#1|) . T)) -(((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051))) (($) |has| |#2| (-172))) +(((|#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051))) (($) |has| |#2| (-172))) (((|#3|) -12 (|has| |#3| (-310 |#3|)) (|has| |#3| (-1102)))) ((((-567) |#1|) . T)) (((|#1|) . T)) @@ -2371,17 +2371,17 @@ ((((-410 (-567))) . T) (($) . T)) ((((-410 (-567))) . T) (($) . T)) ((((-410 (-567))) . T) (($) . T)) -(-2811 (|has| |#1| (-455)) (|has| |#1| (-1223))) +(-2836 (|has| |#1| (-455)) (|has| |#1| (-1223))) ((($) . 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T)) @@ -2472,10 +2472,10 @@ ((((-863)) . T)) ((((-863)) . T)) ((((-539)) |has| |#1| (-615 (-539)))) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) ((((-567)) . T) (($) . T) (((-410 (-567))) . T)) ((((-1179) |#1|) |has| |#1| (-517 (-1179) |#1|)) ((|#1| |#1|) |has| |#1| (-310 |#1|))) -(((|#1|) -2811 (|has| |#1| (-172)) (|has| |#1| (-365)))) +(((|#1|) -2836 (|has| |#1| (-172)) (|has| |#1| (-365)))) (((|#1|) . T) (((-410 (-567))) . T) (($) . T)) ((((-567)) . T) (((-410 (-567))) . T) (($) . T)) (((|#1|) . T) (((-410 (-567))) . T) (($) . T)) @@ -2485,10 +2485,10 @@ (((|#1|) . T) (($) . T) (((-410 (-567))) . T)) (((|#1|) . T) (($) . T) (((-410 (-567))) . T)) (((|#2|) |has| |#2| (-365))) -((($) -2811 (|has| |#1| (-365)) (|has| |#1| (-351))) (((-410 (-567))) -2811 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) +((($) -2836 (|has| |#1| (-365)) (|has| |#1| (-351))) (((-410 (-567))) -2836 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) (((|#2|) . T)) ((((-410 (-567))) . T) (((-700)) . T) (($) . T)) -((($) . T) (((-410 (-567))) -2811 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) +((($) . T) (((-410 (-567))) -2836 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (((#0=(-781 |#1| (-865 |#2|)) #0#) |has| (-781 |#1| (-865 |#2|)) (-310 (-781 |#1| (-865 |#2|))))) ((((-567)) . T) (($) . T)) @@ -2507,13 +2507,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((($ $) . 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T)) ((((-410 (-567))) |has| |#2| (-1040 (-410 (-567)))) (((-567)) |has| |#2| (-1040 (-567))) ((|#2|) . T) (((-865 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-410 (-567))) . T)) ((((-1127 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-567)) |has| |#1| (-1040 (-567))) (((-410 (-567))) |has| |#1| (-1040 (-410 (-567))))) @@ -2546,22 +2546,22 @@ (((|#1| |#2|) . T)) ((((-1179) |#1|) . T)) (((|#4|) . T)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-351))) ((((-1179) (-52)) . T)) ((((-1254 |#2| |#3| |#4|) (-320 |#2| |#3| |#4|)) . T)) ((((-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) (((-567)) |has| |#1| (-1040 (-567))) ((|#1|) . T)) ((((-863)) . 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T)) (((|#1| $) |has| |#1| (-287 |#1| |#1|))) ((((-1255 |#1| |#2| |#3| |#4|)) . T) (((-410 (-567))) . T) (($) . T)) (((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-559)) (($) |has| |#1| (-559))) -((((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2811 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-559))) ((|#1|) . T)) +((((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) -2836 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-559))) ((|#1|) . T)) (|has| |#1| (-365)) -((($) |has| |#1| (-849)) (((-567)) -2811 (|has| |#1| (-21)) (|has| |#1| (-849)))) +((($) |has| |#1| (-849)) (((-567)) -2836 (|has| |#1| (-21)) (|has| |#1| (-849)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-147)) @@ -2574,17 +2574,17 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102)))) (((|#2| |#3|) . T)) -(-2811 (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) +(-2836 (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) (((|#1| (-534 |#2|)) . T)) (((|#1| (-772)) . T)) (((|#1| (-534 (-1090 (-1179)))) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (|has| |#2| (-911)) -(-2811 (|has| |#2| (-794)) (|has| |#2| (-849))) +(-2836 (|has| |#2| (-794)) (|has| |#2| (-849))) ((((-863)) . T)) -(((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)))) -(((|#2|) -2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051))) (($) |has| |#2| (-172))) +(((|#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1051))) (($) |has| |#2| (-172))) ((($ $) . T) ((#0=(-1254 |#2| |#3| |#4|) #0#) . T) ((#1=(-410 (-567)) #1#) |has| #0# (-38 (-410 (-567))))) ((((-912 |#1|)) . T)) (-12 (|has| |#1| (-365)) (|has| |#2| (-821))) @@ -2592,14 +2592,14 @@ ((((-863)) . T)) ((($) . T)) ((($) . T)) -(-2811 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-559))) (|has| |#1| (-365)) (|has| |#1| (-365)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1254 |#2| |#3| |#4|)) . T) (((-410 (-567))) |has| #0# (-38 (-410 (-567))))) ((((-1177 |#1| |#2| |#3|)) |has| |#1| (-365))) -(-2811 (-12 (|has| |#1| (-308)) (|has| |#1| (-911))) (|has| |#1| (-365)) (|has| |#1| (-351))) -(-2811 (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051))) +(-2836 (-12 (|has| |#1| (-308)) (|has| |#1| (-911))) (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051))) ((((-567)) |has| |#1| (-640 (-567))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-863)) . T)) @@ -2644,28 +2644,28 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1102)))) (((|#2|) . T)) -(((|#2|) -2811 (|has| |#2| (-6 (-4424 "*"))) (|has| |#2| (-172)))) -(-2811 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) -(-2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) +(((|#2|) -2836 (|has| |#2| (-6 (-4424 "*"))) (|has| |#2| (-172)))) +(-2836 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) +(-2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) (|has| |#2| (-911)) (|has| |#1| (-911)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) ((((-1261 |#1| |#2| |#3|)) |has| |#1| (-365))) ((((-863)) . T)) ((((-863)) . T)) ((((-539)) . T) (((-567)) . T) (((-894 (-567))) . T) (((-381)) . T) (((-225)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-567)) . T)) -((((-2 (|:| -1809 (-1161)) (|:| -4236 (-52)))) . T)) +((((-2 (|:| -2025 (-1161)) (|:| -2265 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) ((((-863)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-567)) . T)) (((|#1| (-410 (-567))) . T)) (((|#1|) . T)) -(-2811 (|has| |#1| (-291)) (|has| |#1| (-365))) +(-2836 (|has| |#1| (-291)) (|has| |#1| (-365))) ((((-144)) . T)) ((((-410 |#2|)) . T) (((-410 (-567))) . T) (($) . T)) (|has| |#1| (-849)) @@ -2681,7 +2681,7 @@ ((((-863)) . T)) ((((-863)) . T)) ((((-187)) . T) (((-863)) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-863)) . T)) ((((-863)) . T)) @@ -2694,7 +2694,7 @@ ((((-863)) . T)) ((((-1161)) . T)) ((((-1179) |#1|) |has| |#1| (-517 (-1179) |#1|)) ((|#1| |#1|) |has| |#1| (-310 |#1|))) -((((-2 (|:| -1809 (-1161)) (|:| -4236 |#1|))) . T)) +((((-2 (|:| -2025 (-1161)) (|:| -2265 |#1|))) . T)) (|has| |#1| (-851)) ((((-863)) . T)) ((((-539)) |has| |#1| (-615 (-539)))) @@ -2706,16 +2706,16 @@ (((|#2|) . T)) ((((-912 |#1|)) . T) (((-410 (-567))) . T) (($) . T)) ((($) . T) (((-567)) . T) (((-410 (-567))) . T) (((-613 $)) . T)) -(-2811 (|has| |#4| (-172)) (|has| |#4| (-727)) (|has| |#4| (-849)) (|has| |#4| (-1051))) -(-2811 (|has| |#3| (-172)) (|has| |#3| (-727)) (|has| |#3| (-849)) (|has| |#3| (-1051))) +(-2836 (|has| |#4| (-172)) (|has| |#4| (-727)) (|has| |#4| (-849)) (|has| |#4| (-1051))) +(-2836 (|has| |#3| (-172)) (|has| |#3| (-727)) (|has| |#3| (-849)) (|has| |#3| (-1051))) ((((-1179) (-52)) . T)) -(-2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) +(-2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2811 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) -(-2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-849)) (|has| |#2| (-1051))) (|has| |#1| (-911)) ((((-912 |#1|)) . T) (((-410 (-567))) . T) (($) . T) (((-567)) . T)) (|has| |#1| (-911)) @@ -2732,12 +2732,12 @@ (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567)))) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) (|has| |#1| (-821)) (((#0=(-912 |#1|) #0#) . T) (($ $) . T) ((#1=(-410 (-567)) #1#) . T)) ((((-410 |#2|)) . T)) (|has| |#1| (-849)) -((((-1205 |#1|)) . T) (((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) +((((-1205 |#1|)) . T) (((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) (((|#1| |#1|) . T) ((#0=(-410 (-567)) #0#) . T) ((#1=(-567) #1#) . T) (($ $) . T)) ((((-912 |#1|)) . T) (($) . T) (((-410 (-567))) . T)) (((|#2|) |has| |#2| (-1051)) (((-567)) -12 (|has| |#2| (-640 (-567))) (|has| |#2| (-1051)))) @@ -2753,28 +2753,28 @@ (((|#2|) |has| |#2| (-172))) (((|#1|) . T)) (((|#2|) . T)) -(-2811 (|has| |#1| (-145)) (|has| |#1| (-370))) -(-2811 (|has| |#1| (-145)) (|has| |#1| (-370))) -(-2811 (|has| |#1| (-145)) (|has| |#1| (-370))) -((((-2 (|:| -1809 (-1179)) (|:| -4236 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1809 (-1179)) (|:| -4236 #0#))) . T)) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-370))) +((((-2 (|:| -2025 (-1179)) (|:| -2265 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2025 (-1179)) (|:| -2265 #0#))) . T)) (|has| |#1| (-351)) ((((-567)) . T)) ((((-863)) . T)) (((|#1|) . T)) (((#0=(-1255 |#1| |#2| |#3| |#4|) $) |has| #0# (-287 #0# #0#))) (|has| |#1| (-365)) -(((|#1|) -2811 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1051))) (($) -2811 (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051))) (((-567)) -2811 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051)))) +(((|#1|) -2836 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1051))) (($) -2836 (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051))) (((-567)) -2836 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051)))) (((#0=(-1084) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-351))) (((#0=(-410 (-567)) #0#) . T) ((#1=(-700) #1#) . T) (($ $) . T)) ((((-317 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-410 (-567))) |has| |#1| (-365))) ((((-863)) . T)) (|has| |#1| (-1102)) (((|#1|) . T)) -(((|#1|) -2811 (|has| |#2| (-369 |#1|)) (|has| |#2| (-420 |#1|)))) -(((|#1|) -2811 (|has| |#2| (-369 |#1|)) (|has| |#2| (-420 |#1|)))) +(((|#1|) -2836 (|has| |#2| (-369 |#1|)) (|has| |#2| (-420 |#1|)))) +(((|#1|) -2836 (|has| |#2| (-369 |#1|)) (|has| |#2| (-420 |#1|)))) (((|#2|) . T)) ((((-410 (-567))) . T) (((-700)) . T) (($) . T)) ((((-582)) . T)) @@ -2799,7 +2799,7 @@ (((|#1|) . T)) ((((-567)) . T)) (((|#2|) . T) (((-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) ((|#1|) . T) (($) . T) (((-567)) . T)) -(-2811 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) +(-2836 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) (((|#2|) . T) (((-567)) |has| |#2| (-640 (-567)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2843,7 +2843,7 @@ (|has| |#2| (-1024)) ((($) . T)) (|has| |#1| (-911)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2852,10 +2852,10 @@ (|has| |#1| (-365)) ((((-912 |#1|)) . T)) ((($) . T) (((-567)) . T) ((|#1|) . T) (((-410 (-567))) . T)) -((($) -2811 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) -((($) |has| |#1| (-849)) (((-567)) -2811 (|has| |#1| (-21)) (|has| |#1| (-849)))) +((($) -2836 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) |has| |#1| (-849)) (((-567)) -2836 (|has| |#1| (-21)) (|has| |#1| (-849)))) ((($ $) . T) ((#0=(-410 (-567)) #0#) . T)) -(-2811 (|has| |#1| (-370)) (|has| |#1| (-851))) +(-2836 (|has| |#1| (-370)) (|has| |#1| (-851))) (((|#1|) . T)) ((((-772)) . T)) ((((-863)) . T)) @@ -2866,17 +2866,17 @@ ((((-567)) . T) (($) . T)) ((((-567)) . T) (($) . T)) ((((-772) |#1|) . T)) -(((|#2| (-240 (-2423 |#1|) (-772))) . T)) +(((|#2| (-240 (-2498 |#1|) (-772))) . T)) (((|#1| (-534 |#3|)) . T)) ((((-410 (-567))) . T)) -(-2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) +(-2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((((-1161)) . T) (((-863)) . T)) -(((#0=(-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) #0#) |has| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (-310 (-2 (|:| -1809 (-1179)) (|:| -4236 (-52)))))) +(((#0=(-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) #0#) |has| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (-310 (-2 (|:| -2025 (-1179)) (|:| -2265 (-52)))))) ((((-1161)) . T)) (|has| |#1| (-911)) (|has| |#2| (-365)) (((|#1|) . T) (($) . T) (((-567)) . T)) -(-2811 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) ((((-169 (-381))) . T) (((-225)) . T) (((-381)) . T)) ((((-863)) . T)) (((|#1|) . T)) @@ -2893,11 +2893,11 @@ (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567)))) -(-2811 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) (|has| |#1| (-38 (-410 (-567)))) (-12 (|has| |#1| (-548)) (|has| |#1| (-829))) ((((-863)) . T)) -((((-1179)) -2811 (-12 (|has| |#1| (-15 * (|#1| (-567) |#1|))) (|has| |#1| (-902 (-1179)))) (-12 (|has| |#1| (-365)) (|has| |#2| (-902 (-1179)))))) +((((-1179)) -2836 (-12 (|has| |#1| (-15 * (|#1| (-567) |#1|))) (|has| |#1| (-902 (-1179)))) (-12 (|has| |#1| (-365)) (|has| |#2| (-902 (-1179)))))) (|has| |#1| (-365)) ((((-1179)) -12 (|has| |#1| (-15 * (|#1| (-410 (-567)) |#1|))) (|has| |#1| (-902 (-1179))))) (|has| |#1| (-365)) @@ -2909,7 +2909,7 @@ (((|#2|) |has| |#1| (-365))) (((|#2|) |has| |#1| (-365))) ((((-567)) . T) (($) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2939,11 +2939,11 @@ (((|#2|) |has| |#1| (-365))) ((((-381)) -12 (|has| |#1| (-365)) (|has| |#2| (-888 (-381)))) (((-567)) -12 (|has| |#1| (-365)) (|has| |#2| (-888 (-567))))) (|has| |#1| (-365)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-559))) (|has| |#1| (-365)) (((|#1|) . T)) ((($) . T) (((-567)) . T) ((|#2|) . T)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-559))) (|has| |#1| (-365)) (((|#3|) . T)) ((((-1161)) . T) (((-509)) . T) (((-225)) . T) (((-567)) . T)) @@ -2951,23 +2951,23 @@ (|has| |#1| (-559)) (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1102)))) ((((-410 |#2|)) . T) (((-410 (-567))) . T) (($) . T) (((-567)) . T)) -(-2811 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) (((|#2|) . T)) (((|#2|) . T)) -(-2811 (|has| |#2| (-172)) (|has| |#2| (-727)) (|has| |#2| (-849)) (|has| |#2| (-1051))) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) -((((-2 (|:| -1809 (-1161)) (|:| -4236 |#1|))) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +(-2836 (|has| |#2| (-172)) (|has| |#2| (-727)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) +((((-2 (|:| -2025 (-1161)) (|:| -2265 |#1|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) (|has| |#1| (-38 (-410 (-567)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-410 (-567)))) -(-2811 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-370))) ((($) . T)) ((((-1161) |#1|) . T)) (|has| |#1| (-147)) -(-2811 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-370))) (|has| |#1| (-147)) -(-2811 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-370))) ((($) . T)) (|has| |#1| (-147)) ((((-584 |#1|)) . T)) @@ -2981,7 +2981,7 @@ ((((-410 (-567))) |has| |#2| (-1040 (-567))) (((-567)) |has| |#2| (-1040 (-567))) (((-1179)) |has| |#2| (-1040 (-1179))) ((|#2|) . T)) (((#0=(-410 |#2|) #0#) . T) ((#1=(-410 (-567)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2811 (|has| |#1| (-145)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-351))) (|has| |#1| (-147)) ((((-863)) . T)) ((($) . T)) @@ -3006,7 +3006,7 @@ ((((-863)) . T)) ((((-912 |#1|)) . T) (((-410 (-567))) . T) (($) . T) (((-567)) . T)) ((((-539)) |has| |#1| (-615 (-539)))) -((((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-851)) (|has| |#1| (-1102)))) +((((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-851)) (|has| |#1| (-1102)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3028,7 +3028,7 @@ ((((-567)) . T)) ((((-863)) . T)) ((((-567)) . T)) -(-2811 (|has| |#2| (-794)) (|has| |#2| (-849))) +(-2836 (|has| |#2| (-794)) (|has| |#2| (-849))) ((((-169 (-381))) . T) (((-225)) . T) (((-381)) . T)) ((((-863)) . T)) ((((-863)) . T)) @@ -3040,9 +3040,9 @@ (((|#1|) . T) (($) . T) (((-410 (-567))) . T)) (|has| |#1| (-365)) (|has| |#1| (-365)) -((((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) -((((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-476)) (|has| |#1| (-727)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051)) (|has| |#1| (-1114)) (|has| |#1| (-1102))) +((((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) +((((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) +(-2836 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-476)) (|has| |#1| (-727)) (|has| |#1| (-902 (-1179))) (|has| |#1| (-1051)) (|has| |#1| (-1114)) (|has| |#1| (-1102))) (|has| |#1| (-1154)) ((((-912 |#1|)) . T) (((-410 (-567))) . T) (($) . T)) ((((-912 |#1|)) . T) (($) . T) (((-410 (-567))) . T)) @@ -3059,25 +3059,25 @@ (((|#1|) |has| |#1| (-310 |#1|))) ((((-567) |#1|) . T)) ((((-1179) |#1|) . T)) -(((|#1|) -2811 (|has| |#1| (-172)) (|has| |#1| (-365)))) +(((|#1|) -2836 (|has| |#1| (-172)) (|has| |#1| (-365)))) (((|#1|) . T)) -(((|#1|) -2811 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1051)))) +(((|#1|) -2836 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1051)))) ((((-567)) . T) (((-410 (-567))) . T)) (((|#1|) . T)) (|has| |#1| (-559)) ((($) . T) (((-567)) . T) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-365))) ((((-410 |#2|)) . T) (((-410 (-567))) . T) (($) . T)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-559))) ((((-381)) . T)) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-365)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-559))) (|has| |#1| (-365)) (|has| |#1| (-559)) (|has| |#1| (-1102)) ((((-781 |#1| (-865 |#2|))) |has| (-781 |#1| (-865 |#2|)) (-310 (-781 |#1| (-865 |#2|))))) -(-2811 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) +(-2836 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3089,13 +3089,13 @@ (|has| |#2| (-365)) ((((-584 |#1|)) . T) (((-410 (-567))) . T) (($) . T) (((-567)) . T)) ((((-567)) . T) (((-410 (-567))) . T) (($) . T)) -((((-2 (|:| -1809 (-1161)) (|:| -4236 (-52)))) . T)) +((((-2 (|:| -2025 (-1161)) (|:| -2265 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-567)) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) ((((-863)) . T)) ((((-863)) . T)) -(-2811 (|has| |#3| (-794)) (|has| |#3| (-849))) +(-2836 (|has| |#3| (-794)) (|has| |#3| (-849))) ((((-863)) . T)) ((((-1122)) . T) (((-863)) . T)) ((((-539)) . T) (((-863)) . T)) @@ -3106,12 +3106,12 @@ ((((-567)) . T)) (((|#3|) . T)) ((((-863)) . T)) -(-2811 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) -((((-567)) . T) (((-410 (-567))) -2811 (|has| |#2| (-38 (-410 (-567)))) (|has| |#2| (-1040 (-410 (-567))))) ((|#2|) . T) (($) -2811 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) (((-865 |#1|)) . T)) -((((-1127 |#1| |#2|)) . T) ((|#2|) . T) (($) -2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-1040 (-410 (-567))))) (((-567)) . T)) -((((-1175 |#1|)) . T) (((-567)) . T) (($) -2811 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) (((-1084)) . T) ((|#1|) . 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T)) +((((-1175 |#1|)) . T) (((-567)) . T) (($) -2836 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) (((-1084)) . T) ((|#1|) . T) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-1040 (-410 (-567)))))) +(-2836 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-559)) (|has| |#1| (-1051))) +((((-1127 |#1| (-1179))) . T) (((-567)) . T) (((-1090 (-1179))) . T) (($) -2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-1040 (-410 (-567))))) (((-1179)) . T)) (((#0=(-584 |#1|) #0#) . T) (($ $) . T) ((#1=(-410 (-567)) #1#) . T)) ((($ $) . T) ((#0=(-410 (-567)) #0#) . T)) (((|#1|) |has| |#1| (-172))) @@ -3129,7 +3129,7 @@ (((|#1|) . T)) ((((-863)) . T)) ((((-295 |#3|)) . T)) -(((#0=(-410 (-567)) #0#) |has| |#2| (-38 (-410 (-567)))) ((|#2| |#2|) . T) (($ $) -2811 (|has| |#2| (-172)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911)))) +(((#0=(-410 (-567)) #0#) |has| |#2| (-38 (-410 (-567)))) ((|#2| |#2|) . T) (($ $) -2836 (|has| |#2| (-172)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) . T)) @@ -3137,21 +3137,21 @@ (((|#1|) . T) (((-410 (-567))) . T) (($) . T)) (((|#1|) . T) (((-410 (-567))) . T) (($) . T)) (((|#1|) . T) (((-410 (-567))) . T) (($) . T)) -((($ $) -2811 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1| |#1|) . T) ((#0=(-410 (-567)) #0#) |has| |#1| (-38 (-410 (-567))))) -((($ $) -2811 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1| |#1|) . 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T) ((#0=(-410 (-567)) #0#) |has| |#1| (-38 (-410 (-567))))) +((($ $) -2836 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1| |#1|) . T) ((#0=(-410 (-567)) #0#) |has| |#1| (-38 (-410 (-567))))) ((((-863)) . T)) -((($) -2811 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) -((($) -2811 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) (|has| |#2| (-911)) (|has| |#1| (-911)) -((($) -2811 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) ((((-863)) . T)) (((|#1|) . T)) -((((-2 (|:| -1809 (-1161)) (|:| -4236 |#1|))) . T)) +((((-2 (|:| -2025 (-1161)) (|:| -2265 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3170,10 +3170,10 @@ (((#0=(-410 (-567)) #0#) . T)) ((((-410 (-567))) . T)) (((|#1|) |has| |#1| (-172))) -(-2811 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) (((|#1|) . T)) (((|#1|) . T)) -(-2811 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-849)) (|has| |#2| (-1051))) (((|#1|) . T)) ((((-410 (-567))) . T) (((-567)) . T) (($) . T)) ((((-539)) . T)) @@ -3192,14 +3192,14 @@ ((($ $) . T) ((#0=(-410 (-567)) #0#) . T)) ((((-1179)) |has| |#1| (-902 (-1179)))) ((((-912 |#1|)) . T) (((-410 (-567))) . T) (($) . T)) -((($) . T) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) ((|#1|) . T)) -(((#0=(-410 (-567)) #0#) |has| |#1| (-38 (-410 (-567)))) ((|#1| |#1|) . 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T)) (|has| |#2| (-821)) (|has| |#2| (-821)) -((((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) ((|#2|) |has| |#1| (-365)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-410 (-567))) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) . T)) +((((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) ((|#2|) |has| |#1| (-365)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (((|#1|) . T) (((-567)) |has| |#1| (-1040 (-567))) (((-410 (-567))) |has| |#1| (-1040 (-410 (-567))))) ((((-567)) |has| |#1| (-888 (-567))) (((-381)) |has| |#1| (-888 (-381)))) @@ -3236,7 +3236,7 @@ (((|#1|) . 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T)) -(-2811 (|has| |#2| (-794)) (|has| |#2| (-849))) -(-2811 (-12 (|has| |#1| (-794)) (|has| |#2| (-794))) (-12 (|has| |#1| (-851)) (|has| |#2| (-851)))) +(-2836 (|has| |#2| (-794)) (|has| |#2| (-849))) +(-2836 (-12 (|has| |#1| (-794)) (|has| |#2| (-794))) (-12 (|has| |#1| (-851)) (|has| |#2| (-851)))) ((((-871 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-370)) @@ -3282,7 +3282,7 @@ (((|#1|) . T)) ((((-863)) . T)) (|has| |#2| (-911)) -((((-2 (|:| -1809 (-1179)) (|:| -4236 (-52)))) . T)) +((((-2 (|:| -2025 (-1179)) (|:| -2265 (-52)))) . T)) ((((-539)) |has| |#2| (-615 (-539))) (((-894 (-381))) |has| |#2| (-615 (-894 (-381)))) (((-894 (-567))) |has| |#2| (-615 (-894 (-567))))) ((((-863)) . T)) ((((-863)) . T)) @@ -3309,7 +3309,7 @@ ((((-1184)) . T)) ((((-645 |#1|)) . T)) ((($) . T) (((-567)) . T) (((-1255 |#1| |#2| |#3| |#4|)) . T) (((-410 (-567))) . 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T)) -(-2811 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) ((((-567)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -3342,9 +3342,9 @@ ((($) . T) (((-410 (-567))) . T)) ((($) . T)) ((($) . T)) -(-2811 (|has| |#1| (-851)) (|has| |#1| (-1102))) +(-2836 (|has| |#1| (-851)) (|has| |#1| (-1102))) (((|#1|) . T)) -((($) -2811 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) ((((-863)) . T)) ((((-144)) . T)) (((|#1|) . T) (((-410 (-567))) . T)) @@ -3376,7 +3376,7 @@ (|has| |#1| (-1102)) (|has| |#1| (-1102)) (|has| |#2| (-365)) -(((|#1|) . T) (($) -2811 (|has| |#1| (-291)) (|has| |#1| (-365))) (((-410 (-567))) |has| |#1| (-365))) +(((|#1|) . T) (($) -2836 (|has| |#1| (-291)) (|has| |#1| (-365))) (((-410 (-567))) |has| |#1| (-365))) (|has| |#1| (-365)) (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567)))) @@ -3385,32 +3385,32 @@ ((((-1179)) -12 (|has| |#3| (-902 (-1179))) (|has| |#3| (-1051)))) (((|#1|) . T)) (|has| |#1| (-233)) -(((|#2| (-240 (-2423 |#1|) (-772))) . T)) +(((|#2| (-240 (-2498 |#1|) (-772))) . T)) (((|#1| (-534 |#3|)) . T)) (|has| |#1| (-370)) (|has| |#1| (-370)) (|has| |#1| (-370)) (((|#1|) . T) (($) . T)) (((|#1| (-534 |#2|)) . T)) -(-2811 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) (((|#1| (-772)) . 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T)) +((((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-851)) (|has| |#1| (-1102)))) ((((-539)) |has| |#1| (-615 (-539)))) (((|#1|) . T) (((-410 (-567))) . T) (($) . T) (((-567)) . T)) (((|#1|) . T) (((-410 (-567))) . T) (($) . T) (((-567)) . T)) @@ -3429,14 +3429,14 @@ (((|#2|) |has| |#2| (-1051)) (((-567)) -12 (|has| |#2| (-640 (-567))) (|has| |#2| (-1051)))) (((|#1|) . T)) (|has| |#2| (-365)) -(((#0=(-410 (-567)) #0#) |has| |#2| (-38 (-410 (-567)))) ((|#2| |#2|) . T) (($ $) -2811 (|has| |#2| (-172)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911)))) -((($ $) -2811 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1| |#1|) . T) ((#0=(-410 (-567)) #0#) |has| |#1| (-38 (-410 (-567))))) +(((#0=(-410 (-567)) #0#) |has| |#2| (-38 (-410 (-567)))) ((|#2| |#2|) . 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T) (($) -2836 (|has| |#2| (-172)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911)))) +((($) -2836 (|has| |#1| (-172)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) (((|#1|) . T) (($) . T) (((-410 (-567))) . T)) (((|#1|) . T) (($) . T) (((-410 (-567))) . T)) (((|#1|) . T) (($) . T) (((-410 (-567))) . T)) @@ -3448,12 +3448,12 @@ (((|#1|) . 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T)) ((((-863)) . T) (((-1184)) . T)) ((((-863)) . T) (((-1184)) . T)) -((((-645 |#1|)) . T) (((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-851)) (|has| |#1| (-1102)))) +((((-645 |#1|)) . T) (((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-851)) (|has| |#1| (-1102)))) ((((-1184)) . T)) ((((-1184)) . T)) ((((-1184)) . T)) @@ -3476,23 +3476,23 @@ ((((-1184)) . T)) ((((-863)) . T) (((-1184)) . T)) ((((-1184)) . T)) -((((-2 (|:| -1809 (-1179)) (|:| -4236 (-52)))) |has| (-2 (|:| -1809 (-1179)) (|:| -4236 (-52))) (-310 (-2 (|:| -1809 (-1179)) (|:| -4236 (-52)))))) -(-2811 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) +((((-2 (|:| -2025 (-1179)) (|:| -2265 (-52)))) |has| (-2 (|:| -2025 (-1179)) (|:| -2265 (-52))) (-310 (-2 (|:| -2025 (-1179)) (|:| -2265 (-52)))))) +(-2836 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) ((((-567) |#1|) . T)) ((((-567) |#1|) . T)) ((((-567) |#1|) . 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T) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) -2836 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) (((-567)) . T) (($) -2836 (|has| |#1| (-365)) (|has| |#1| (-559)))) ((($ $) . T) ((#0=(-865 |#1|) $) . T) ((#0# |#2|) . T)) ((((-1127 |#1| (-1179))) . T) (((-819 (-1179))) . T) ((|#1|) . T) (((-567)) |has| |#1| (-1040 (-567))) (((-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) (((-1179)) . T)) ((($) . T)) @@ -3533,12 +3533,12 @@ (((#0=(-1255 |#1| |#2| |#3| |#4|)) |has| #0# (-310 #0#))) ((($) . T)) (((|#1|) . T)) -((($ $) -2811 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-559))) ((#0=(-410 (-567)) #0#) -2811 (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-365))) ((|#2| |#2|) |has| |#1| (-365)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . 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T)) -(-2811 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) -(-2811 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-794)) (|has| |#2| (-794)))) +(-2836 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-794)) (|has| |#2| (-794)))) ((((-1261 |#1| |#2| |#3|)) |has| |#1| (-365))) ((($) . T) (((-871 |#1|)) . T) (((-410 (-567))) . T)) ((((-1261 |#1| |#2| |#3|)) |has| |#1| (-365))) @@ -3580,15 +3580,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-410 |#2|)) . 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T)) (((|#2| |#2|) . T) ((#0=(-410 (-567)) #0#) . T) (($ $) . T)) ((((-567)) . T)) @@ -3619,17 +3619,17 @@ ((($) . T) (((-567)) . T) (((-116 |#1|)) . T) (((-410 (-567))) . T)) (((|#1| |#2| (-240 |#1| |#2|) (-240 |#1| |#2|)) . T)) ((((-863)) . T)) -((((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) |has| |#2| (-172)) (($) -2811 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911)))) +((((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) |has| |#2| (-172)) (($) -2836 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) . T)) ((($) . T) (((-567)) . T)) -((($) -2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) ((((-1106)) . T)) ((((-863)) . T)) -((($) -2811 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) ((($) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((|#1|) . T)) ((($) . T)) -((($) -2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) +((($) -2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((|#1|) |has| |#1| (-172)) (((-410 (-567))) |has| |#1| (-38 (-410 (-567))))) ((((-1261 |#1| |#2| |#3|)) . T)) ((((-1261 |#1| |#2| |#3|)) |has| |#1| (-365))) (|has| |#1| (-365)) @@ -3642,7 +3642,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-172))) ((((-700)) . T)) -((((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) +((((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) ((((-1184)) . T)) (((|#1|) |has| |#1| (-172))) ((((-1184)) . T)) @@ -3659,13 +3659,13 @@ ((((-1184)) . T)) ((((-1184)) . T)) ((((-1184)) . T)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-351))) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-351))) ((((-1184)) . T)) ((((-1184)) . T)) (|has| |#1| (-365)) (|has| |#1| (-365)) -(-2811 (|has| |#1| (-172)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-172)) (|has| |#1| (-559))) (((|#1| (-567)) . T)) (((|#1| (-410 (-567))) . T)) (((|#1| (-772)) . T)) @@ -3680,16 +3680,16 @@ ((((-894 (-381))) . T) (((-894 (-567))) . T) (((-1179)) . T) (((-539)) . T)) (((|#1|) . T)) ((((-863)) . T)) -(-2811 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) -(-2811 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-794)) (|has| |#2| (-794)))) +(-2836 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-794)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-794)) (|has| |#2| (-794)))) ((((-567)) . T)) ((((-567)) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2811 (|has| |#2| (-172)) (|has| |#2| (-727)) (|has| |#2| (-849)) (|has| |#2| (-1051))) +(-2836 (|has| |#2| (-172)) (|has| |#2| (-727)) (|has| |#2| (-849)) (|has| |#2| (-1051))) ((((-1179)) -12 (|has| |#2| (-902 (-1179))) (|has| |#2| (-1051)))) -(-2811 (-12 (|has| |#1| (-476)) (|has| |#2| (-476))) (-12 (|has| |#1| (-727)) (|has| |#2| (-727)))) +(-2836 (-12 (|has| |#1| (-476)) (|has| |#2| (-476))) (-12 (|has| |#1| (-727)) (|has| |#2| (-727)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-365)) @@ -3720,7 +3720,7 @@ (((|#1| |#2|) . T)) ((((-567)) . T) ((|#2|) |has| |#2| (-172))) ((((-114)) . T) ((|#1|) . T) (((-567)) . T)) -(-2811 (|has| |#1| (-351)) (|has| |#1| (-370))) +(-2836 (|has| |#1| (-351)) (|has| |#1| (-370))) (((|#1| |#2|) . T)) ((((-225)) . T)) ((((-410 (-567))) . T) (($) . T) (((-567)) . T)) @@ -3732,7 +3732,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-539)) |has| |#1| (-615 (-539)))) -((((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-851)) (|has| |#1| (-1102)))) +((((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-851)) (|has| |#1| (-1102)))) ((($) . T) (((-410 (-567))) . T)) (|has| |#1| (-911)) (|has| |#1| (-911)) @@ -3743,14 +3743,14 @@ (((|#1| |#1|) |has| |#1| (-172))) (((|#1|) . T) (((-567)) . T)) ((((-1184)) . T)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-559))) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-849))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-559))) +(-2836 (|has| |#1| (-21)) (|has| |#1| (-849))) (((|#2|) . T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-849))) +(-2836 (|has| |#1| (-21)) (|has| |#1| (-849))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (((|#1|) . T)) -((((-863)) -2811 (-12 (|has| |#1| (-614 (-863))) (|has| |#2| (-614 (-863)))) (-12 (|has| |#1| (-1102)) (|has| |#2| (-1102))))) +((((-863)) -2836 (-12 (|has| |#1| (-614 (-863))) (|has| |#2| (-614 (-863)))) (-12 (|has| |#1| (-1102)) (|has| |#2| (-1102))))) ((((-410 |#2|) |#3|) . T)) ((((-410 (-567))) . T) (($) . T)) (|has| |#1| (-38 (-410 (-567)))) @@ -3764,19 +3764,19 @@ (((|#1|) . T) (((-410 (-567))) . T) (((-567)) . T) (($) . T)) (((#0=(-567) #0#) . T)) ((($) . T) (((-410 (-567))) . T)) -(-2811 (|has| |#4| (-172)) (|has| |#4| (-727)) (|has| |#4| (-849)) (|has| |#4| (-1051))) -(-2811 (|has| |#3| (-172)) (|has| |#3| (-727)) (|has| |#3| (-849)) (|has| |#3| (-1051))) +(-2836 (|has| |#4| (-172)) (|has| |#4| (-727)) (|has| |#4| (-849)) (|has| |#4| (-1051))) +(-2836 (|has| |#3| (-172)) (|has| |#3| (-727)) (|has| |#3| (-849)) (|has| |#3| (-1051))) ((((-863)) . T) (((-1184)) . T)) (|has| |#4| (-794)) -(-2811 (|has| |#4| (-794)) (|has| |#4| (-849))) +(-2836 (|has| |#4| (-794)) (|has| |#4| (-849))) (|has| |#4| (-849)) (|has| |#3| (-794)) ((((-1184)) . T)) -(-2811 (|has| |#3| (-794)) (|has| |#3| (-849))) +(-2836 (|has| |#3| (-794)) (|has| |#3| (-849))) (|has| |#3| (-849)) ((((-567)) . T)) (((|#2|) . T)) -((((-1179)) -2811 (-12 (|has| (-1177 |#1| |#2| |#3|) (-902 (-1179))) (|has| |#1| (-365))) (-12 (|has| |#1| (-15 * (|#1| (-567) |#1|))) (|has| |#1| (-902 (-1179)))))) +((((-1179)) -2836 (-12 (|has| (-1177 |#1| |#2| |#3|) (-902 (-1179))) (|has| |#1| (-365))) (-12 (|has| |#1| (-15 * (|#1| (-567) |#1|))) (|has| |#1| (-902 (-1179)))))) ((((-1179)) -12 (|has| |#1| (-15 * (|#1| (-410 (-567)) |#1|))) (|has| |#1| (-902 (-1179))))) ((((-1179)) -12 (|has| |#1| (-15 * (|#1| (-772) |#1|))) (|has| |#1| (-902 (-1179))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3791,11 +3791,11 @@ ((((-1177 |#1| |#2| |#3|)) |has| |#1| (-365))) ((((-1142 |#1| |#2|)) . T)) ((((-1177 |#1| |#2| |#3|)) |has| |#1| (-365))) -(((|#2|) . T) (((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) -((((-2 (|:| -1809 (-1179)) (|:| -4236 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) +((((-2 (|:| -2025 (-1179)) (|:| -2265 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1024)) -(((|#2|) . T) (((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) ((((-863)) . T)) ((((-539)) |has| |#2| (-615 (-539))) (((-894 (-567))) |has| |#2| (-615 (-894 (-567)))) (((-894 (-381))) |has| |#2| (-615 (-894 (-381)))) (((-381)) . #0=(|has| |#2| (-1024))) (((-225)) . #0#)) ((((-295 |#3|)) . T)) @@ -3812,15 +3812,15 @@ ((((-1177 |#1| |#2| |#3|)) . T)) ((((-1177 |#1| |#2| |#3|)) . T) (((-1170 |#1| |#2| |#3|)) . T)) ((((-863)) . T)) -((((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) +((((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) ((((-567) |#1|) . T)) ((((-1177 |#1| |#2| |#3|)) |has| |#1| (-365))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-365)) -(((|#3|) . T) ((|#2|) . T) (($) -2811 (|has| |#4| (-172)) (|has| |#4| (-849)) (|has| |#4| (-1051))) ((|#4|) -2811 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1051)))) -(((|#2|) . T) (($) -2811 (|has| |#3| (-172)) (|has| |#3| (-849)) (|has| |#3| (-1051))) ((|#3|) -2811 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051)))) +(((|#3|) . T) ((|#2|) . T) (($) -2836 (|has| |#4| (-172)) (|has| |#4| (-849)) (|has| |#4| (-1051))) ((|#4|) -2836 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1051)))) +(((|#2|) . T) (($) -2836 (|has| |#3| (-172)) (|has| |#3| (-849)) (|has| |#3| (-1051))) ((|#3|) -2836 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1051)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-365)) @@ -3835,7 +3835,7 @@ ((((-187)) . T) (((-863)) . T)) ((((-863)) . T)) (((|#1|) . T)) -((((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) +((((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) ((((-129)) . T) (((-863)) . T)) ((((-567) |#1|) . T)) ((((-129)) . T)) @@ -3844,13 +3844,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-365)) (|has| |#2| (-287 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-911))) -(-2811 (|has| |#1| (-851)) (|has| |#1| (-1102))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-911))) +(-2836 (|has| |#1| (-851)) (|has| |#1| (-1102))) ((((-863)) . T)) ((((-863)) . T)) ((((-863)) . T)) (((|#1| (-534 |#2|)) . T)) -((((-2 (|:| -1809 (-1179)) (|:| -4236 (-52)))) . T)) +((((-2 (|:| -2025 (-1179)) (|:| -2265 (-52)))) . T)) ((((-567) (-129)) . T)) (((|#1| (-567)) . T)) (((|#1| (-410 (-567))) . T)) @@ -3865,8 +3865,8 @@ ((((-1184)) . T)) ((((-863)) . T) (((-1184)) . T)) ((((-863)) . T) (((-1184)) . T)) -(-2811 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) -(-2811 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) +(-2836 (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) +(-2836 (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) ((($) . T)) (((|#2| (-534 (-865 |#1|))) . T)) ((((-1184)) . T)) @@ -3881,13 +3881,13 @@ ((((-1184)) . T)) ((((-863)) . T) (((-1184)) . T)) ((((-1184)) . T)) -((((-863)) -2811 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) +((((-863)) -2836 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) (((|#1|) . T)) (((|#2| (-772)) . T)) (((|#1| |#2|) . T)) ((((-1161) |#1|) . T)) ((((-410 |#2|)) . T)) -((((-2 (|:| -1809 |#1|) (|:| -4236 |#2|))) . T)) +((((-2 (|:| -2025 |#1|) (|:| -2265 |#2|))) . T)) (|has| |#1| (-559)) (|has| |#1| (-559)) ((($) . T) ((|#2|) . T)) @@ -3898,14 +3898,14 @@ ((((-567)) . T) (($) . T)) (((|#2| $) |has| |#2| (-287 |#2| |#2|))) (((|#1| (-645 |#1|)) |has| |#1| (-849))) -(-2811 (|has| |#1| (-233)) (|has| |#1| (-351))) -(-2811 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-233)) (|has| |#1| (-351))) +(-2836 (|has| |#1| (-365)) (|has| |#1| (-351))) ((((-1265 |#1|)) . T) (((-567)) . T) ((|#2|) . T) (((-410 (-567))) |has| |#2| (-1040 (-410 (-567))))) (|has| |#1| (-1102)) (((|#1|) . T)) -((((-1265 |#1|)) . T) (((-567)) . T) (($) -2811 (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) (((-1084)) . T) ((|#2|) . T) (((-410 (-567))) -2811 (|has| |#2| (-38 (-410 (-567)))) (|has| |#2| (-1040 (-410 (-567)))))) +((((-1265 |#1|)) . T) (((-567)) . T) (($) -2836 (|has| |#2| (-365)) (|has| |#2| (-455)) (|has| |#2| (-559)) (|has| |#2| (-911))) (((-1084)) . T) ((|#2|) . T) (((-410 (-567))) -2836 (|has| |#2| (-38 (-410 (-567)))) (|has| |#2| (-1040 (-410 (-567)))))) ((((-410 (-567))) . T) (($) . T)) -((((-1001 |#1|)) . T) ((|#1|) . T) (((-567)) -2811 (|has| (-1001 |#1|) (-1040 (-567))) (|has| |#1| (-1040 (-567)))) (((-410 (-567))) -2811 (|has| (-1001 |#1|) (-1040 (-410 (-567)))) (|has| |#1| (-1040 (-410 (-567)))))) +((((-1001 |#1|)) . T) ((|#1|) . T) (((-567)) -2836 (|has| (-1001 |#1|) (-1040 (-567))) (|has| |#1| (-1040 (-567)))) (((-410 (-567))) -2836 (|has| (-1001 |#1|) (-1040 (-410 (-567)))) (|has| |#1| (-1040 (-410 (-567)))))) ((((-912 |#1|)) . T) (((-410 (-567))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) @@ -3921,10 +3921,10 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1142 |#1| |#2|) #0#) |has| (-1142 |#1| |#2|) (-310 (-1142 |#1| |#2|)))) (((|#1|) . 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. -93) T) ((-323 . -1058) 181837) ((-252 . -792) 181816) ((-252 . -795) 181767) ((-31 . -493) 181748) ((-252 . -794) 181727) ((-251 . -792) 181706) ((-251 . -795) 181657) ((-251 . -794) 181636) ((-31 . -614) 181602) ((-50 . -1060) T) ((-252 . -727) 181512) ((-251 . -727) 181422) ((-1213 . -1102) T) ((-671 . -23) T) ((-584 . -1060) T) ((-521 . -1060) T) ((-381 . -1058) 181387) ((-323 . -111) 181362) ((-73 . -385) T) ((-73 . -398) T) ((-1026 . -38) 181299) ((-695 . -403) 181281) ((-99 . -102) T) ((-712 . -1102) T) ((-1297 . -1053) 181268) ((-1005 . -145) 181240) ((-1005 . -147) 181212) ((-871 . -647) 181184) ((-381 . -111) 181140) ((-320 . -1223) 181119) ((-477 . -1004) 181085) ((-356 . -38) 181050) ((-40 . -372) 181022) ((-874 . -614) 180894) ((-127 . -125) 180878) ((-121 . -125) 180862) ((-837 . -1058) 180832) ((-834 . -21) 180784) ((-828 . -1058) 180768) ((-834 . -25) 180720) ((-320 . -559) 180671) ((-520 . -617) 180652) ((-567 . -829) T) ((-240 . -1219) T) ((-1036 . -617) 180621) 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-25) T) ((-816 . -23) 177663) ((-1179 . -614) 177645) ((-59 . -19) 177629) ((-1179 . -615) 177551) ((-1175 . -727) T) ((-1127 . -727) T) ((-519 . -19) 177535) ((-499 . -19) 177519) ((-59 . -605) 177496) ((-1089 . -1102) T) ((-903 . -102) 177474) ((-855 . -727) T) ((-783 . -1102) T) ((-519 . -605) 177451) ((-499 . -605) 177428) ((-781 . -1102) T) ((-781 . -1067) 177395) ((-464 . -1102) T) ((-457 . -1102) T) ((-588 . -718) 177370) ((-650 . -1102) T) ((-1261 . -47) 177347) ((-1255 . -102) T) ((-1254 . -47) 177317) ((-1233 . -47) 177294) ((-1213 . -172) 177245) ((-1176 . -308) 177224) ((-1170 . -308) 177203) ((-1098 . -617) 177184) ((-1092 . -617) 177165) ((-1082 . -559) 177116) ((-1006 . -902) NIL) ((-1082 . -1223) 177067) ((-671 . -131) T) ((-628 . -1114) T) ((-1075 . -617) 177048) ((-1068 . -617) 177029) ((-1038 . -617) 177010) ((-1021 . -617) 176991) ((-700 . -647) 176941) ((-276 . -1102) T) ((-85 . -444) T) ((-85 . -398) T) ((-715 . -1058) 176911) ((-712 . -172) T) ((-50 . -1102) T) 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T) ((-137 . -93) T) ((-1213 . -517) 174212) ((-1143 . -614) 174194) ((-1122 . -641) 174181) ((-820 . -727) T) ((-820 . -858) T) ((-603 . -289) 174158) ((-584 . -718) 174123) ((-482 . -615) NIL) ((-482 . -614) 174105) ((-521 . -718) 174050) ((-317 . -102) T) ((-314 . -102) T) ((-290 . -23) T) ((-152 . -131) T) ((-1122 . -1053) 174037) ((-912 . -614) 174019) ((-389 . -727) T) ((-873 . -1058) 173971) ((-912 . -615) 173953) ((-873 . -111) 173891) ((-715 . -1051) T) ((-713 . -1245) 173875) ((-695 . -351) NIL) ((-136 . -102) T) ((-114 . -102) T) ((-139 . -102) T) ((-522 . -614) 173807) ((-381 . -796) T) ((-223 . -1102) T) ((-381 . -793) T) ((-225 . -795) T) ((-225 . -792) T) ((-59 . -615) 173768) ((-59 . -614) 173680) ((-225 . -727) T) ((-519 . -615) 173641) ((-519 . -614) 173553) ((-500 . -614) 173485) ((-499 . -615) 173446) ((-499 . -614) 173358) ((-1082 . -365) 173309) ((-40 . -414) 173286) ((-77 . -1219) T) ((-872 . -911) NIL) ((-361 . -330) 173270) ((-361 . -365) T) ((-355 . -330) 173254) ((-355 . -365) T) ((-347 . -330) 173238) ((-347 . -365) T) ((-317 . -285) 173217) ((-108 . -365) T) ((-70 . -1219) T) ((-1233 . -340) 173169) ((-872 . -649) 173114) ((-1233 . -379) 173066) ((-966 . -131) 172921) ((-816 . -131) 172791) ((-960 . -652) 172775) ((-1089 . -172) 172686) ((-960 . -375) 172670) ((-1064 . -795) T) ((-1064 . -792) T) ((-873 . -617) 172568) ((-783 . -172) 172459) ((-781 . -172) 172370) ((-817 . -47) 172332) ((-1064 . -727) T) ((-328 . -492) 172316) ((-954 . -727) T) ((-1282 . -310) 172254) ((-457 . -172) 172165) ((-245 . -287) 172142) ((-1261 . -902) 172055) ((-1254 . -902) 171961) ((-1253 . -1058) 171796) ((-484 . -727) T) ((-1233 . -902) 171629) ((-1232 . -1058) 171437) ((-1213 . -291) 171416) ((-1189 . -1219) T) ((-1186 . -370) T) ((-1185 . -370) T) ((-1148 . -151) 171400) ((-1122 . -102) T) ((-1120 . -1102) T) ((-1082 . -23) T) ((-1082 . -1114) T) ((-1077 . -102) T) ((-1059 . -614) 171367) ((-929 . -957) T) ((-738 . -310) 171305) ((-75 . -1219) T) 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170258) ((-334 . -1102) T) ((-655 . -641) 170228) ((-1255 . -38) 170120) ((-1242 . -911) 170099) ((-112 . -1102) T) ((-1037 . -102) T) ((-1242 . -649) 170024) ((-872 . -795) NIL) ((-856 . -649) 169998) ((-872 . -792) NIL) ((-817 . -888) NIL) ((-872 . -727) T) ((-1089 . -517) 169871) ((-783 . -517) 169818) ((-781 . -517) 169770) ((-574 . -649) 169757) ((-817 . -1040) 169585) ((-457 . -517) 169528) ((-391 . -392) T) ((-1253 . -617) 169341) ((-1232 . -617) 169089) ((-60 . -1219) T) ((-622 . -851) 169068) ((-503 . -662) T) ((-1148 . -978) 169037) ((-1026 . -647) 168974) ((-1005 . -455) T) ((-700 . -849) T) ((-513 . -793) T) ((-477 . -1058) 168809) ((-345 . -1102) T) ((-314 . -1154) NIL) ((-290 . -131) T) ((-397 . -1102) T) ((-871 . -1060) T) ((-695 . -372) 168776) ((-356 . -647) 168706) ((-223 . -621) 168683) ((-328 . -287) 168660) ((-477 . -111) 168481) ((-1253 . -1051) T) ((-1232 . -1051) T) ((-817 . -379) 168465) ((-169 . -727) T) ((-655 . -102) T) ((-1253 . -243) 168444) ((-1253 . -233) 168396) ((-1232 . -233) 168301) ((-1232 . -243) 168280) ((-1005 . -405) NIL) ((-671 . -640) 168228) ((-317 . -38) 168138) ((-314 . -38) 168067) ((-69 . -614) 168049) ((-320 . -496) 168015) ((-48 . -647) 167965) ((-1192 . -289) 167944) ((-1227 . -851) T) ((-1115 . -1114) 167854) ((-83 . -1219) T) ((-61 . -614) 167836) ((-482 . -289) 167815) ((-1284 . -1040) 167792) ((-1167 . -1102) T) ((-1115 . -23) 167662) ((-817 . -902) 167598) ((-1242 . -727) T) ((-1104 . -1219) T) ((-477 . -617) 167424) ((-1089 . -291) 167355) ((-968 . -1102) T) ((-895 . -102) T) ((-783 . -291) 167266) ((-328 . -19) 167250) ((-59 . -289) 167227) ((-781 . -291) 167158) ((-856 . -727) T) ((-117 . -849) NIL) ((-519 . -289) 167135) ((-328 . -605) 167112) ((-499 . -289) 167089) ((-457 . -291) 167020) ((-1037 . -310) 166871) ((-877 . -493) 166852) ((-877 . -614) 166818) ((-682 . -493) 166799) ((-574 . -727) T) ((-677 . -493) 166780) ((-682 . -614) 166730) ((-677 . -614) 166696) ((-663 . -614) 166678) ((-481 . -493) 166659) ((-481 . -614) 166625) ((-245 . -615) 166586) ((-245 . -493) 166563) ((-138 . -493) 166544) ((-137 . -493) 166525) ((-133 . -493) 166506) ((-245 . -614) 166398) ((-213 . -102) T) ((-138 . -614) 166364) ((-137 . -614) 166330) ((-133 . -614) 166296) ((-1149 . -34) T) ((-945 . -1219) T) ((-345 . -718) 166241) ((-671 . -25) T) ((-671 . -21) T) ((-1179 . -617) 166222) ((-477 . -1051) T) ((-636 . -420) 166187) ((-608 . -420) 166152) ((-1122 . -1154) T) ((-713 . -1053) 165975) ((-584 . -291) T) ((-521 . -291) T) ((-1254 . -308) 165954) ((-477 . -233) 165906) ((-477 . -243) 165885) ((-1233 . -308) 165864) ((-713 . -641) 165693) ((-1233 . -1024) NIL) ((-1082 . -131) T) ((-873 . -796) 165672) ((-144 . -102) T) ((-40 . -1102) T) ((-873 . -793) 165651) ((-645 . -1012) 165635) ((-583 . -1060) T) ((-567 . -1060) T) ((-498 . -1060) T) ((-410 . -455) T) ((-361 . -131) T) ((-317 . -403) 165619) ((-314 . -403) 165580) ((-355 . -131) T) ((-347 . -131) T) ((-1184 . -1102) T) ((-1122 . -38) 165567) 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161662) ((-247 . -327) 161619) ((-265 . -233) 161598) ((-1159 . -151) 161582) ((-252 . -902) 161514) ((-251 . -902) 161446) ((-1084 . -851) T) ((-417 . -1114) T) ((-1056 . -23) T) ((-912 . -1051) T) ((-323 . -649) 161428) ((-1026 . -849) T) ((-1213 . -1004) 161394) ((-1176 . -922) 161373) ((-1170 . -922) 161352) ((-1170 . -821) NIL) ((-1001 . -1053) 161248) ((-912 . -243) T) ((-818 . -365) 161227) ((-387 . -23) T) ((-127 . -1102) 161205) ((-121 . -1102) 161183) ((-912 . -233) T) ((-128 . -34) T) ((-381 . -649) 161148) ((-1001 . -641) 161096) ((-871 . -718) 161083) ((-1297 . -647) 161055) ((-1048 . -151) 161020) ((-40 . -172) T) ((-695 . -414) 161002) ((-713 . -310) 160989) ((-837 . -649) 160949) ((-828 . -649) 160923) ((-320 . -25) T) ((-320 . -21) T) ((-659 . -287) 160902) ((-583 . -1102) T) ((-567 . -1102) T) ((-498 . -1102) T) ((-245 . -289) 160879) ((-314 . -231) 160840) ((-1175 . -888) NIL) ((-55 . -1102) T) ((-1127 . -888) 160699) ((-129 . -851) T) ((-1175 . -1040) 160579) 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. -47) 139088) ((-534 . -512) 139065) ((-583 . -617) 139037) ((-567 . -617) 139009) ((-498 . -617) 138942) ((-1076 . -1219) T) ((-1002 . -1219) T) ((-1261 . -23) T) ((-700 . -1058) 138907) ((-1261 . -1114) T) ((-1254 . -1114) T) ((-1254 . -23) T) ((-1233 . -1114) T) ((-1233 . -23) T) ((-1005 . -372) 138879) ((-112 . -370) T) ((-477 . -902) 138785) ((-1213 . -727) T) ((-906 . -614) 138767) ((-55 . -617) 138749) ((-91 . -107) 138733) ((-1122 . -291) T) ((-907 . -851) 138684) ((-702 . -1154) T) ((-700 . -111) 138640) ((-844 . -647) 138557) ((-598 . -1114) T) ((-597 . -1114) T) ((-713 . -718) 138386) ((-712 . -727) T) ((-1006 . -131) T) ((-973 . -131) T) ((-490 . -851) T) ((-916 . -131) T) ((-800 . -25) T) ((-800 . -21) T) ((-217 . -851) T) ((-410 . -647) 138323) ((-583 . -1051) T) ((-567 . -1051) T) ((-498 . -1051) T) ((-598 . -23) T) ((-345 . -1288) 138300) ((-320 . -455) 138279) ((-341 . -310) 138266) ((-597 . -23) T) ((-430 . -131) T) ((-659 . -649) 138240) ((-245 . -1012) 138224) 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-641) 135832) ((-488 . -25) T) ((-488 . -21) T) ((-1232 . -1024) 135784) ((-1059 . -1219) T) ((-624 . -1051) T) ((-381 . -407) T) ((-393 . -102) T) ((-1107 . -619) 135699) ((-265 . -902) 135645) ((-247 . -902) 135622) ((-117 . -1051) T) ((-817 . -1114) T) ((-1089 . -727) T) ((-624 . -233) 135601) ((-622 . -102) T) ((-783 . -727) T) ((-781 . -727) T) ((-416 . -1114) T) ((-117 . -243) T) ((-40 . -370) NIL) ((-117 . -233) NIL) ((-1224 . -851) T) ((-457 . -727) T) ((-817 . -23) T) ((-732 . -25) T) ((-732 . -21) T) ((-1079 . -287) 135580) ((-78 . -399) T) ((-78 . -398) T) ((-536 . -768) 135562) ((-695 . -1058) 135512) ((-1261 . -131) T) ((-1254 . -131) T) ((-1233 . -131) T) ((-1177 . -25) T) ((-1144 . -414) 135496) ((-636 . -369) 135428) ((-608 . -369) 135360) ((-1159 . -1151) 135344) ((-103 . -1102) 135322) ((-1177 . -21) T) ((-1176 . -21) T) ((-866 . -614) 135304) ((-1001 . -718) 135252) ((-223 . -649) 135219) ((-695 . -111) 135153) ((-50 . -727) T) ((-1176 . -25) T) ((-353 . -351) T) 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134093) ((-69 . -1219) T) ((-1026 . -1058) 134030) ((-353 . -647) 133960) ((-867 . -1060) T) ((-240 . -640) 133866) ((-695 . -1051) T) ((-356 . -1058) 133811) ((-61 . -1219) T) ((-1026 . -111) 133727) ((-903 . -614) 133638) ((-695 . -243) T) ((-695 . -233) NIL) ((-844 . -849) 133617) ((-700 . -796) T) ((-700 . -793) T) ((-1005 . -414) 133594) ((-356 . -111) 133523) ((-381 . -922) T) ((-410 . -849) 133502) ((-713 . -291) 133413) ((-223 . -727) T) ((-1261 . -496) 133379) ((-1254 . -496) 133345) ((-1233 . -496) 133311) ((-581 . -1102) T) ((-317 . -1004) 133290) ((-222 . -1102) 133268) ((-1226 . -845) T) ((-320 . -975) 133230) ((-105 . -102) T) ((-48 . -1058) 133195) ((-1293 . -102) T) ((-383 . -102) T) ((-48 . -111) 133151) ((-1006 . -640) 133133) ((-1255 . -614) 133115) ((-534 . -102) T) ((-503 . -102) T) ((-1135 . -1136) 133099) ((-152 . -1276) 133083) ((-245 . -1219) T) ((-1218 . -102) T) ((-1026 . -617) 133020) ((-1175 . -1223) 132999) ((-356 . -617) 132929) ((-1127 . -1223) 132908) 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. -21) T) ((-916 . -25) T) ((-430 . -21) T) ((-430 . -25) T) ((-844 . -414) 131664) ((-48 . -1051) T) ((-1291 . -1283) 131648) ((-1289 . -1283) 131632) ((-1037 . -605) 131607) ((-317 . -615) 131468) ((-317 . -614) 131450) ((-314 . -615) NIL) ((-314 . -614) 131432) ((-48 . -243) T) ((-48 . -233) T) ((-655 . -287) 131393) ((-553 . -235) 131343) ((-139 . -614) 131310) ((-136 . -614) 131292) ((-114 . -614) 131274) ((-480 . -38) 131239) ((-1293 . -1290) 131218) ((-1284 . -131) T) ((-1292 . -1060) T) ((-1084 . -102) T) ((-88 . -1219) T) ((-503 . -310) NIL) ((-1002 . -107) 131202) ((-891 . -1102) T) ((-887 . -1102) T) ((-1269 . -652) 131186) ((-1269 . -375) 131170) ((-328 . -1219) T) ((-595 . -851) T) ((-1144 . -1102) T) ((-1144 . -1055) 131110) ((-103 . -517) 131043) ((-929 . -614) 131025) ((-345 . -727) T) ((-30 . -614) 131007) ((-867 . -1102) T) ((-844 . -1060) 130986) ((-40 . -649) 130931) ((-225 . -1223) T) ((-410 . -1060) T) ((-1161 . -151) 130913) ((-1001 . -291) 130864) ((-618 . -1102) T) ((-225 . -559) T) ((-320 . -1250) 130848) ((-320 . -1247) 130818) ((-702 . -647) 130790) ((-1192 . -1195) 130769) ((-1077 . -614) 130751) ((-1192 . -107) 130701) ((-648 . -151) 130685) ((-633 . -151) 130631) ((-116 . -647) 130603) ((-482 . -1195) 130582) ((-490 . -147) T) ((-490 . -145) NIL) ((-1122 . -615) 130497) ((-441 . -614) 130479) ((-217 . -147) T) ((-217 . -145) NIL) ((-1122 . -614) 130461) ((-129 . -102) T) ((-52 . -102) T) ((-1233 . -640) 130413) ((-482 . -107) 130363) ((-995 . -23) T) ((-1293 . -38) 130333) ((-1175 . -1114) T) ((-1127 . -1114) T) ((-1064 . -1223) T) ((-312 . -102) T) ((-855 . -1114) T) ((-954 . -1223) 130312) ((-484 . -1223) 130291) ((-1064 . -559) T) ((-954 . -559) 130222) ((-1175 . -23) T) ((-1153 . -1085) T) ((-1127 . -23) T) ((-855 . -23) T) ((-484 . -559) 130153) ((-1144 . -718) 130085) ((-671 . -1053) 130069) ((-1148 . -517) 130002) ((-671 . -641) 129986) ((-1037 . -615) NIL) ((-1037 . -614) 129968) ((-96 . -1085) T) ((-867 . -718) 129938) ((-1213 . -47) 129907) ((-252 . -131) T) ((-251 . -131) T) ((-1106 . -1102) T) ((-1005 . -1102) T) ((-62 . -614) 129889) ((-1170 . -851) NIL) ((-1026 . -793) T) ((-1026 . -796) T) ((-1297 . -1058) 129876) ((-1297 . -111) 129861) ((-1261 . -25) T) ((-1261 . -21) T) ((-871 . -649) 129848) ((-1254 . -21) T) ((-1254 . -25) T) ((-1233 . -21) T) ((-1233 . -25) T) ((-1029 . -151) 129832) ((-873 . -821) 129811) ((-873 . -922) T) ((-713 . -287) 129738) ((-598 . -21) T) ((-341 . -647) 129697) ((-598 . -25) T) ((-597 . -21) T) ((-174 . -647) 129614) ((-40 . -727) T) ((-222 . -517) 129547) ((-597 . -25) T) ((-479 . -151) 129531) ((-466 . -151) 129515) ((-923 . -795) T) ((-923 . -727) T) ((-772 . -794) T) ((-772 . -795) T) ((-509 . -1102) T) ((-505 . -1102) T) ((-772 . -727) T) ((-225 . -365) T) ((-1291 . -1053) 129499) ((-1289 . -1053) 129483) ((-1291 . -641) 129453) ((-1159 . -1102) 129431) ((-872 . -1223) T) ((-1289 . -641) 129401) ((-655 . -614) 129383) ((-872 . -559) T) ((-695 . -370) NIL) ((-44 . -1053) 129367) ((-1297 . -617) 129349) ((-1292 . -1102) T) ((-671 . -102) T) ((-361 . -1276) 129333) ((-355 . -1276) 129317) ((-44 . -641) 129301) ((-347 . -1276) 129285) ((-551 . -102) T) ((-523 . -851) 129264) ((-1048 . -1102) T) ((-818 . -455) 129243) ((-152 . -1053) 129227) ((-1048 . -1073) 129156) ((-1029 . -978) 129125) ((-820 . -1114) T) ((-1005 . -718) 129070) ((-152 . -641) 129054) ((-389 . -1114) T) ((-479 . -978) 129023) ((-466 . -978) 128992) ((-110 . -151) 128974) ((-73 . -614) 128956) ((-895 . -614) 128938) ((-1082 . -725) 128917) ((-1297 . -1051) T) ((-817 . -640) 128865) ((-295 . -1060) 128807) ((-169 . -1223) 128712) ((-225 . -1114) T) ((-325 . -23) T) ((-1170 . -994) 128664) ((-844 . -1102) T) ((-1255 . -1058) 128569) ((-1128 . -741) 128548) ((-1253 . -922) 128527) ((-1232 . -922) 128506) ((-871 . -727) T) ((-169 . -559) 128417) ((-583 . -649) 128404) ((-567 . -649) 128391) ((-410 . -1102) T) ((-264 . -1102) T) ((-213 . -614) 128373) ((-498 . -649) 128338) 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. -1102) T) ((-608 . -1102) T) ((-965 . -147) 127268) ((-1006 . -851) T) ((-736 . -147) 127247) ((-736 . -145) 127226) ((-973 . -851) T) ((-834 . -647) 127143) ((-477 . -922) 127122) ((-320 . -1053) 126957) ((-317 . -1058) 126867) ((-314 . -1058) 126796) ((-1001 . -287) 126754) ((-410 . -718) 126706) ((-320 . -641) 126547) ((-702 . -849) T) ((-1255 . -1051) T) ((-317 . -111) 126443) ((-314 . -111) 126356) ((-966 . -102) T) ((-816 . -102) 126146) ((-713 . -615) NIL) ((-713 . -614) 126128) ((-659 . -1040) 126024) ((-1255 . -327) 125968) ((-1037 . -289) 125943) ((-583 . -727) T) ((-567 . -795) T) ((-169 . -365) 125894) ((-567 . -792) T) ((-567 . -727) T) ((-498 . -727) T) ((-1148 . -492) 125878) ((-1089 . -888) NIL) ((-872 . -1114) T) ((-117 . -911) NIL) ((-1291 . -1290) 125854) ((-1289 . -1290) 125833) ((-783 . -888) NIL) ((-781 . -888) 125692) ((-1284 . -25) T) ((-1284 . -21) T) ((-1216 . -102) 125670) ((-1108 . -398) T) ((-624 . -649) 125657) ((-457 . -888) NIL) ((-676 . -102) 125635) 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. -1102) T) ((-1036 . -25) T) ((-1036 . -21) T) ((-1005 . -1058) 107782) ((-907 . -102) T) ((-867 . -1051) T) ((-695 . -902) NIL) ((-357 . -330) 107766) ((-357 . -365) T) ((-354 . -330) 107750) ((-354 . -365) T) ((-346 . -330) 107734) ((-346 . -365) T) ((-490 . -102) T) ((-1281 . -38) 107704) ((-549 . -851) T) ((-526 . -688) 107654) ((-217 . -102) T) ((-1026 . -1040) 107534) ((-1005 . -111) 107463) ((-1177 . -975) 107432) ((-523 . -151) 107416) ((-1082 . -372) 107395) ((-353 . -614) 107377) ((-323 . -21) T) ((-356 . -1040) 107354) ((-323 . -25) T) ((-1176 . -975) 107316) ((-1170 . -975) 107285) ((-76 . -614) 107267) ((-1128 . -975) 107234) ((-700 . -308) T) ((-129 . -845) T) ((-912 . -365) T) ((-381 . -25) T) ((-381 . -21) T) ((-912 . -330) 107221) ((-86 . -614) 107203) ((-700 . -1024) T) ((-678 . -851) T) ((-1253 . -131) T) ((-1232 . -131) T) ((-903 . -1012) 107187) ((-837 . -21) T) ((-48 . -1040) 107130) ((-837 . -25) T) ((-828 . -25) T) ((-828 . -21) T) ((-1115 . -647) 106880) 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. -23) T) ((-490 . -310) NIL) ((-1292 . -617) 105943) ((-477 . -131) T) ((-217 . -310) NIL) ((-410 . -111) 105881) ((-816 . -1060) 105811) ((-738 . -1100) 105795) ((-1253 . -496) 105761) ((-1232 . -496) 105727) ((-551 . -845) T) ((-141 . -1100) 105709) ((-480 . -291) T) ((-1292 . -1051) T) ((-1224 . -102) T) ((-1065 . -102) T) ((-844 . -617) 105577) ((-503 . -517) NIL) ((-485 . -238) 105556) ((-410 . -617) 105454) ((-965 . -1053) 105337) ((-736 . -1053) 105307) ((-965 . -641) 105204) ((-1175 . -145) 105183) ((-736 . -641) 105153) ((-456 . -1053) 105123) ((-1175 . -147) 105102) ((-1127 . -147) 105081) ((-1127 . -145) 105060) ((-636 . -1058) 105044) ((-608 . -1058) 105028) ((-456 . -641) 104998) ((-1177 . -1260) 104982) ((-1177 . -1247) 104959) ((-671 . -1102) T) ((-671 . -1055) 104899) ((-1176 . -1252) 104860) ((-551 . -1102) T) ((-490 . -1154) T) ((-1176 . -1247) 104830) ((-1176 . -1250) 104814) ((-1170 . -1231) 104775) ((-217 . -1154) T) ((-345 . -922) T) ((-819 . -267) 104759) ((-636 . -111) 104738) ((-608 . -111) 104717) ((-1170 . -1247) 104694) ((-844 . -1051) 104673) ((-1170 . -1229) 104657) ((-518 . -25) T) ((-498 . -303) T) ((-514 . -23) T) ((-513 . -25) T) ((-511 . -25) T) ((-510 . -23) T) ((-421 . -1053) 104631) ((-410 . -1051) T) ((-320 . -1060) T) ((-695 . -308) T) ((-421 . -641) 104605) ((-108 . -849) T) ((-713 . -727) T) ((-410 . -243) T) ((-410 . -233) 104584) ((-490 . -38) 104534) ((-217 . -38) 104484) ((-477 . -496) 104450) ((-1226 . -370) T) ((-1161 . -1146) T) ((-1103 . -102) T) ((-702 . -614) 104432) ((-702 . -615) 104347) ((-715 . -21) T) ((-715 . -25) T) ((-1137 . -102) T) ((-485 . -647) 104097) ((-134 . -614) 104079) ((-116 . -614) 104061) ((-157 . -25) T) ((-1291 . -1102) T) ((-873 . -640) 104009) ((-1289 . -1102) T) ((-965 . -102) T) ((-736 . -102) T) ((-716 . -102) T) ((-456 . -102) T) ((-817 . -455) 103960) ((-44 . -1102) T) ((-1090 . -851) T) ((-1065 . -310) 103811) ((-665 . -131) T) ((-1056 . -647) 103780) ((-671 . -718) 103764) ((-290 . 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. -102) T) ((-1127 . -102) T) ((-855 . -102) T) ((-227 . -492) 77620) ((-1291 . -111) 77599) ((-1289 . -111) 77578) ((-44 . -1058) 77562) ((-1291 . -617) 77508) ((-1242 . -1245) 77492) ((-856 . -853) 77476) ((-1291 . -1051) T) ((-1181 . -291) 77455) ((-110 . -287) 77430) ((-1289 . -617) 77359) ((-128 . -151) 77341) ((-1144 . -902) 77300) ((-44 . -111) 77279) ((-1224 . -1102) T) ((-1184 . -1264) T) ((-1169 . -493) 77260) ((-1169 . -614) 77226) ((-671 . -1051) T) ((-1161 . -615) NIL) ((-1161 . -614) 77208) ((-1065 . -611) 77183) ((-1065 . -1102) T) ((-996 . -493) 77164) ((-74 . -444) T) ((-74 . -398) T) ((-996 . -614) 77130) ((-152 . -1058) 77114) ((-671 . -233) 77093) ((-574 . -557) 77077) ((-357 . -147) 77056) ((-357 . -145) 77007) ((-354 . -147) 76986) ((-354 . -145) 76937) ((-346 . -147) 76916) ((-346 . -145) 76867) ((-265 . -145) 76846) ((-265 . -147) 76825) ((-252 . -38) 76795) ((-247 . -147) 76774) ((-117 . -365) T) ((-247 . -145) 76753) ((-251 . -38) 76723) ((-152 . -111) 76702) 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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 eed89d43..51bb1852 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3467417888) +(30 . 3474699320) (4425 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -481,660 +481,663 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |normInvertible?| |setPredicates| |result| - |primitive?| |B1solve| |unknownEndian| |groebnerIdeal| |mkcomm| - |printCode| |sort| |newLine| |primPartElseUnitCanonical| - |outputMeasure| |s15adf| |reset| |series| |zero| |mathieu11| - |isAbsolutelyIrreducible?| |linearAssociatedExp| 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|showTheFTable| |viewDeltaXDefault| |multiEuclidean| - |tanIfCan| |OMReadError?| |OMgetEndApp| |create3Space| |slex| - |basisOfRightNucloid| |lyndonIfCan| |f01bsf| |connectTo| |true| - |biRank| |lighting| |components| |structuralConstants| |pi| |setleft!| - |diag| |generalInfiniteProduct| |setPrologue!| |unitNormal| - |pointPlot| |lineColorDefault| |viewSizeDefault| |cSech| |select!| - |infinity| |highCommonTerms| |totalfract| |compiledFunction| - |showScalarValues| |setTex!| |listLoops| |expintfldpoly| |ricDsolve| - |trapezoidalo| |rootSplit| |position!| |hermite| |graphState| - |numberOfFactors| |semiResultantEuclideannaif| |lifting1| |chiSquare1| - |s21bcf| |defineProperty| |cycleElt| |singular?| |setMinPoints| - |currentScope| |graphCurves| |node?| |aCubic| |primlimitedint| |head| - |mainVariable?| |outlineRender| |selectIntegrationRoutines| - |rootProduct| |qqq| |polCase| |traverse| |solveLinear| |expint| |dn| - |e02adf| |factorList| |imagJ| |cAcos| |arbitrary| |graeffe| |separant| - |nthCoef| |removeRedundantFactors| |makeCrit| |fortran| |categories| - |complexLimit| |abs| |shrinkable| |semiSubResultantGcdEuclidean2| - |solveRetract| |curveColorPalette| |bivariatePolynomials| |isImplies| - |karatsubaOnce| |OMputSymbol| |uniform| |bitLength| |c06gbf| |tRange| - |chebyshevT| |minus!| |outerProduct| |size?| |allRootsOf| - |normalizedDivide| |rk4qc| |badValues| |mindeg| |delete| |rotatez| - |d03eef| |divisor| |setelt!| |fortranLogical| |brillhartIrreducible?| - |readInt8!| |sdf2lst| RF2UTS |testDim| |symbolTableOf| |top!| - |squareFreePrim| |groebgen| |randomR| |safeCeiling| |conical| - |OMgetEndBind| |rightRankPolynomial| |countRealRootsMultiple| - |bitCoef| |trapezoidal| |byteBuffer| |externalList| - |ScanFloatIgnoreSpaces| |front| |setOfMinN| |singularAtInfinity?| - |critT| |interpolate| |palgextint0| |s19aaf| |reverse!| |vector| - |iCompose| |rationalIfCan| |headAst| |makingStats?| |comment| - |fracPart| |iisech| |listOfMonoms| |stoseInvertibleSetreg| 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|linearDependenceOverZ| |ode1| |bat| |normal01| - |normDeriv2| |high| |normFactors| |signatureAst| |alphabetic| |e04dgf| - |parabolicCylindrical| |pushNewContour| |moduleSum| |totalGroebner| - |OMputVariable| |setProperty| |virtualDegree| |iisqrt2| |collectUpper| - |goto| |OMgetString| |rootOf| |points| |nthExponent| - |removeRoughlyRedundantFactorsInPols| |gcdprim| |printHeader| - |mainExpression| |uncouplingMatrices| |leftFactorIfCan| |extract!| - |universe| |cAcosh| |SturmHabicht| |lfextendedint| |f02abf| |exp| - |getProperties| |OMsend| |startTableGcd!| |algSplitSimple| - |printingInfo?| |readInt32!| |c06gqf| |topPredicate| - |replaceKthElement| |perfectSquare?| |tableau| |someBasis| - |removeIrreducibleRedundantFactors| |floor| |antiCommutative?| - |halfExtendedResultant1| |patternVariable| |maxPoints3D| - |numberOfPrimitivePoly| |initTable!| |drawComplex| |trigs| |ipow| - |sylvesterSequence| |queue| |conditionsForIdempotents| |firstNumer| - |id| |headReduce| |generalSqFr| |identification| |limit| |makeMulti| - |viewZoomDefault| |second| |algebraicCoefficients?| |invertible?| - |sech2cosh| |euler| |infRittWu?| |f02aef| |commutator| |OMputEndBVar| - |expandLog| |close| |contract| |schema| |third| |asechIfCan| - |shufflein| |cot2tan| |setref| |revert| |oneDimensionalArray| |swap| - |transform| |thetaCoord| |hdmpToDmp| |wholePart| |supDimElseRittWu?| - |setRealSteps| |setrest!| |numberOfNormalPoly| |resetNew| |readBytes!| - |search| |coord| |meshPar1Var| |notelem| |display| |argumentListOf| - |simpsono| |obj| |realElementary| |identityMatrix| - |radicalEigenvectors| |palglimint| |weighted| |Aleph| - |chineseRemainder| |asinhIfCan| |characteristicSerie| |deepestInitial| - |addPoint2| |lazyPseudoDivide| |cAtanh| |untab| |realEigenvectors| - |cycleSplit!| |generic?| |rename| |fullPartialFraction| - |extendedResultant| |sinIfCan| |antisymmetric?| |startTableInvSet!| - |pushdterm| |open?| |getGoodPrime| |partition| |bezoutDiscriminant| - |cAcsc| |entry?| 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|zeroDimensional?| |exQuo| |systemCommand| - |c06ecf| |height| |quoted?| |aLinear| |reseed| - |numberOfImproperPartitions| |transpose| |getCurve| |generalPosition| - |arg1| |construct| |elseBranch| |bit?| |trace2PowMod| |ODESolve| - |toScale| |factorsOfCyclicGroupSize| |nthFactor| |d01apf| - |selectfirst| |set| |makeGraphImage| |mapMatrixIfCan| |cPower| |arg2| - |setPosition| |s19adf| |trueEqual| |symmetricProduct| |kind| - |outputSpacing| |quotedOperators| |upperCase?| |nextPrime| - |sizePascalTriangle| |OMgetObject| |rename!| |in?| |coshIfCan| - |symFunc| |readIfCan!| |arguments| |resultantEuclidean| |op| |normal| - |integralBasis| |janko2| |laurentRep| |polarCoordinates| |maxrank| - |conditions| |ord| |qualifier| |compdegd| - |stoseInternalLastSubResultant| |cSin| |firstDenom| |script| - |superHeight| |hasTopPredicate?| |stoseInvertible?reg| - |clearTheFTable| |match| |bezoutMatrix| |att2Result| - |factorSquareFreeByRecursion| |fixedDivisor| |f01qcf| |lambert| - |iicsch| |tubeRadiusDefault| |decomposeFunc| |ffactor| |mat| - |modularGcdPrimitive| |moebius| |maxPoints| |leviCivitaSymbol| - |selectFiniteRoutines| |cAcoth| |shuffle| |cAsinh| |generators| - |numberOfCycles| |diagonals| |cotIfCan| |mainCoefficients| |stirling1| - |leftScalarTimes!| |tex| |atanIfCan| |acscIfCan| |minColIndex| - |critMTonD1| |factorials| |insertionSort!| |makeFloatFunction| - |quoByVar| |every?| |rspace| |roughBasicSet| |entry| |OMputInteger| - |iFTable| |makeYoungTableau| |genericLeftNorm| |hostByteOrder| - |exactQuotient!| |cyclicEntries| |union| |laguerre| |countRealRoots| - |fi2df| |internalSubPolSet?| |formula| |vconcat| |solveid| |harmonic| - |getOrder| |oblateSpheroidal| |intPatternMatch| |gbasis| |f01rcf| - |binaryFunction| |rightGcd| |recoverAfterFail| |extendedint| - |basisOfRightNucleus| |s19acf| |lyndon?| - |halfExtendedSubResultantGcd2| |e01sbf| |powern| |compactFraction| - |show| |weierstrass| |selectPDERoutines| |csubst| - |createPrimitiveElement| |d01gbf| |asimpson| |readLineIfCan!| - |rootSimp| |headReduced?| |fortranLiteralLine| |resetVariableOrder| - |rootBound| |extractBottom!| |call| |tail| |setelt| |elliptic?| - |unitCanonical| |bumptab1| |tan2trig| |createLowComplexityTable| - |explicitlyEmpty?| |s21bdf| |trace| |aQuartic| |curryLeft| |nrows| - |rightUnit| |setsubMatrix!| |e02bef| |useNagFunctions| - |increasePrecision| |scalarMatrix| |cfirst| |d02cjf| - |zeroSetSplitIntoTriangularSystems| |number?| |ncols| |pascalTriangle| - |copy| |df2st| |mulmod| |strongGenerators| |removeCoshSq| - |tracePowMod| |branchPointAtInfinity?| |singularitiesOf| - |attributeData| |leftExtendedGcd| |whileLoop| |bounds| - |localIntegralBasis| |reducedQPowers| |row| |void| |littleEndian| - |lowerCase!| |df2ef| |overlap| |errorInfo| |identitySquareMatrix| - |returns| |cot2trig| |leftDivide| |maxdeg| |reducedContinuedFraction| - |iisec| |setClipValue| |wronskianMatrix| |realZeros| - |expenseOfEvaluationIF| |makeUnit| |basisOfMiddleNucleus| |readByte!| - |dflist| |hasSolution?| |one?| |f02awf| |homogeneous?| |OMbindTCP| - |currentSubProgram| |expandPower| |cosh2sech| |setClosed| - |newTypeLists| |transcendenceDegree| |c06ekf| |s17ahf| |tanSum| - |cyclicCopy| |chainSubResultants| |cyclicParents| |checkForZero| - |taylorIfCan| |indices| |lowerCase| |readUInt32!| |principalIdeal| - |jordanAlgebra?| |unit| |overbar| |removeCosSq| |linkToFortran| - |dominantTerm| |cCoth| |coerceL| |normalDenom| |lexGroebner| - |torsionIfCan| |rootNormalize| |nextIrreduciblePoly| - |reduceBasisAtInfinity| |c06frf| |palgint0| |LyndonWordsList| |point| - |removeSquaresIfCan| |iterationVar| |noncommutativeJordanAlgebra?| - |e02bbf| |toroidal| |factorSFBRlcUnit| |setvalue!| |signAround| - |rightExactQuotient| |fractionFreeGauss!| |outputArgs| |elRow2!| |tab| - |fillPascalTriangle| |eyeDistance| |iisinh| |distFact| |nil| - |infinite| |arbitraryExponent| |approximate| |complex| + |Record| |Union| |currentEnv| |leadingIndex| |dAndcExp| + |extractSplittingLeaf| |triangulate| |filterUntil| |homogeneous?| + |separant| |baseRDEsys| |trim| |setProperties!| |f02adf| + |extendedSubResultantGcd| |merge| |select| |digit?| |OMbindTCP| + |nthCoef| |OMgetError| |symmetricDifference| |convert| |mainContent| + |toseLastSubResultant| |yellow| |tanintegrate| |distdfact| |sh| + |log10| |makeObject| |currentSubProgram| |removeRedundantFactors| + |pToDmp| |LazardQuotient2| |cLog| |dot| |height| |systemCommand| + |decreasePrecision| |setMinPoints3D| |nary?| |particularSolution| + |bitand| |coef| |expandPower| |makeCrit| |hexDigit?| + |linearlyDependentOverZ?| |outputFixed| |idealSimplify| |qfactor| + |useSingleFactorBound| |lepol| |fractRadix| |bitior| |complexLimit| + |addMatch| |split!| |even?| |linearDependenceOverZ| |d01gaf| + |complexElementary| UTS2UP |f07fdf| |symbol| |critMTonD1| |acsc| |abs| + |npcoef| |Gamma| |hessian| |ode1| |inverseIntegralMatrixAtInfinity| + |normal| |rightMinimalPolynomial| |trailingCoefficient| |recip| + |expression| |factorials| |sinh| |kroneckerDelta| |shrinkable| + |setErrorBound| |initializeGroupForWordProblem| |createRandomElement| + |bat| |basisOfNucleus| |divideIfCan!| |makeRecord| |content| + |stopTable!| |integer| |insertionSort!| |cosh| |squareTop| + |semiSubResultantGcdEuclidean2| |separateFactors| |pile| |normal01| + |setValue!| |setleaves!| |systemSizeIF| |coerceListOfPairs| + |viewThetaDefault| |makeFloatFunction| |tanh| |doublyTransitive?| + |solveRetract| |decimal| |predicates| |unitNormalize| |normDeriv2| + |initial| |nextNormalPoly| |isPower| |space| |checkRur| |coth| + |quoByVar| |solid| |curveColorPalette| |inverseIntegralMatrix| + |f02bbf| |iiabs| |high| |rightTraceMatrix| |splitNodeOf!| |OMgetBind| + |rectangularMatrix| |every?| |sech| |bivariatePolynomials| |reflect| + |lastSubResultantElseSplit| |maxint| |normFactors| |comparison| + |OMreceive| |unvectorise| |changeName| |algebraicDecompose| |rspace| + |csch| |factors| |isImplies| |max| |bumptab| |low| |signatureAst| + |triangularSystems| |cycles| |hasHi| |isConnected?| |printInfo!| + |roughBasicSet| |asinh| |btwFact| |karatsubaOnce| |ref| ** + |alphabetic| |ScanRoman| |rootRadius| |matrixConcat3D| |writeBytes!| + |squareFree| |OMputInteger| |acosh| |OMputSymbol| |label| |rank| + |bindings| |permanent| |e04dgf| |selectAndPolynomials| + |deleteProperty!| |numberOfComposites| |leftUnits| |optpair| |iFTable| + |atanh| |uniform| |genericRightTraceForm| |evaluate| + |parabolicCylindrical| |Nul| |f2df| |normalize| + |createIrreduciblePoly| |addPointLast| |makeYoungTableau| |acoth| + |tail| |bitLength| |iiacoth| |symmetricTensors| |laguerreL| + |pushNewContour| |rules| |iiatanh| |octon| |listBranches| |real?| + |genericLeftNorm| |asech| |setprevious!| |c06gbf| |OMputApp| + |removeSinSq| |moduleSum| |rightRecip| |keys| |sumSquares| |errorKind| + |userOrdered?| |coefficients| |hostByteOrder| |eof?| |tRange| + |constantIfCan| |fortranLinkerArgs| |indicialEquation| |totalGroebner| + |edf2ef| |factorset| |eigenvectors| |rational?| |multiple| + |exactQuotient!| |chebyshevT| |OMputVariable| |blankSeparate| + |mathieu22| |indiceSubResultant| Y |cn| |iiexp| |s17acf| |subCase?| + |quasiRegular?| |applyQuote| |cyclicEntries| |minus!| |optAttributes| + |component| |setProperty| |subscript| |constructor| |eigenvector| + |numerator| |goodPoint| |irreducibleFactors| |laguerre| |unknown| + |size?| |lists| |normalDeriv| |OMputObject| |virtualDegree| |key?| + |balancedFactorisation| |minimumDegree| |isOp| |definingInequation| + |countRealRoots| |option| |allRootsOf| |s01eaf| |sincos| |iisqrt2| + |ptFunc| |showSummary| |yCoord| |stripCommentsAndBlanks| + |lazyGintegrate| |RemainderList| |fi2df| |ruleset| |normalizedDivide| + |pleskenSplit| |pushdown| |collectUpper| |closedCurve| |say| + |sylvesterMatrix| |powerAssociative?| |f04axf| |setfirst!| + |internalSubPolSet?| |rk4qc| |powmod| |s17agf| |goto| |s13acf| + |showAttributes| |linearMatrix| |hyperelliptic| + |univariatePolynomials| UP2UTS |vconcat| |badValues| |cup| + |characteristicSet| |OMgetString| |subSet| |pointColorPalette| + |rightNorm| |backOldPos| |processTemplate| |rightTrim| |solveid| + |suchThat| |mindeg| |lintgcd| |removeSuperfluousQuasiComponents| |po| + |rootOf| |createMultiplicationMatrix| |irreducibleRepresentation| + |Frobenius| |solveLinearPolynomialEquation| |leftTrim| |harmonic| + |rotatez| |result| |iteratedInitials| |SturmHabichtMultiple| + |updateStatus!| |points| |ocf2ocdf| |showIntensityFunctions| + |removeConstantTerm| |modifyPointData| |getOrder| |d03eef| + |monomialIntPoly| |mesh?| |nthExponent| |compose| |reset| + |complementaryBasis| |sumOfKthPowerDivisors| |orbit| |getMeasure| + |oblateSpheroidal| |name| |divisor| |substring?| |stoseInvertible?| + |stronglyReduced?| |nonSingularModel| + |removeRoughlyRedundantFactorsInPols| |gcdcofact| |meshFun2Var| + |setMaxPoints3D| |inverse| |intPatternMatch| |setelt!| |updatD| + |acoshIfCan| |insertTop!| |gcdprim| |write| |delete!| |ksec| + |putColorInfo| |null?| |gbasis| |fortranLogical| |suffix?| |f02xef| + |diophantineSystem| |iiasec| |printHeader| |save| F |printTypes| + |extend| |has?| |unary?| |f01rcf| |brillhartIrreducible?| + |relationsIdeal| |c06ebf| |simplifyLog| |mainExpression| + |musserTrials| |OMopenString| |OMserve| |patternMatchTimes| + |binaryFunction| |open| |readInt8!| |prefix?| |remove| |branchIfCan| + |smith| |uncouplingMatrices| |iicot| |halfExtendedResultant2| |e01bhf| + |badNum| |alphabetic?| |drawStyle| |rightGcd| |getIdentifier| + |sdf2lst| |shiftRoots| |laurent| |factorFraction| |leftFactorIfCan| + |makeViewport2D| |extract!| |ran| |back| |f02aff| |s20acf| |dihedral| + |recoverAfterFail| |null| |solveLinearPolynomialEquationByFractions| + |pattern| RF2UTS |f04jgf| |last| |puiseux| |setchildren!| + |mergeFactors| |logpart| |createPrimitiveNormalPoly| |controlPanel| + |extendedint| |assoc| |testDim| |consnewpol| |not| |initiallyReduced?| + |universe| |evaluateInverse| |getlo| |leftDiscriminant| |c05nbf| + |sturmVariationsOf| |lo| |basisOfRightNucleus| |operations| |cAcosh| + |d03edf| |symbolTableOf| |and| |shiftLeft| |inv| |readLine!| |clip| + |OMconnInDevice| |tanhIfCan| |innerSolve| |incr| |s19acf| |top!| + |clipBoolean| |ground?| |or| |SturmHabichtSequence| |gramschmidt| + |SturmHabicht| |computeCycleLength| |stiffnessAndStabilityOfODEIF| + |OMsetEncoding| |semicolonSeparate| |unitVector| |stop| |lyndon?| + |ground| |squareFreePrim| |infix?| |message| |create| |xor| |ranges| + |lfextendedint| |flatten| |splitConstant| |nextPartition| + |bipolarCylindrical| |ratDsolve| |expenseOfEvaluation| + |halfExtendedSubResultantGcd2| |mask| |groebgen| |curryRight| |f02abf| + |antiCommutator| |case| |normInvertible?| |leadingMonomial| + |constantCoefficientRicDE| |viewPosDefault| |addmod| |getBadValues| + |e01sbf| |numerators| |getProperties| |entries| |randomR| |f04asf| + |Zero| |setPredicates| |leadingCoefficient| + |generalizedContinuumHypothesisAssumed| |llprop| |latex| |polygon?| + |startPolynomial| |powern| |primitive?| |safeCeiling| + |primitiveMonomials| |sequences| |One| |se2rfi| |output| |OMsend| + |sncndn| |Vectorise| |minGbasis| |denomRicDE| |compactFraction| + |conical| |leftAlternative?| |lcm| |B1solve| |reductum| |OMgetFloat| + |startTableGcd!| |Hausdorff| |nand| |redPo| |e02zaf| |simplifyExp| + |weierstrass| |unknownEndian| |topFortranOutputStack| |OMgetEndBVar| + |computeCycleEntry| |algSplitSimple| |f01ref| |ListOfTerms| |cons| + |SFunction| |pdf2df| |selectPDERoutines| |viewDeltaXDefault| + |groebnerIdeal| |makeEq| |append| |monomRDE| |RittWuCompare| + |printingInfo?| |fortranCompilerName| |reduceByQuasiMonic| + |completeHensel| |shiftRight| |csubst| |multiEuclidean| |mkcomm| + |readInt32!| |antisymmetricTensors| |meatAxe| |gcd| + |unrankImproperPartitions1| |bigEndian| |primitivePart| |leftGcd| + |curve| |createPrimitiveElement| |var2Steps| |tanIfCan| |printCode| + |c06gqf| |removeZeroes| |elt| |false| |extensionDegree| |An| |pr2dmp| + |d01gbf| |OMReadError?| |newLine| |numberOfOperations| |BasicMethod| + |rombergo| |categories| |topPredicate| |weight| |outerProduct| |style| + |increment| |asimpson| |OMgetEndApp| |outputGeneral| |innerSolve1| + |csc2sin| |primPartElseUnitCanonical| |replaceKthElement| + |leastAffineMultiple| |gethi| |cycleEntry| |readLineIfCan!| + |create3Space| |outputMeasure| |expintegrate| |deref| |perfectSquare?| + |roman| |pol| |exportedOperators| |graphImage| |rootSimp| |slex| + |numberOfMonomials| |s15adf| |tableau| |approxSqrt| |iitan| + |palgextint| |headReduced?| |basisOfRightNucloid| |distribute| + |diagonal| |someBasis| |mathieu11| |dequeue!| |pquo| |minPoly| + |ramified?| |fortranLiteralLine| |lyndonIfCan| |finiteBound| |hcrf| + |isAbsolutelyIrreducible?| |hermiteH| + |removeIrreducibleRedundantFactors| |ode2| |fibonacci| |symbolIfCan| + |resetVariableOrder| |f01bsf| |leftRank| |selectOptimizationRoutines| + |linearAssociatedExp| |floor| |cosSinInfo| |integral| |rootBound| + |connectTo| |e04mbf| |opeval| |antiCommutative?| |cAcsch| + |showClipRegion| |df2fi| |associatedEquations| |triangSolve| + |extractBottom!| |biRank| |problemPoints| |Is| + |halfExtendedResultant1| |qelt| |ScanArabic| |leaf?| |scripted?| + |minimumExponent| |resultantReduitEuclidean| |elliptic?| |lighting| + |pomopo!| |palgRDE0| |qsetelt| |getGraph| |patternVariable| |check| + |integralRepresents| |elliptic| |satisfy?| |unitCanonical| + |components| |rightLcm| |wholeRadix| |xRange| |sup| |stFunc2| + |OMgetBVar| |vectorise| |bumptab1| |appendPoint| |structuralConstants| + |cCsch| |resultantnaif| |asecIfCan| |yRange| |trunc| |iilog| + |idealiserMatrix| |legendreP| |plusInfinity| |tan2trig| |setleft!| + |showFortranOutputStack| |readUInt16!| |collectQuasiMonic| |norm| + |zRange| |c02agf| |d01ajf| |swapRows!| |crushedSet| |minusInfinity| + |createLowComplexityTable| |map!| |diag| |mainCharacterization| + |nextColeman| |key| |numberOfComputedEntries| |d02gbf| |OMlistSymbols| + |phiCoord| |drawComplexVectorField| |range| |imaginary| + |generalInfiniteProduct| |reify| |alternative?| |qsetelt!| + |coerceImages| |alternatingGroup| |datalist| |eigenMatrix| + |wordsForStrongGenerators| |froot| |outputSpacing| |filename| + |setPrologue!| |commutativeEquality| |mainVariable| |bracket| |child?| + |cosIfCan| |sorted?| |KrullNumber| |quotedOperators| |unitNormal| + |rCoord| |getOperands| |just| |addiag| |showAllElements| |write!| + |bivariateSLPEBR| |upperCase?| |integerIfCan| |pointPlot| |d02raf| + |parse| |approximants| |groebSolve| |complexNormalize| |prime| + |inverseColeman| |type| |nextPrime| |next| |normalElement| + |lineColorDefault| |explimitedint| |diff| |OMread| |sort| + |raisePolynomial| |iiperm| |besselY| |sizePascalTriangle| + |stopMusserTrials| |viewSizeDefault| |Si| |FormatRoman| + |completeEchelonBasis| |acsch| |cardinality| |f02fjf| |resize| + |previous| |OMgetObject| |cSech| |lazyEvaluate| |repeating?| |e02ddf| + |overlabel| |indicialEquationAtInfinity| |sizeMultiplication| + |modularFactor| |rename!| |select!| |iisin| |subspace| |OMgetVariable| + |lllp| |retractable?| |useSingleFactorBound?| |outputForm| |in?| + |highCommonTerms| |integralBasisAtInfinity| + |createNormalPrimitivePoly| |part?| |mindegTerm| |random| |acschIfCan| + |parent| |multMonom| |linearlyDependent?| |coshIfCan| |rule| + |mainKernel| |totalfract| |lhs| |unexpand| |box| |operators| |s18acf| + |chvar| |lazy?| |leftZero| |mapUnivariateIfCan| |symFunc| |tubePlot| + |compiledFunction| |const| |rhs| |lowerCase?| + |ScanFloatIgnoreSpacesIfCan| |pmComplexintegrate| |e01bgf| |s18def| EQ + |prinshINFO| |readIfCan!| |integralMatrix| |showScalarValues| + |leftNorm| |superscript| |getMatch| |asinIfCan| |presuper| |f04arf| + |solveInField| |resultantEuclidean| |rewriteIdealWithRemainder| + |rootsOf| |setTex!| |decrease| |setLength!| |numberOfFractionalTerms| + |OMwrite| |nilFactor| |removeRoughlyRedundantFactorsInContents| + |f04atf| |separate| |integralBasis| |interval| |arg1| |e01sff| + |listLoops| |transcendentalDecompose| |monicDivide| |padicFraction| + |symbolTable| |mainDefiningPolynomial| |whitePoint| |iisqrt3| |twist| + |readUInt8!| |janko2| |convergents| |expintfldpoly| |index| |vspace| + |isTerm| |polyPart| |s17def| |writeLine!| |infinite?| |exponential| + |OMputError| |laurentRep| |pushFortranOutputStack| |dec| |e01daf| + |ricDsolve| |e02akf| |member?| |assign| |coercePreimagesImages| + |pack!| |figureUnits| |is?| |polarCoordinates| |ramifiedAtInfinity?| + |popFortranOutputStack| |trapezoidalo| |noKaratsuba| |characteristic| + |tab1| |logIfCan| |subQuasiComponent?| |makeFR| |mkAnswer| |maxrank| + |init| |eq?| |rootSplit| |outputFloating| |relerror| |pair| |delay| + |palginfieldint| |outputAsFortran| |fortranCharacter| |parseString| + |infieldIntegrate| |value| |ord| |ratPoly| |position!| + |fortranComplex| |genericLeftTraceForm| |updatF| |multiplyExponents| + |minordet| |aspFilename| |wordInStrongGenerators| |qualifier| + |maximumExponent| |hermite| |mirror| |sinhcosh| |parametersOf| + |scanOneDimSubspaces| |directory| |extractTop!| |fixedPoint| + |discriminant| |compdegd| |factorial| |graphState| |plenaryPower| + |SturmHabichtCoefficients| |rightDiscriminant| + |squareFreeLexTriangular| |quickSort| |s18dcf| |wordInGenerators| + |entry| |stoseInternalLastSubResultant| |numberOfFactors| + |schwerpunkt| |curve?| |xn| |LiePolyIfCan| |OMputAtp| + |factorSquareFreePolynomial| |diagonalProduct| |cSin| + |semiResultantEuclideannaif| |e01bef| |rroot| + |cyclotomicDecomposition| |f02bjf| |thenBranch| |critM| |drawToScale| + |firstDenom| |lifting1| |tree| |leastMonomial| |moreAlgebraic?| + |decompose| |initials| |prem| |charpol| |monicCompleteDecompose| + |superHeight| |bright| |chiSquare1| |generalizedEigenvectors| + |OMgetApp| |nonLinearPart| |compBound| |predicate| |swapColumns!| + |redPol| |resultant| |hasTopPredicate?| |call| |s21bcf| |redmat| + |indiceSubResultantEuclidean| |leftPower| |imagk| |OMconnectTCP| + |s21bbf| |adaptive?| |stoseInvertible?reg| |defineProperty| |logical?| + |charthRoot| |empty?| |limitPlus| |cycle| |getZechTable| |build| + |clearTheFTable| |cycleElt| |multiEuclideanTree| |atanhIfCan| + |factorGroebnerBasis| |polygon| |primitivePart!| |dualSignature| + |intChoose| |bezoutMatrix| |singular?| |generator| |binary| |enqueue!| + |eulerPhi| |coefChoose| |tanQ| |c06gsf| |fortran| |rationalFunction| + |att2Result| |setMinPoints| |maxIndex| |quatern| |tanNa| |loopPoints| + |getDatabase| |doubleComplex?| |middle| |factorSquareFreeByRecursion| + |currentScope| |exprToXXP| |localAbs| |outputBinaryFile| LODO2FUN + |palgLODE| |exprHasLogarithmicWeights| |setScreenResolution| + |fixedDivisor| |graphCurves| |choosemon| |makeprod| |e04fdf| + |rowEchelon| |derivative| |spherical| |moebiusMu| |int| |f01qcf| + |node?| |setImagSteps| |cothIfCan| |reverseLex| |boundOfCauchy| + |generate| |radicalSolve| |complexRoots| |viewpoint| |lambert| + |aCubic| |sin?| |cCosh| |constantOpIfCan| |rangeIsFinite| |condition| + |parameters| |zag| |setRow!| |iipow| |iicsch| |primlimitedint| + |mapUnivariate| |mergeDifference| |exteriorDifferential| + |degreePartition| |incrementBy| |prevPrime| |divide| |ridHack1| + |tubeRadiusDefault| |head| |hconcat| |implies| |minIndex| + |discriminantEuclidean| |groebnerFactorize| |physicalLength!| |level| + |search| |connect| |decomposeFunc| |mainVariable?| |genericRightTrace| + |nthRootIfCan| |getMultiplicationMatrix| |calcRanges| |fprindINFO| + |hex| |divergence| |ffactor| |dim| |outlineRender| |e02baf| + |whatInfinity| |endOfFile?| |htrigs| |mapExpon| |c06fqf| |rem| + |numFunEvals3D| |mat| |selectIntegrationRoutines| |f02akf| + |changeMeasure| |denomLODE| |var1StepsDefault| |escape| |commutative?| + |lazyPremWithDefault| |quo| |rightFactorCandidate| + |modularGcdPrimitive| |matrix| |prepareDecompose| |clearDenominator| + |primaryDecomp| |rotate!| |showArrayValues| |status| |OMreadFile| + |block| |constantLeft| |buildSyntax| |moebius| |d01fcf| |ldf2lst| + |cAsec| |imports| |divideExponents| |branchPoint?| |variable?| + |euclideanSize| |selectMultiDimensionalRoutines| |div| |script| + |maxPoints| |shallowExpand| |tablePow| |s17dlf| |infinityNorm| + |e02bcf| |zeroMatrix| |times!| |nodeOf?| |exquo| |leviCivitaSymbol| + |erf| |iiacosh| |pToHdmp| |crest| |acosIfCan| |rational| |generic| ~= + |oddInfiniteProduct| |selectFiniteRoutines| |lagrange| |knownInfBasis| + |subresultantSequence| |exactQuotient| |enterInCache| + |quasiAlgebraicSet| |c05adf| |pseudoRemainder| |#| |tex| |cAcoth| + |lfunc| |rischDEsys| |newSubProgram| |coerce| |iiasinh| |rdHack1| + |symbol?| |mkIntegral| ~ |solve| |dilog| |shuffle| |normalise| + |polynomialZeros| |f07aef| |construct| |nextPrimitiveNormalPoly| + |point?| |iiacsc| |PDESolve| |hi| |viewport3D| |cAsinh| |sin| + |irreducible?| |clearCache| |primes| |typeList| |axesColorDefault| + |firstUncouplingMatrix| |semiResultantEuclidean1| |generators| |cos| + |critpOrder| |leftExactQuotient| |createGenericMatrix| |modTree| + |stoseIntegralLastSubResultant| |compile| |lazyPseudoQuotient| + |jacobiIdentity?| |/\\| |showTheIFTable| |numberOfCycles| |tan| + |leftFactor| |binding| |refine| |fortranLiteral| |seriesToOutputForm| + |besselK| |\\/| |lexico| |OMencodingXML| |cot| |diagonals| |composite| + |setLabelValue| |primeFrobenius| |char| |complexSolve| |kmax| + |closed?| |cotIfCan| |sec| |f07fef| |s17dgf| |colorDef| + |GospersMethod| |routines| |skewSFunction| |curry| + |LagrangeInterpolation| |second| |mainCoefficients| |csc| + |radicalEigenvalues| |d01akf| |factorPolynomial| |leadingBasisTerm| + |OMunhandledSymbol| |delta| |mkPrim| |mathieu12| |negative?| + |stirling1| |third| |asin| |dimension| |OMgetEndObject| |bivariate?| + |socf2socdf| |determinant| |linearPart| |failed| |tubePoints| + |setFieldInfo| |leftScalarTimes!| |acos| |purelyAlgebraic?| |rotatex| + |hasPredicate?| |void| |printInfo| |credPol| |lift| |OMgetSymbol| + |upDateBranches| |atanIfCan| |atan| |polygamma| |getExplanations| + |typeLists| |exp1| |monomials| |tan2cot| |reduce| |exponent| |arity| + |acscIfCan| |acot| |constant?| |trigs2explogs| |d01aqf| |ldf2vmf| + |leftRankPolynomial| |float| |yCoordinates| |children| |direction| + |minColIndex| |asec| |contains?| |bipolar| |pushucoef| |option?| + |leadingExponent| |omError| |zeroDimPrime?| |linearDependence| + |listRepresentation| |remainder| |trivialIdeal?| |lazyPseudoRemainder| + |mapdiv| |changeNameToObjf| |adaptive| |f01brf| |gensym| |copies| + |sinhIfCan| |toseSquareFreePart| |completeHermite| |invmultisect| + |lambda| |s17aff| |point| |lfintegrate| |cTanh| |algDsolve| + |OMputAttr| |s17aef| |equiv| |rischDE| |setOrder| |neglist| |lookup| + |selectsecond| |leftLcm| |rightUnits| + |semiIndiceSubResultantEuclidean| |bat1| |printStatement| + |completeSmith| |fortranDouble| |hue| |seed| |e04jaf| |realRoots| + |optional?| |midpoints| |expr| |pureLex| |zero?| |largest| |series| + |rationalPoints| |stronglyReduce| |OMgetEndAttr| |reducedSystem| + |iprint| |quadratic| |basisOfCommutingElements| + |tableForDiscreteLogarithm| |intcompBasis| |iomode| + |genericRightDiscriminant| |diagonal?| |linSolve| |anticoord| + |squareFreePolynomial| |palgintegrate| |e02bdf| GE |inconsistent?| + |traceMatrix| |selectOrPolynomials| |purelyAlgebraicLeadingMonomial?| + |dequeue| |linearAssociatedLog| |e02ahf| |cTan| |lazyPrem| GT FG2F + |lazyPquo| |subResultantGcd| |setlast!| |repeatUntilLoop| + |triangular?| |distance| |variable| |curveColor| |algint| LE + |leftTrace| |min| |rootOfIrreduciblePoly| |bandedJacobian| + |dictionary| |weakBiRank| |createNormalPoly| |euclideanGroebner| |log| + |iterators| |youngGroup| |list?| LT |byte| |permutationGroup| + |lifting| |prod| |lfextlimint| |minPol| |pastel| |collectUnder| + |pushuconst| |stopTableGcd!| |nullary| |bandedHessian| |rotate| + |exponential1| |rubiksGroup| |stiffnessAndStabilityFactor| |fmecg| + |univariateSolve| |positiveSolve| |numericIfCan| |insertRoot!| + |completeEval| |oddlambert| |constantOperator| |initiallyReduce| + |getConstant| BY |numberOfHues| |sort!| |s17akf| |freeOf?| + |degreeSubResultant| |modularGcd| |depth| |c06gcf| |acothIfCan| + |internalInfRittWu?| |zerosOf| |sign| |explicitEntries?| |flexible?| + |birth| |poisson| |factorsOfDegree| |definingPolynomial| + |transcendent?| |rootPoly| |polar| |writeInt8!| |inputBinaryFile| + |mappingAst| |univcase| |dark| |integral?| |areEquivalent?| + |prinpolINFO| |cSinh| |mix| |setright!| |unravel| |setStatus!| + |physicalLength| |fixPredicate| |solveLinearlyOverQ| + |complexEigenvalues| |startTable!| |simplify| |extendIfCan| |region| + |critMonD1| |componentUpperBound| |currentCategoryFrame| |mpsode| + |limitedint| |generalTwoFactor| |tValues| |nor| + |getSyntaxFormsFromFile| |capacity| |genus| |sPol| |inRadical?| + |airyAi| |product| |external?| |elem?| |OMencodingSGML| NOT + |outputList| |difference| |lflimitedint| |isOr| |cyclicEqual?| + |LiePoly| |horizConcat| |cyclePartition| |internalZeroSetSplit| OR + |graphs| |iicos| |closeComponent| |expPot| |getPickedPoints| + |extractPoint| |tanh2trigh| |safetyMargin| |exprex| |debug| |monic?| + AND |OMputBind| |unrankImproperPartitions0| |arrayStack| + |euclideanNormalForm| |setTopPredicate| |sts2stst| |subResultantChain| + D |imagK| |deepestTail| |bernoulliB| |getProperty| |palgLODE0| + |associator| |symmetricPower| |nextsousResultant2| |internalIntegrate| + |nthFractionalTerm| |preprocess| |changeVar| |zeroVector| |edf2df| + |nextNormalPrimitivePoly| |digits| |isExpt| |properties| |e02dff| + |stirling2| |f04mcf| |setButtonValue| |adaptive3D?| |localReal?| + |minimize| |zeroDimPrimary?| |setMaxPoints| |translate| |finiteBasis| + |radPoly| |alternating| |OMsupportsSymbol?| |nthExpon| + |internalIntegrate0| |extractClosed| |nextSubsetGray| |submod| + |function| |groebner?| |reduceLODE| |expressIdealMember| |parabolic| + |listYoungTableaus| |column| |setEpilogue!| |multiset| |removeZero| + |charClass| |jordanAdmissible?| |bytes| |besselI| |e04naf| + |reducedForm| |changeThreshhold| |OMputString| |light| |eval| + |functionIsOscillatory| |solid?| |inR?| |iiasin| |nextPrimitivePoly| + |index?| |invertibleSet| |createMultiplicationTable| |oddintegers| + |univariatePolynomial| |infix| |numberOfComponents| |mapBivariate| + |movedPoints| |argument| |leftMult| |fill!| |wrregime| |subtractIfCan| + |optimize| |cross| |monomialIntegrate| * |internalDecompose| + |computePowers| |overset?| |purelyTranscendental?| |inHallBasis?| + |perfectNthPower?| |discreteLog| |print| |startStats!| |prime?| + |zeroDimensional?| |e02ajf| |nthFlag| |closedCurve?| + |LyndonWordsList1| |atrapezoidal| |resolve| |mightHaveRoots| + |divisorCascade| |unparse| |exQuo| GF2FG |patternMatch| |mainMonomial| + |ParCond| |string?| |interpret| |denominator| |e01bff| + |orthonormalBasis| |c06ecf| = |cAtan| |setnext!| + |semiDegreeSubResultantEuclidean| |mapExponents| |empty| + |deleteRoutine!| |leadingIdeal| |tanh2coth| |quoted?| |f04mbf| + |bfKeys| |writeByte!| |writable?| |UP2ifCan| |returnType!| |recur| + |splitDenominator| < |aLinear| |cyclotomic| |find| |dmpToHdmp| + |increase| |s17dhf| |fixedPointExquo| |digit| |square?| > |reseed| + |paren| |partialNumerators| |OMParseError?| |cscIfCan| |besselJ| + |divideIfCan| |setAttributeButtonStep| |validExponential| <= + |numberOfImproperPartitions| |changeWeightLevel| |ip4Address| + |nullSpace| |semiResultantEuclidean2| |cycleRagits| |hitherPlane| + |cyclotomicFactorization| |e02daf| >= |transpose| |inspect| + |showTheFTable| |cRationalPower| |numericalIntegration| + |numberOfIrreduciblePoly| |true| |mathieu24| |ef2edf| |directSum| + |getCurve| |rightRank| |doubleDisc| |noLinearFactor?| |nextSublist| + |subResultantGcdEuclidean| |normalForm| |lazyIntegrate| + |generalPosition| |mantissa| |sparsityIF| |bringDown| |pointColor| + |binomial| |lllip| |primPartElseUnitCanonical!| |getOperator| + |elseBranch| + |algintegrate| |nodes| |removeDuplicates!| + |leftQuotient| |bit?| |bumprow| |rdregime| |digamma| - |varList| + |exptMod| |conjugates| |normalizedAssociate| |relativeApprox| + |iflist2Result| |tryFunctionalDecomposition| |nil| |trace2PowMod| / + |pade| |mvar| |frst| |s18aff| |addMatchRestricted| |element?| + |bothWays| |subst| |ODESolve| |functorData| |shift| |coordinate| + |randnum| |mainPrimitivePart| |category| |toseInvertibleSet| + |createLowComplexityNormalBasis| |rst| |toScale| |extendedIntegrate| + |aQuadratic| |wreath| |rur| |domain| |derivationCoordinates| + |quadraticNorm| |s13adf| |approximate| |factorsOfCyclicGroupSize| + |retract| |swap!| |integers| |package| |BumInSepFFE| |hexDigit| + |complex| |indicialEquations| |nthFactor| |subset?| |nextItem| + |basisOfCentroid| |splitSquarefree| |rangePascalTriangle| |property| + |computeInt| |insertMatch| |d01apf| |sum| |getRef| |color| |show| + |c06fpf| |algebraicSort| |center| |leftRemainder| |f01mcf| |powers| + |selectfirst| |removeRedundantFactorsInContents| |usingTable?| + |functionIsFracPolynomial?| |subNode?| |infieldint| |makeGraphImage| + |objects| |cap| |categoryFrame| |trace| |sayLength| + |rightAlternative?| |sortConstraints| |slash| |safeFloor| |units| + |mapMatrixIfCan| |base| |rk4f| |isOpen?| |HermiteIntegrate| |elements| + |lp| |inverseLaplace| |cCsc| |zeroSetSplit| |cPower| |identity| + |e02agf| |separateDegrees| |totalDegree| |seriesSolve| + |shanksDiscLogAlgorithm| |limitedIntegrate| |setPosition| |vertConcat| + |isAnd| |conjug| |copyInto!| |jacobian| |semiResultantReduitEuclidean| + |s19adf| |mapUp!| |c06eaf| |viewDefaults| |ddFact| |aromberg| |vark| + |romberg| |multiplyCoefficients| |trueEqual| |plus| |exponents| + |showTheSymbolTable| |primeFactor| |ReduceOrder| |code| |prinb| + |minRowIndex| |monicDecomposeIfCan| |symmetricProduct| |f04adf| + |minrank| |move| |uniform01| |linear| |Lazard| |primintfldpoly| + |s17adf| |varselect| |baseRDE| |bfEntry| |elColumn2!| |merge!| + |s18adf| |complexEigenvectors| |asinhIfCan| |reopen!| |zeroDim?| + |pair?| |compound?| |polynomial| |perfectSqrt| |iibinom| + |pseudoDivide| |characteristicSerie| |times| |s15aef| |goodnessOfFit| + |taylorQuoByVar| |totolex| |linGenPos| |ratDenom| |qinterval| + |deepestInitial| |dihedralGroup| |pole?| |findConstructor| + |factorOfDegree| |dom| |rationalApproximation| + |rewriteSetByReducingWithParticularGenerators| |outputAsTex| + |addPoint2| |forLoop| |commonDenominator| |powerSum| + |lazyIrreducibleFactors| |cosh2sech| |rightFactorIfCan| |rightDivide| + |removeRedundantFactorsInPols| |lazyPseudoDivide| |zeroOf| + |coordinates| |setProperties| |clipParametric| |setClosed| + |stoseInvertibleSetsqfreg| |colorFunction| |integer?| |cAtanh| |monom| + |node| |reverse| |integralMatrixAtInfinity| |cExp| |nil?| + |getVariableOrder| |newTypeLists| |binaryTree| |laplace| |c02aff| + |untab| |vedf2vef| |complexIntegrate| |augment| |scale| + |transcendenceDegree| |top| |OMsupportsCD?| + |rewriteIdealWithHeadRemainder| |possiblyNewVariety?| + |realEigenvectors| |OMreadStr| |explicitlyFinite?| |associates?| + |subNodeOf?| |c06ekf| |interactiveEnv| + |setLegalFortranSourceExtensions| |complexForm| |title| |comp| + |cycleSplit!| |common| |ellipticCylindrical| |fortranCarriageReturn| + |associatedSystem| |d01alf| |s17ahf| |interReduce| |super| |mesh| + |karatsubaDivide| |generic?| |options| |edf2fi| |Beta| |atoms| + |coleman| |tanSum| |continue| |double?| |shallowCopy| |listOfLists| + |rename| |sequence| |nullity| |droot| + |generalizedContinuumHypothesisAssumed?| |cyclicCopy| |e| + |rischNormalize| |conjugate| |partialDenominators| + |symmetricRemainder| |fullPartialFraction| + |removeRoughlyRedundantFactorsInPol| |coHeight| + |basisOfRightAnnihilator| |linearPolynomials| |chainSubResultants| + |list| |irreducibleFactor| |mapSolve| |d01anf| + |semiSubResultantGcdEuclidean1| |extendedResultant| |string| + |integralAtInfinity?| |selectNonFiniteRoutines| + |genericLeftDiscriminant| |pointData| |cyclicParents| |car| |bottom!| + |equality| |df2mf| |sinIfCan| |flagFactor| + |rewriteIdealWithQuasiMonicGenerators| |f01qef| |sqfree| + |checkForZero| |hMonic| |cdr| |basicSet| |var1Steps| |unit?| + |antisymmetric?| |primextendedint| |cAcot| |rowEchelonLocal| + |monicRightFactorIfCan| |deepCopy| |taylorIfCan| |setDifference| + |extension| |gcdcofactprim| |nothing| |coth2tanh| |startTableInvSet!| + |imagi| |debug3D| |antiAssociative?| |d01bbf| |indices| + |setIntersection| |tubePointsDefault| |leftUnit| |approxNthRoot| + |pushdterm| |numeric| |doubleFloatFormat| |gcdPrimitive| |conditionP| + |putGraph| |lowerCase| |setUnion| |radicalEigenvector| + |binaryTournament| |OMgetAttr| |open?| |innerint| |radical| + |minPoints3D| |degree| |monicModulo| |equation| |readUInt32!| |apply| + |bezoutResultant| |OMputEndAtp| |OMlistCDs| |getGoodPrime| |matrixGcd| + |subPolSet?| |cyclicGroup| |algebraic?| |principalIdeal| |central?| + |OMputEndBind| |generalLambert| |partition| |zero| |e01baf| + |acotIfCan| |paraboloidal| |squareMatrix| |jordanAlgebra?| |size| + |OMputEndError| |cCos| |d02ejf| |bezoutDiscriminant| |complex?| + |push!| |sinh2csch| |width| |truncate| |unit| |readInt16!| |concat!| + |evenlambert| |cAcsc| |And| |clearTheSymbolTable| |less?| |callForm?| + |beauzamyBound| |overbar| |subresultantVector| |deepExpand| + |frobenius| |entry?| |Or| |any| |represents| |stoseInvertibleSet| + |rightZero| |composites| |removeCosSq| |first| |OMencodingUnknown| + |f07adf| |nextsubResultant2| |f02agf| |Not| |zeroSquareMatrix| + |henselFact| |repSq| |f02aaf| |linkToFortran| |rest| |operation| + |sturmSequence| |any?| |pow| |fractRagits| |palgRDE| |rightRemainder| + |linear?| |viewDeltaYDefault| |dominantTerm| |substitute| |leader| + |quasiMonic?| |reduction| |zCoord| |normalized?| |partialQuotients| + |isEquiv| |weights| |extractIfCan| |parts| |cCoth| |removeDuplicates| + |ceiling| |anfactor| |addPoint| |pointSizeDefault| |localUnquote| + |complexZeros| |associatorDependence| |numericalOptimization| |hash| + |coerceL| |makeViewport3D| |mr| |setCondition!| |karatsuba| + |leftMinimalPolynomial| |count| |symmetricSquare| + |univariatePolynomialsGcds| |optional| |extractIndex| + |pointColorDefault| |normalDenom| |OMputEndAttr| |nullary?| + |enterPointData| |doubleResultant| |rightPower| |partitions| + |plotPolar| |f01maf| |body| |lexGroebner| |reindex| |lieAdmissible?| + |s14baf| |createThreeSpace| |mainForm| |green| |domainTemplate| + |OMgetEndAtp| |torsionIfCan| |specialTrigs| |dimensionsOf| |contours| + |coth2trigh| |elRow1!| |round| |pdf2ef| |dmpToP| |rootNormalize| + |stack| |leftCharacteristicPolynomial| |setColumn!| |setAdaptive| + |sin2csc| |tower| |associative?| |palglimint0| |makeop| + |headRemainder| |nextIrreduciblePoly| |writeUInt8!| |idealiser| + |quadraticForm| |rootPower| |singRicDE| |minPoints| |rightExtendedGcd| + |squareFreeFactors| |reduceBasisAtInfinity| |quasiMonicPolynomials| + |rightCharacteristicPolynomial| |parametric?| |integerBound| + |fortranReal| |groebner| |sumOfDivisors| |rk4a| |c06frf| |summation| + |UnVectorise| |commaSeparate| SEGMENT |error| |fortranDoubleComplex| + |basisOfLeftNucloid| |testModulus| |port| |expandTrigProducts| |axes| + |palgint0| |constant| |finite?| |basisOfCenter| |shade| |quadratic?| + |assert| |nsqfree| |lprop| |bits| |contractSolve| |LyndonWordsList| + |exprToUPS| |fixedPoints| |lex| |withPredicates| |complexNumeric| + |inputOutputBinaryFile| |makeSeries| |lexTriangular| |makeTerm| |t| + |vector| |removeSquaresIfCan| |fortranInteger| + |resultantEuclideannaif| |univariate?| |OMconnOutDevice| + |matrixDimensions| |variationOfParameters| |changeBase| + |differentiate| |rarrow| |iterationVar| |f02axf| |exprToGenUPS| + |removeSinhSq| |bsolve| |kernels| |balancedBinaryTree| |split| + |ParCondList| |regime| |noncommutativeJordanAlgebra?| + |generalizedEigenvector| |shellSort| |dmp2rfi| |quasiComponent| + |operator| |f2st| |c05pbf| |rk4| |length| |removeSuperfluousCases| + |monomial?| |e02bbf| |continuedFraction| |genericLeftTrace| + |stoseSquareFreePart| |sumOfSquares| |radicalOfLeftTraceForm| + |leadingTerm| |FormatArabic| |scripts| |cyclic?| |inGroundField?| + |toroidal| |packageCall| |loadNativeModule| |genericPosition| + |corrPoly| |symmetricGroup| |univariate| |logGamma| |positive?| + |insert!| |tube| |factorSFBRlcUnit| |tubeRadius| |s17ajf| |iroot| + |denominators| |d02bhf| |concat| |mapDown!| |cSec| |setvalue!| + |OMgetEndBind| |lowerPolynomial| |subTriSet?| |OMgetInteger| + |selectPolynomials| |halfExtendedSubResultantGcd1| |torsion?| |isPlus| + |signAround| |rightRankPolynomial| |rationalPoint?| |d01amf| + |combineFeatureCompatibility| |factor| F2FG + |semiDiscriminantEuclidean| |reciprocalPolynomial| |deriv| + |rightExactQuotient| |countRealRootsMultiple| |iiatan| |OMcloseConn| + |integrate| |sqrt| |leastPower| |constantRight| |step| + |fractionFreeGauss!| |bitCoef| |getMultiplicationTable| |unmakeSUP| + |e02dcf| |real| |createZechTable| |failed?| |pointLists| + |flexibleArray| |outputArgs| |trapezoidal| |cCot| |mainSquareFreePart| + |possiblyInfinite?| |imag| |abelianGroup| |mainValue| |quotient| + |realEigenvalues| |elRow2!| |byteBuffer| |numFunEvals| + |semiLastSubResultantEuclidean| |readable?| |directProduct| + |genericRightMinimalPolynomial| |s14abf| |lieAlgebra?| |mdeg| |tab| + |externalList| |imagI| |OMputEndApp| |source| |numberOfChildren| + |ptree| |iicoth| |listexp| |fillPascalTriangle| + |ScanFloatIgnoreSpaces| |OMmakeConn| |printStats!| |invmod| |brace| + |host| |sec2cos| |ignore?| |s14aaf| |eyeDistance| |front| |makeSin| + |supersub| |ideal| |destruct| |representationType| |roughUnitIdeal?| + |s18aef| |reducedDiscriminant| |iisinh| |setOfMinN| |heapSort| + |jacobi| |permutations| |normal?| |symmetric?| |distFact| + |singularAtInfinity?| |lfinfieldint| |s17dcf| |iiGamma| + |intermediateResultsIF| |realSolve| |restorePrecision| |orbits| + |critT| |c06fuf| |OMclose| |more?| |normalizeAtInfinity| |target| + |viewWriteDefault| |red| |sample| |interpolate| |supRittWu?| + |factorSquareFree| |inc| |encodingDirectory| |monomial| |kovacic| + |adjoint| |recolor| |dimensionOfIrreducibleRepresentation| + |palgextint0| |scaleRoots| |nextLatticePermutation| |multivariate| + |isobaric?| |sub| |qPot| |pdct| |kind| |s19aaf| |simplifyPower| + |useEisensteinCriterion| |messagePrint| |maxPoints3D| |variables| + |geometric| |terms| |mapGen| |tensorProduct| |op| + |numberOfPrimitivePoly| |reverse!| |OMgetAtp| |plot| |partialFraction| + |stFuncN| |showTheRoutinesTable| |quartic| |d01asf| |hdmpToP| + |getButtonValue| |iCompose| |binarySearchTree| |maxColIndex| + |clearFortranOutputStack| |initTable!| |ravel| |elementary| |odd?| + |e01saf| |f02wef| |rationalIfCan| |iiasech| |d02bbf| |drawComplex| + |child| |regularRepresentation| |setPoly| |viewport2D| |reshape| + |stosePrepareSubResAlgo| |explicitlyEmpty?| |headAst| |leftRecip| + |e02aef| |setelt| |heap| |trigs| |iitanh| |makeCos| |setVariableOrder| + |clikeUniv| |s21bdf| |precision| |makingStats?| |setAdaptive3D| + |LazardQuotient| |ipow| |hasoln| |taylor| |mathieu23| + |lazyResidueClass| |fullDisplay| |polyred| |aQuartic| |rightOne| + |fracPart| |copy| |upperCase!| |sylvesterSequence| |gderiv| + |sqfrFactor| |stopTableInvSet!| |binomThmExpt| |stFunc1| |curryLeft| + |union| |iisech| |gcdPolynomial| |before?| |queue| |upperCase| + |basisOfLeftNucleus| |belong?| |saturate| |squareFreePart| |rightUnit| + |listOfMonoms| |hclf| |unaryFunction| |conditionsForIdempotents| + |mainVariables| |inf| |lyndon| |intersect| + |internalSubQuasiComponent?| |update| |setsubMatrix!| |airyBi| + |stoseInvertibleSetreg| |autoCoerce| |cycleLength| |firstNumer| + |primitiveElement| |cschIfCan| |selectSumOfSquaresRoutines| |cos2sec| + |showRegion| |e02bef| |d02gaf| |prepareSubResAlgo| |f02ajf| + |OMputFloat| |numberOfVariables| |headReduce| |parents| |leaves| + |bombieriNorm| |radicalRoots| |functionIsContinuousAtEndPoints| + |clearTheIFTable| |sn| |useNagFunctions| |setFormula!| |argscript| + |palgint| |order| |ratpart| |generalSqFr| |minimalPolynomial| + |setEmpty!| |cAsech| |monomRDEsys| |increasePrecision| |makeResult| + |selectODEIVPRoutines| |returnTypeOf| |identification| |rquo| |isMult| + |clipPointsDefault| |laplacian| |declare| |explogs2trigs| + |scalarMatrix| |OMputEndObject| |complement| |imagj| |limit| |presub| + |generalizedInverse| |clipSurface| |radix| |position| + |interpretString| |cfirst| |zoom| |constDsolve| |roughBase?| + |factorAndSplit| |makeMulti| |insertBottom!| |multinomial| + |resetBadValues| |match?| |makeSketch| |scalarTypeOf| |d02cjf| + |leadingCoefficientRicDE| |push| |e04gcf| |nlde| |viewZoomDefault| + |myDegree| |internalLastSubResultant| |alphanumeric?| + |algebraicVariables| |zeroSetSplitIntoTriangularSystems| + |outputAsScript| |critBonD| |argumentList!| |coerceS| + |algebraicCoefficients?| |cylindrical| |getCode| |replace| + |lowerBound| |evenInfiniteProduct| |number?| |rowEchLocal| + |leftRegularRepresentation| |linears| |s20adf| |invertible?| + |makeVariable| |fglmIfCan| |collect| |quote| |tanAn| |pascalTriangle| + |arg2| |isNot| |meshPar2Var| |unprotectedRemoveRedundantFactors| + |countable?| |sech2cosh| |prolateSpheroidal| |s21baf| |power| |f04qaf| + |fractionPart| |df2st| |rowEch| |doubleRank| |twoFactor| |double| + |blue| |euler| |var2StepsDefault| |expextendedint| |quotientByP| + |enumerate| |iExquo| |bernoulli| |mulmod| |conditions| |atom?| + |createNormalElement| |monicRightDivide| |iiacsch| |infRittWu?| + |integralDerivationMatrix| |f04maf| |f04faf| |multiple?| |s19abf| + |strongGenerators| |match| |expIfCan| |constantToUnaryFunction| + |characteristicPolynomial| |f02aef| |redpps| |differentialVariables| + |close!| |iidprod| |e02def| |complexNumericIfCan| |removeCoshSq| + |arguments| |li| |infiniteProduct| |e04ycf| |polyRDE| |commutator| + |integralLastSubResultant| |character?| |genericLeftMinimalPolynomial| + |f01rdf| |coefficient| |tracePowMod| |lquo| |screenResolution3D| + |intensity| |duplicates| |OMputEndBVar| |monicLeftDivide| + |certainlySubVariety?| |toseInvertible?| |csch2sinh| + |branchPointAtInfinity?| |prefixRagits| |leftOne| |randomLC| + |padicallyExpand| |expandLog| |factor1| |isTimes| |close| + |tryFunctionalDecomposition?| |resultantReduit| |singularitiesOf| + |quasiRegular| |Ei| |minset| |contract| |sechIfCan| + |linearAssociatedOrder| |definingEquations| |findBinding| + |rewriteSetWithReduction| |attributeData| |iiacos| |constantKernel| + |degreeSubResultantEuclidean| |declare!| |schema| |endSubProgram| + |newReduc| |divisors| |display| |d02kef| |screenResolution| + |leftExtendedGcd| |nativeModuleExtension| |algebraicOf| |findCycle| + |applyRules| |asechIfCan| |subMatrix| |roughEqualIdeals?| + |permutation| |imagE| |whileLoop| |iifact| |bitTruth| |simpson| + |e01sef| |shufflein| |dfRange| |primextintfrac| |iiacot| + |OMgetEndError| |bounds| |lSpaceBasis| |moduloP| |medialSet| |d03faf| + |cot2tan| |pmintegrate| |totalLex| |root?| |hostPlatform| + |localIntegralBasis| |gradient| |rightTrace| |reduced?| |setref| + |bubbleSort!| |read!| |useEisensteinCriterion?| |accuracyIF| + |cycleTail| |reducedQPowers| |chebyshevU| |iidsum| |exponentialOrder| + |log2| |revert| |test| |input| |OMgetType| |mapmult| + |subscriptedVariables| |measure2Result| |row| |internal?| |inrootof| + |principal?| |oneDimensionalArray| |duplicates?| |singleFactorBound| + |fTable| |library| |rightMult| |xCoord| |littleEndian| |comment| + |power!| |mainMonomials| |wholeRagits| |segment| |swap| |showAll?| + |root| |psolve| |hypergeometric0F1| |subHeight| |secIfCan| + |lowerCase!| |taylorRep| |OMencodingBinary| |nonQsign| |transform| + |makeSUP| |leadingSupport| |solve1| |OMUnknownSymbol?| |expt| |df2ef| + |factorByRecursion| |rightRegularRepresentation| |eigenvalues| + |LyndonBasis| |primintegrate| |thetaCoord| |sizeLess?| + |primlimintfrac| |rightScalarTimes!| |eq| |clearTable!| |overlap| + |prefix| |numberOfDivisors| |invertIfCan| |rootDirectory| |HenselLift| + |hdmpToDmp| |iter| |id| |postfix| |modulus| |set| |OMUnknownCD?| + |midpoint| |errorInfo| |incrementKthElement| |OMputBVar| |remove!| + |addBadValue| |wholePart| |members| |measure| |listConjugateBases| + |nthRoot| |identitySquareMatrix| |autoReduced?| |PollardSmallFactor| + |magnitude| |getStream| |supDimElseRittWu?| |edf2efi| + |positiveRemainder| |table| |iicosh| |internalAugment| |returns| + |splitLinear| |diagonalMatrix| |unitsColorDefault| |setRealSteps| + |over| |leftTraceMatrix| |insert| |new| |modifyPoint| |bag| + |UpTriBddDenomInv| |cot2trig| |pseudoQuotient| |obj| |reorder| + |module| |cyclicSubmodule| |cubic| |setrest!| + |solveLinearPolynomialEquationByRecursion| |maxrow| |brillhartTrials| + |scopes| |critB| |leftDivide| |coerceP| |companionBlocks| |cache| + |maxRowIndex| |rootKerSimp| |numberOfNormalPoly| |checkPrecision| + |legendre| |perspective| |copy!| |OMopenFile| |maxdeg| + |clipWithRanges| |chiSquare| |exprHasAlgebraicWeight| |resetNew| + |stoseInvertible?sqfreg| |laurentIfCan| |viewPhiDefault| |repeating| + |signature| |reducedContinuedFraction| |rootProduct| + |invertibleElseSplit?| |ode| |extendedEuclidean| |readBytes!| + |principalAncestors| |setProperty!| |perfectNthRoot| + |absolutelyIrreducible?| |exp| |iisec| |qqq| |retractIfCan| |e02gaf| + |setStatus| |coord| |lazyVariations| |generateIrredPoly| |delete| + |standardBasisOfCyclicSubmodule| |lastSubResultantEuclidean| + |permutationRepresentation| |setClipValue| |polCase| |hspace| + |exists?| |fortranTypeOf| |cartesian| |meshPar1Var| + |basisOfLeftAnnihilator| |fintegrate| |numer| |wronskianMatrix| + |polyRicDE| |traverse| |totalDifferential| |prindINFO| |notelem| + |roughSubIdeal?| |cyclic| |iicsc| |simpleBounds?| |surface| |denom| + |realZeros| |solveLinear| |scan| |drawCurves| |Ci| |argumentListOf| + |subResultantsChain| |complete| |qroot| |lastSubResultant| + |expenseOfEvaluationIF| |expint| |padecf| |Lazard2| |simpsono| + |extractProperty| |integralCoordinates| |multisect| |formula| + |complexExpand| |graphStates| |makeUnit| |pi| |dn| |realElementary| + |rightQuotient| |morphism| |firstSubsetGray| |left| |mapCoef| |s13aaf| + |basisOfMiddleNucleus| |infinity| |e02adf| |float?| |prologue| + |exprHasWeightCosWXorSinWX| |identityMatrix| |innerEigenvectors| + |LyndonCoordinates| |right| |e04ucf| |LowTriBddDenomInv| |readByte!| + |factorList| |genericRightNorm| |pop!| |normalizeIfCan| + |radicalEigenvectors| |rotatey| |rationalPower| |dioSolve| |cAsin| + |dflist| |probablyZeroDim?| |imagJ| |epilogue| |map| |palglimint| + |f01qdf| |lookupFunction| |computeBasis| |kernel| |hasSolution?| + |nrows| |cAcos| |eisensteinIrreducible?| |basis| |isQuotient| + |weighted| |viewWriteAvailable| |resetAttributeButtons| |alphanumeric| + |dimensions| |eulerE| |expand| |draw| |one?| |ncols| |arbitrary| + |plus!| |isList| |Aleph| |setScreenResolution3D| |createPrimitivePoly| + |radicalSimplify| |stoseLastSubResultant| |upperBound| |filterWhile| + |cond| |f02awf| |graeffe| |nthr| |infLex?| |chineseRemainder| |pushup| + |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 340dc6e0..46298bbc 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5340 +1,5340 @@ -(3223342 . 3467417912) -((-3531 (((-112) (-1 (-112) |#2| |#2|) $) 87) (((-112) $) NIL)) (-2676 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-4285 ((|#2| $ (-567) |#2|) NIL) ((|#2| $ (-1236 (-567)) |#2|) 44)) (-1602 (($ $) 81)) (-2494 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50) ((|#2| (-1 |#2| |#2| |#2|) $) 49)) (-2578 (((-567) (-1 (-112) |#2|) $) 27) (((-567) |#2| $) NIL) (((-567) |#2| $ (-567)) 97)) (-2799 (((-645 |#2|) $) 13)) (-2473 (($ (-1 (-112) |#2| |#2|) $ $) 64) (($ $ 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T) ((-902 (-1179)) |has| |#1| (-902 (-1179))) ((-888 (-381)) |has| |#1| (-888 (-381))) ((-888 (-567)) |has| |#1| (-888 (-567))) ((-886 |#1|) . T) ((-911) -12 (|has| |#1| (-308)) (|has| |#1| (-911))) ((-922) -2811 (|has| |#1| (-351)) (|has| |#1| (-365)) (|has| |#1| (-308))) ((-1004) -12 (|has| |#1| (-1004)) (|has| |#1| (-1204))) ((-1040 (-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) ((-1040 (-567)) |has| |#1| (-1040 (-567))) ((-1040 |#1|) . T) ((-1053 #0#) -2811 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-1053 |#1|) . T) ((-1053 $) . T) ((-1058 #0#) -2811 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-1058 |#1|) . T) ((-1058 $) . T) ((-1051) . T) ((-1060) . T) ((-1114) . T) ((-1102) . T) ((-1154) |has| |#1| (-351)) ((-1204) |has| |#1| (-1204)) ((-1207) |has| |#1| (-1204)) ((-1219) . 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T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2811 (|has| |#2| (-1102)) (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-727)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2811 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2811 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-617 #0=(-410 (-567))) -12 (|has| |#2| (-1040 (-410 (-567)))) (|has| |#2| (-1102))) ((-617 (-567)) -2811 (|has| |#2| (-1051)) (-12 (|has| |#2| (-1040 (-567))) (|has| |#2| (-1102))) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-617 |#2|) -2811 (|has| |#2| (-1102)) (|has| |#2| (-172))) ((-614 (-863)) -2811 (|has| |#2| (-1102)) (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-727)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-614 (-863))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-614 (-1269 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1051)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1051))) ((-287 #1=(-567) |#2|) . T) ((-289 #1# |#2|) . T) ((-310 |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) ((-370) |has| |#2| (-370)) ((-379 |#2|) |has| |#2| (-1051)) ((-414 |#2|) |has| |#2| (-1102)) ((-492 |#2|) . T) ((-605 #1# |#2|) . T) ((-517 |#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) ((-647 (-567)) -2811 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-647 |#2|) -2811 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-647 $) -2811 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-649 |#2|) -2811 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-649 $) -2811 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-641 |#2|) -2811 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-640 (-567)) -12 (|has| |#2| (-640 (-567))) (|has| |#2| (-1051))) ((-640 |#2|) |has| |#2| (-1051)) ((-718 |#2|) -2811 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-727) -2811 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-727)) (|has| |#2| (-172))) ((-792) |has| |#2| (-849)) ((-793) -2811 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-794) |has| |#2| (-794)) ((-795) -2811 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-796) -2811 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-849) |has| |#2| (-849)) ((-851) -2811 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-902 (-1179)) -12 (|has| |#2| (-902 (-1179))) (|has| |#2| (-1051))) ((-1040 #0#) -12 (|has| |#2| (-1040 (-410 (-567)))) (|has| |#2| (-1102))) ((-1040 (-567)) -12 (|has| |#2| (-1040 (-567))) (|has| |#2| (-1102))) ((-1040 |#2|) |has| |#2| (-1102)) ((-1053 |#2|) -2811 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1053 $) |has| |#2| (-172)) ((-1058 |#2|) -2811 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1058 $) |has| |#2| (-172)) ((-1051) -2811 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-1060) -2811 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-1114) -2811 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-727)) (|has| |#2| (-172))) ((-1102) -2811 (|has| |#2| (-1102)) (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-727)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1219) . T) ((-1276 |#2|) |has| |#2| (-365))) -((-3400 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-2494 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-3841 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -3400 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2494 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3841 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-772) (-1219) (-1219)) (T -239)) -((-3841 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-772)) (-4 *6 (-1219)) (-4 *7 (-1219)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-2494 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-772)) (-4 *6 (-1219)) (-4 *2 (-1219)) (-5 *1 (-239 *5 *6 *2)))) (-3400 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-772)) (-4 *7 (-1219)) (-4 *5 (-1219)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 -3400 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2494 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3841 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) -((-2412 (((-112) $ $) NIL (|has| |#2| (-1102)))) (-3791 (((-112) $) NIL (|has| |#2| (-131)))) (-3624 (($ (-923)) 65 (|has| |#2| (-1051)))) (-3843 (((-1274) $ (-567) (-567)) NIL (|has| $ (-6 -4423)))) (-1325 (($ $ $) 70 (|has| |#2| (-794)))) (-2376 (((-3 $ "failed") $ $) 57 (|has| |#2| (-131)))) (-1563 (((-112) $ (-772)) 17)) (-2384 (((-772)) NIL (|has| |#2| (-370)))) (-2677 (((-567) $) NIL (|has| |#2| (-849)))) (-4285 ((|#2| $ (-567) |#2|) NIL (|has| $ (-6 -4423)))) (-3647 (($) NIL T CONST)) (-3765 (((-3 (-567) "failed") $) NIL (-12 (|has| |#2| (-1040 (-567))) (|has| |#2| (-1102)))) (((-3 (-410 (-567)) "failed") $) NIL (-12 (|has| |#2| (-1040 (-410 (-567)))) (|has| |#2| (-1102)))) (((-3 |#2| "failed") $) 34 (|has| |#2| (-1102)))) (-2051 (((-567) $) NIL (-12 (|has| |#2| (-1040 (-567))) (|has| |#2| (-1102)))) (((-410 (-567)) $) NIL (-12 (|has| |#2| (-1040 (-410 (-567)))) (|has| |#2| (-1102)))) ((|#2| $) 32 (|has| |#2| (-1102)))) (-1423 (((-690 (-567)) (-690 $)) NIL (-12 (|has| |#2| (-640 (-567))) (|has| |#2| (-1051)))) (((-2 (|:| -4208 (-690 (-567))) (|:| |vec| (-1269 (-567)))) (-690 $) (-1269 $)) NIL (-12 (|has| |#2| (-640 (-567))) (|has| |#2| (-1051)))) (((-2 (|:| -4208 (-690 |#2|)) (|:| |vec| (-1269 |#2|))) (-690 $) (-1269 $)) NIL (|has| |#2| (-1051))) (((-690 |#2|) (-690 $)) NIL (|has| |#2| (-1051)))) (-3588 (((-3 $ "failed") $) 61 (|has| |#2| (-727)))) (-1359 (($) NIL (|has| |#2| (-370)))) (-3760 ((|#2| $ (-567) |#2|) NIL (|has| $ (-6 -4423)))) (-3703 ((|#2| $ (-567)) 59)) (-3137 (((-112) $) NIL (|has| |#2| (-849)))) (-2799 (((-645 |#2|) $) 15 (|has| $ (-6 -4422)))) (-4346 (((-112) $) NIL (|has| |#2| (-727)))) (-3465 (((-112) $) NIL (|has| |#2| (-849)))) (-4093 (((-112) $ (-772)) NIL)) (-3895 (((-567) $) 20 (|has| (-567) (-851)))) (-1365 (($ $ $) NIL (-2811 (|has| |#2| (-794)) (|has| |#2| (-849))))) (-1942 (((-645 |#2|) $) NIL (|has| $ (-6 -4422)))) (-3237 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4422)) (|has| |#2| (-1102))))) (-3255 (((-567) $) 58 (|has| (-567) (-851)))) (-3002 (($ $ $) NIL (-2811 (|has| |#2| (-794)) (|has| |#2| (-849))))) (-3751 (($ (-1 |#2| |#2|) $) NIL (|has| $ (-6 -4423)))) (-3841 (($ (-1 |#2| |#2|) $) 47)) (-3474 (((-923) $) NIL (|has| |#2| (-370)))) (-1986 (((-112) $ (-772)) NIL)) (-2516 (((-1161) $) NIL (|has| |#2| (-1102)))) (-4364 (((-645 (-567)) $) NIL)) (-3188 (((-112) (-567) $) NIL)) (-3779 (($ (-923)) NIL (|has| |#2| (-370)))) (-3437 (((-1122) $) NIL (|has| |#2| (-1102)))) (-2418 ((|#2| $) NIL (|has| (-567) (-851)))) (-3823 (($ $ |#2|) NIL (|has| $ (-6 -4423)))) (-4233 (((-112) (-1 (-112) |#2|) $) 24 (|has| $ (-6 -4422)))) (-2642 (($ $ (-645 (-295 |#2|))) NIL (-12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102)))) (($ $ (-295 |#2|)) NIL (-12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102)))) (($ $ |#2| |#2|) NIL (-12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102)))) (($ $ (-645 |#2|) (-645 |#2|)) NIL (-12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))))) (-3875 (((-112) $ $) NIL)) (-4058 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4422)) (|has| |#2| (-1102))))) (-2190 (((-645 |#2|) $) NIL)) (-3885 (((-112) $) NIL)) (-2701 (($) NIL)) (-1801 ((|#2| $ (-567) |#2|) NIL) ((|#2| $ (-567)) 21)) (-3917 ((|#2| $ $) NIL (|has| |#2| (-1051)))) (-2760 (($ (-1269 |#2|)) 18)) (-1412 (((-134)) NIL (|has| |#2| (-365)))) (-1616 (($ $) NIL (-12 (|has| |#2| (-233)) (|has| |#2| (-1051)))) (($ $ (-772)) NIL (-12 (|has| |#2| (-233)) (|has| |#2| (-1051)))) (($ $ (-1179)) NIL (-12 (|has| |#2| (-902 (-1179))) (|has| |#2| (-1051)))) (($ $ (-645 (-1179))) NIL (-12 (|has| |#2| (-902 (-1179))) (|has| |#2| (-1051)))) (($ $ (-1179) (-772)) NIL (-12 (|has| |#2| (-902 (-1179))) (|has| |#2| (-1051)))) (($ $ (-645 (-1179)) (-645 (-772))) NIL (-12 (|has| |#2| (-902 (-1179))) (|has| |#2| (-1051)))) (($ $ (-1 |#2| |#2|) (-772)) NIL (|has| |#2| (-1051))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1051)))) (-3447 (((-772) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4422))) (((-772) |#2| $) NIL (-12 (|has| $ (-6 -4422)) (|has| |#2| (-1102))))) (-4309 (($ $) NIL)) (-4129 (((-1269 |#2|) $) 10) (($ (-567)) NIL (-2811 (-12 (|has| |#2| (-1040 (-567))) (|has| |#2| (-1102))) (|has| |#2| (-1051)))) (($ (-410 (-567))) NIL (-12 (|has| |#2| (-1040 (-410 (-567)))) (|has| |#2| (-1102)))) (($ |#2|) 13 (|has| |#2| (-1102))) (((-863) $) NIL (|has| |#2| (-614 (-863))))) (-2746 (((-772)) NIL (|has| |#2| (-1051)) CONST)) (-3357 (((-112) $ $) NIL (|has| |#2| (-1102)))) (-3436 (((-112) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4422)))) (-1547 (($ $) NIL (|has| |#2| (-849)))) (-1733 (($) 40 (|has| |#2| (-131)) CONST)) (-1744 (($) 44 (|has| |#2| (-727)) CONST)) (-2647 (($ $) NIL (-12 (|has| |#2| (-233)) (|has| |#2| (-1051)))) (($ $ (-772)) NIL (-12 (|has| |#2| (-233)) (|has| |#2| (-1051)))) (($ $ (-1179)) NIL (-12 (|has| |#2| (-902 (-1179))) (|has| |#2| (-1051)))) (($ $ (-645 (-1179))) NIL (-12 (|has| |#2| (-902 (-1179))) (|has| |#2| (-1051)))) (($ $ (-1179) (-772)) NIL (-12 (|has| |#2| (-902 (-1179))) (|has| |#2| (-1051)))) (($ $ (-645 (-1179)) (-645 (-772))) NIL (-12 (|has| |#2| (-902 (-1179))) (|has| |#2| (-1051)))) (($ $ (-1 |#2| |#2|) (-772)) NIL (|has| |#2| (-1051))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1051)))) (-3004 (((-112) $ $) NIL (-2811 (|has| |#2| (-794)) (|has| |#2| (-849))))) (-2980 (((-112) $ $) NIL (-2811 (|has| |#2| (-794)) (|has| |#2| (-849))))) (-2946 (((-112) $ $) 31 (|has| |#2| (-1102)))) (-2993 (((-112) $ $) NIL (-2811 (|has| |#2| (-794)) (|has| |#2| (-849))))) (-2968 (((-112) $ $) 68 (-2811 (|has| |#2| (-794)) (|has| |#2| (-849))))) (-3069 (($ $ |#2|) NIL (|has| |#2| (-365)))) (-3053 (($ $ $) NIL (|has| |#2| (-1051))) (($ $) NIL (|has| |#2| (-1051)))) (-3041 (($ $ $) 38 (|has| |#2| (-25)))) (** (($ $ (-772)) NIL (|has| |#2| (-727))) (($ $ (-923)) NIL (|has| |#2| (-727)))) (* (($ (-567) $) NIL (|has| |#2| (-1051))) (($ $ $) 50 (|has| |#2| (-727))) (($ $ |#2|) 48 (|has| |#2| (-727))) (($ |#2| $) 49 (|has| |#2| (-727))) (($ (-772) $) NIL (|has| |#2| (-131))) (($ (-923) $) NIL (|has| |#2| (-25)))) (-2423 (((-772) $) NIL (|has| $ (-6 -4422))))) +((-3700 (*1 *1 *2) (-12 (-5 *2 (-1269 *4)) (-4 *4 (-1219)) (-4 *1 (-238 *3 *4)))) (-1771 (*1 *1 *2) (-12 (-5 *2 (-923)) (-4 *1 (-238 *3 *4)) (-4 *4 (-1051)) (-4 *4 (-1219)))) (-1336 (*1 *2 *1 *1) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1219)) (-4 *2 (-1051)))) (* (*1 *1 *1 *2) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1219)) (-4 *2 (-727)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1219)) (-4 *2 (-727))))) +(-13 (-605 (-567) |t#2|) (-614 (-1269 |t#2|)) (-10 -8 (-6 -4422) (-15 -3700 ($ (-1269 |t#2|))) (IF (|has| |t#2| (-1102)) (-6 (-414 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1051)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-231 |t#2|)) (-6 (-379 |t#2|)) (-15 -1771 ($ (-923))) (-15 -1336 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-131)) (-6 (-131)) |%noBranch|) (IF (|has| |t#2| (-727)) (PROGN (-6 (-727)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-370)) (-6 (-370)) |%noBranch|) (IF (|has| |t#2| (-172)) (PROGN (-6 (-38 |t#2|)) (-6 (-172))) |%noBranch|) (IF (|has| |t#2| (-6 -4419)) (-6 -4419) |%noBranch|) (IF (|has| |t#2| (-849)) (-6 (-849)) |%noBranch|) (IF (|has| |t#2| (-794)) (-6 (-794)) |%noBranch|) (IF (|has| |t#2| (-365)) (-6 (-1276 |t#2|)) |%noBranch|))) +(((-21) -2836 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-23) -2836 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-25) -2836 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2836 (|has| |#2| (-1102)) (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-727)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2836 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2836 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-617 #0=(-410 (-567))) -12 (|has| |#2| (-1040 (-410 (-567)))) (|has| |#2| (-1102))) ((-617 (-567)) -2836 (|has| |#2| (-1051)) (-12 (|has| |#2| (-1040 (-567))) (|has| |#2| (-1102))) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-617 |#2|) -2836 (|has| |#2| (-1102)) (|has| |#2| (-172))) ((-614 (-863)) -2836 (|has| |#2| (-1102)) (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-727)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-614 (-863))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-614 (-1269 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1051)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1051))) ((-287 #1=(-567) |#2|) . T) ((-289 #1# |#2|) . T) ((-310 |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) ((-370) |has| |#2| (-370)) ((-379 |#2|) |has| |#2| (-1051)) ((-414 |#2|) |has| |#2| (-1102)) ((-492 |#2|) . T) ((-605 #1# |#2|) . T) ((-517 |#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) ((-647 (-567)) -2836 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-647 |#2|) -2836 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-647 $) -2836 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-649 |#2|) -2836 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-649 $) -2836 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-641 |#2|) -2836 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-640 (-567)) -12 (|has| |#2| (-640 (-567))) (|has| |#2| (-1051))) ((-640 |#2|) |has| |#2| (-1051)) ((-718 |#2|) -2836 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-727) -2836 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-727)) (|has| |#2| (-172))) ((-792) |has| |#2| (-849)) ((-793) -2836 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-794) |has| |#2| (-794)) ((-795) -2836 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-796) -2836 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-849) |has| |#2| (-849)) ((-851) -2836 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-902 (-1179)) -12 (|has| |#2| (-902 (-1179))) (|has| |#2| (-1051))) ((-1040 #0#) -12 (|has| |#2| (-1040 (-410 (-567)))) (|has| |#2| (-1102))) ((-1040 (-567)) -12 (|has| |#2| (-1040 (-567))) (|has| |#2| (-1102))) ((-1040 |#2|) |has| |#2| (-1102)) ((-1053 |#2|) -2836 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1053 $) |has| |#2| (-172)) ((-1058 |#2|) -2836 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1058 $) |has| |#2| (-172)) ((-1051) -2836 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-1060) -2836 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-1114) -2836 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-727)) (|has| |#2| (-172))) ((-1102) -2836 (|has| |#2| (-1102)) (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-727)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1219) . 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T) ((-641 #0#) |has| |#1| (-38 (-410 (-567)))) ((-641 |#1|) |has| |#1| (-172)) ((-641 $) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455))) ((-640 (-567)) |has| |#1| (-640 (-567))) ((-640 |#1|) . T) ((-718 #0#) |has| |#1| (-38 (-410 (-567)))) ((-718 |#1|) |has| |#1| (-172)) ((-718 $) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455))) ((-727) . T) ((-902 (-1179)) |has| |#1| (-902 (-1179))) ((-902 |#3|) . T) ((-888 (-381)) -12 (|has| |#1| (-888 (-381))) (|has| |#3| (-888 (-381)))) ((-888 (-567)) -12 (|has| |#1| (-888 (-567))) (|has| |#3| (-888 (-567)))) ((-951 |#1| |#4| |#3|) . T) ((-911) |has| |#1| (-911)) ((-1040 (-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) ((-1040 (-567)) |has| |#1| (-1040 (-567))) ((-1040 |#1|) . T) ((-1040 |#2|) . T) ((-1040 |#3|) . T) ((-1053 #0#) |has| |#1| (-38 (-410 (-567)))) ((-1053 |#1|) . T) ((-1053 $) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-172))) ((-1058 #0#) |has| |#1| (-38 (-410 (-567)))) ((-1058 |#1|) . T) ((-1058 $) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-172))) ((-1051) . T) ((-1060) . T) ((-1114) . T) ((-1102) . T) ((-1223) |has| |#1| (-911))) -((-2412 (((-112) $ $) 19 (|has| |#1| (-1102)))) (-1581 ((|#1| $) 55)) (-2270 ((|#1| $) 45)) (-1563 (((-112) $ (-772)) 8)) (-3647 (($) 7 T CONST)) (-3900 (($ $) 61)) (-1602 (($ $) 49)) (-1985 ((|#1| |#1| $) 47)) (-2142 ((|#1| $) 46)) (-2799 (((-645 |#1|) $) 31 (|has| $ (-6 -4422)))) (-4093 (((-112) $ (-772)) 9)) (-1942 (((-645 |#1|) $) 30 (|has| $ (-6 -4422)))) (-3237 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1102)) (|has| $ (-6 -4422))))) (-3751 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4423)))) (-3841 (($ (-1 |#1| |#1|) $) 36)) (-1986 (((-112) $ (-772)) 10)) (-2334 (((-772) $) 62)) (-2516 (((-1161) $) 22 (|has| |#1| (-1102)))) (-2706 ((|#1| $) 40)) (-2826 ((|#1| |#1| $) 53)) (-1387 ((|#1| |#1| $) 52)) (-2646 (($ |#1| $) 41)) (-4136 (((-772) $) 56)) (-3437 (((-1122) $) 21 (|has| |#1| (-1102)))) (-1595 ((|#1| $) 63)) (-1806 ((|#1| $) 51)) (-4282 ((|#1| $) 50)) (-3949 ((|#1| $) 42)) (-4233 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4422)))) (-2642 (($ $ (-645 (-295 |#1|))) 27 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (($ $ (-295 |#1|)) 26 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (($ $ (-645 |#1|) (-645 |#1|)) 24 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102))))) (-3875 (((-112) $ $) 14)) (-3254 ((|#1| |#1| $) 59)) (-3885 (((-112) $) 11)) (-2701 (($) 12)) (-2852 ((|#1| $) 60)) (-1425 (($) 58) (($ (-645 |#1|)) 57)) (-3289 (((-772) $) 44)) (-3447 (((-772) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4422))) (((-772) |#1| $) 29 (-12 (|has| |#1| (-1102)) (|has| $ (-6 -4422))))) (-4309 (($ $) 13)) (-4129 (((-863) $) 18 (|has| |#1| (-614 (-863))))) (-1675 ((|#1| $) 54)) (-3357 (((-112) $ $) 23 (|has| |#1| (-1102)))) (-3700 (($ (-645 |#1|)) 43)) (-1877 ((|#1| $) 64)) (-3436 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4422)))) (-2946 (((-112) $ $) 20 (|has| |#1| (-1102)))) (-2423 (((-772) $) 6 (|has| $ (-6 -4422))))) +((-3973 (*1 *2 *3) (-12 (-4 *4 (-1051)) (-4 *3 (-851)) (-4 *5 (-267 *3)) (-4 *6 (-794)) (-5 *2 (-1 *1 (-772))) (-4 *1 (-254 *4 *3 *5 *6)))) (-4022 (*1 *2 *1) (-12 (-4 *1 (-254 *3 *4 *5 *6)) (-4 *3 (-1051)) (-4 *4 (-851)) (-4 *5 (-267 *4)) (-4 *6 (-794)) (-5 *2 (-645 *4)))) (-3905 (*1 *2 *1 *3) (-12 (-4 *1 (-254 *4 *3 *5 *6)) (-4 *4 (-1051)) (-4 *3 (-851)) (-4 *5 (-267 *3)) (-4 *6 (-794)) (-5 *2 (-772)))) (-3905 (*1 *2 *1) (-12 (-4 *1 (-254 *3 *4 *5 *6)) (-4 *3 (-1051)) (-4 *4 (-851)) (-4 *5 (-267 *4)) (-4 *6 (-794)) (-5 *2 (-772)))) (-3380 (*1 *2 *1 *3) (-12 (-4 *1 (-254 *4 *3 *5 *6)) (-4 *4 (-1051)) (-4 *3 (-851)) (-4 *5 (-267 *3)) (-4 *6 (-794)) (-5 *2 (-772)))) (-3466 (*1 *2 *1) (-12 (-4 *1 (-254 *3 *4 *5 *6)) (-4 *3 (-1051)) (-4 *4 (-851)) (-4 *5 (-267 *4)) (-4 *6 (-794)) (-5 *2 (-645 (-772))))) (-1895 (*1 *2 *1) (-12 (-4 *1 (-254 *3 *4 *5 *6)) (-4 *3 (-1051)) (-4 *4 (-851)) (-4 *5 (-267 *4)) (-4 *6 (-794)) (-5 *2 (-772)))) (-3466 (*1 *2 *1 *3) (-12 (-4 *1 (-254 *4 *3 *5 *6)) (-4 *4 (-1051)) (-4 *3 (-851)) (-4 *5 (-267 *3)) (-4 *6 (-794)) (-5 *2 (-645 (-772))))) (-1895 (*1 *2 *1 *3) (-12 (-4 *1 (-254 *4 *3 *5 *6)) (-4 *4 (-1051)) (-4 *3 (-851)) (-4 *5 (-267 *3)) (-4 *6 (-794)) (-5 *2 (-772)))) (-3773 (*1 *2 *1) (-12 (-4 *1 (-254 *3 *4 *5 *6)) (-4 *3 (-1051)) (-4 *4 (-851)) (-4 *5 (-267 *4)) (-4 *6 (-794)) (-5 *2 (-112)))) (-3459 (*1 *2 *1) (-12 (-4 *1 (-254 *3 *4 *2 *5)) (-4 *3 (-1051)) (-4 *4 (-851)) (-4 *5 (-794)) (-4 *2 (-267 *4)))) (-1413 (*1 *1 *1) (-12 (-4 *1 (-254 *2 *3 *4 *5)) (-4 *2 (-1051)) (-4 *3 (-851)) (-4 *4 (-267 *3)) (-4 *5 (-794)))) (-1309 (*1 *1 *1) (-12 (-4 *1 (-254 *2 *3 *4 *5)) (-4 *2 (-1051)) (-4 *3 (-851)) (-4 *4 (-267 *3)) (-4 *5 (-794)))) (-3973 (*1 *2 *1) (-12 (-4 *3 (-233)) (-4 *3 (-1051)) (-4 *4 (-851)) (-4 *5 (-267 *4)) (-4 *6 (-794)) (-5 *2 (-1 *1 (-772))) (-4 *1 (-254 *3 *4 *5 *6))))) +(-13 (-951 |t#1| |t#4| |t#3|) (-231 |t#1|) (-1040 |t#2|) (-10 -8 (-15 -3973 ((-1 $ (-772)) |t#2|)) (-15 -4022 ((-645 |t#2|) $)) (-15 -3905 ((-772) $ |t#2|)) (-15 -3905 ((-772) $)) (-15 -3380 ((-772) $ |t#2|)) (-15 -3466 ((-645 (-772)) $)) (-15 -1895 ((-772) $)) (-15 -3466 ((-645 (-772)) $ |t#2|)) (-15 -1895 ((-772) $ |t#2|)) (-15 -3773 ((-112) $)) (-15 -3459 (|t#3| $)) (-15 -1413 ($ $)) (-15 -1309 ($ $)) (IF (|has| |t#1| (-233)) (PROGN (-6 (-517 |t#2| |t#1|)) (-6 (-517 |t#2| $)) (-6 (-310 $)) (-15 -3973 ((-1 $ (-772)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-410 (-567)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-617 #0#) -2836 (|has| |#1| (-1040 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567))))) ((-617 (-567)) . T) ((-617 |#1|) . T) ((-617 |#2|) . T) ((-617 |#3|) . T) ((-617 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455))) ((-614 (-863)) . T) ((-172) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-172))) ((-615 (-539)) -12 (|has| |#1| (-615 (-539))) (|has| |#3| (-615 (-539)))) ((-615 (-894 (-381))) -12 (|has| |#1| (-615 (-894 (-381)))) (|has| |#3| (-615 (-894 (-381))))) ((-615 (-894 (-567))) -12 (|has| |#1| (-615 (-894 (-567)))) (|has| |#3| (-615 (-894 (-567))))) ((-231 |#1|) . T) ((-233) |has| |#1| (-233)) ((-291) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455))) ((-310 $) . T) ((-327 |#1| |#4|) . T) ((-379 |#1|) . T) ((-414 |#1|) . T) ((-455) -2836 (|has| |#1| (-911)) (|has| |#1| (-455))) ((-517 |#2| |#1|) |has| |#1| (-233)) ((-517 |#2| $) |has| |#1| (-233)) ((-517 |#3| |#1|) . T) ((-517 |#3| $) . T) ((-517 $ $) . T) ((-559) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455))) ((-647 #0#) |has| |#1| (-38 (-410 (-567)))) ((-647 (-567)) . T) ((-647 |#1|) . T) ((-647 $) . T) ((-649 #0#) |has| |#1| (-38 (-410 (-567)))) ((-649 |#1|) . T) ((-649 $) . T) ((-641 #0#) |has| |#1| (-38 (-410 (-567)))) ((-641 |#1|) |has| |#1| (-172)) ((-641 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455))) ((-640 (-567)) |has| |#1| (-640 (-567))) ((-640 |#1|) . T) ((-718 #0#) |has| |#1| (-38 (-410 (-567)))) ((-718 |#1|) |has| |#1| (-172)) ((-718 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455))) ((-727) . T) ((-902 (-1179)) |has| |#1| (-902 (-1179))) ((-902 |#3|) . T) ((-888 (-381)) -12 (|has| |#1| (-888 (-381))) (|has| |#3| (-888 (-381)))) ((-888 (-567)) -12 (|has| |#1| (-888 (-567))) (|has| |#3| (-888 (-567)))) ((-951 |#1| |#4| |#3|) . T) ((-911) |has| |#1| (-911)) ((-1040 (-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) ((-1040 (-567)) |has| |#1| (-1040 (-567))) ((-1040 |#1|) . T) ((-1040 |#2|) . T) ((-1040 |#3|) . T) ((-1053 #0#) |has| |#1| (-38 (-410 (-567)))) ((-1053 |#1|) . T) ((-1053 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-172))) ((-1058 #0#) |has| |#1| (-38 (-410 (-567)))) ((-1058 |#1|) . T) ((-1058 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-172))) ((-1051) . T) ((-1060) . T) ((-1114) . T) ((-1102) . T) ((-1223) |has| |#1| (-911))) +((-2487 (((-112) $ $) 19 (|has| |#1| (-1102)))) (-1760 ((|#1| $) 55)) (-3262 ((|#1| $) 45)) (-1555 (((-112) $ (-772)) 8)) (-3758 (($) 7 T CONST)) (-2450 (($ $) 61)) (-3790 (($ $) 49)) (-3410 ((|#1| |#1| $) 47)) (-4353 ((|#1| $) 46)) (-3468 (((-645 |#1|) $) 31 (|has| $ (-6 -4422)))) (-3753 (((-112) $ (-772)) 9)) (-4200 (((-645 |#1|) $) 30 (|has| $ (-6 -4422)))) (-2203 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1102)) (|has| $ (-6 -4422))))) (-2021 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4423)))) (-4364 (($ (-1 |#1| |#1|) $) 36)) (-3421 (((-112) $ (-772)) 10)) (-3613 (((-772) $) 62)) (-1812 (((-1161) $) 22 (|has| |#1| (-1102)))) (-3018 ((|#1| $) 40)) (-1661 ((|#1| |#1| $) 53)) (-3940 ((|#1| |#1| $) 52)) (-3636 (($ |#1| $) 41)) (-1337 (((-772) $) 56)) (-3479 (((-1122) $) 21 (|has| |#1| (-1102)))) (-3725 ((|#1| $) 63)) (-2252 ((|#1| $) 51)) (-1965 ((|#1| $) 50)) (-1713 ((|#1| $) 42)) (-1430 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4422)))) (-2913 (($ $ (-645 (-295 |#1|))) 27 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (($ $ (-295 |#1|)) 26 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102)))) (($ $ (-645 |#1|) (-645 |#1|)) 24 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1102))))) (-2222 (((-112) $ $) 14)) (-2337 ((|#1| |#1| $) 59)) (-2319 (((-112) $) 11)) (-2973 (($) 12)) (-1933 ((|#1| $) 60)) (-2709 (($) 58) (($ (-645 |#1|)) 57)) (-2772 (((-772) $) 44)) (-3486 (((-772) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4422))) (((-772) |#1| $) 29 (-12 (|has| |#1| (-1102)) (|has| $ (-6 -4422))))) (-3846 (($ $) 13)) (-2504 (((-863) $) 18 (|has| |#1| (-614 (-863))))) (-3329 ((|#1| $) 54)) (-3858 (((-112) $ $) 23 (|has| |#1| (-1102)))) (-4225 (($ (-645 |#1|)) 43)) (-1715 ((|#1| $) 64)) (-3450 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4422)))) (-2968 (((-112) $ $) 20 (|has| |#1| (-1102)))) (-2498 (((-772) $) 6 (|has| $ (-6 -4422))))) (((-255 |#1|) (-140) (-1219)) (T -255)) -((-1425 (*1 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1219)))) (-1425 (*1 *1 *2) (-12 (-5 *2 (-645 *3)) (-4 *3 (-1219)) (-4 *1 (-255 *3)))) (-4136 (*1 *2 *1) (-12 (-4 *1 (-255 *3)) (-4 *3 (-1219)) (-5 *2 (-772)))) (-1581 (*1 *2 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1219)))) (-1675 (*1 *2 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1219)))) (-2826 (*1 *2 *2 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1219)))) (-1387 (*1 *2 *2 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1219)))) (-1806 (*1 *2 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1219)))) (-4282 (*1 *2 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1219)))) (-1602 (*1 *1 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1219))))) -(-13 (-1123 |t#1|) (-997 |t#1|) (-10 -8 (-15 -1425 ($)) (-15 -1425 ($ (-645 |t#1|))) (-15 -4136 ((-772) $)) (-15 -1581 (|t#1| $)) (-15 -1675 (|t#1| $)) (-15 -2826 (|t#1| |t#1| $)) (-15 -1387 (|t#1| |t#1| $)) (-15 -1806 (|t#1| $)) (-15 -4282 (|t#1| $)) (-15 -1602 ($ $)))) -(((-34) . 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"Range not yet evaluated")))))))) 27)) (-2265 (((-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| (-1159 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2031 (-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| (-1179)) (|:| |fn| (-317 (-225))) (|:| -2031 (-1096 (-844 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) 39)) (-1804 (((-645 (-2 (|:| -2025 (-2 (|:| |var| (-1179)) (|:| |fn| 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T) ((-649 #0#) |has| |#1| (-38 (-410 (-567)))) ((-649 |#1|) . T) ((-649 $) . T) ((-641 #0#) |has| |#1| (-38 (-410 (-567)))) ((-641 |#1|) |has| |#1| (-172)) ((-641 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455))) ((-640 (-567)) |has| |#1| (-640 (-567))) ((-640 |#1|) . T) ((-718 #0#) |has| |#1| (-38 (-410 (-567)))) ((-718 |#1|) |has| |#1| (-172)) ((-718 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455))) ((-727) . T) ((-902 |#3|) . T) ((-888 (-381)) -12 (|has| |#1| (-888 (-381))) (|has| |#3| (-888 (-381)))) ((-888 (-567)) -12 (|has| |#1| (-888 (-567))) (|has| |#3| (-888 (-567)))) ((-951 |#1| |#2| |#3|) . T) ((-911) |has| |#1| (-911)) ((-1040 (-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) ((-1040 (-567)) |has| |#1| (-1040 (-567))) ((-1040 |#1|) . T) ((-1040 |#3|) . T) ((-1053 #0#) |has| |#1| (-38 (-410 (-567)))) ((-1053 |#1|) . 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T) ((-647 |#1|) . T) ((-647 |#2|) |has| |#1| (-365)) ((-647 $) . T) ((-649 #1#) -2811 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-649 |#1|) . T) ((-649 |#2|) |has| |#1| (-365)) ((-649 $) . T) ((-641 #1#) -2811 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-641 |#1|) |has| |#1| (-172)) ((-641 |#2|) |has| |#1| (-365)) ((-641 $) -2811 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-640 (-567)) -12 (|has| |#1| (-365)) (|has| |#2| (-640 (-567)))) ((-640 |#2|) |has| |#1| (-365)) ((-718 #1#) -2811 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-718 |#1|) |has| |#1| (-172)) ((-718 |#2|) |has| |#1| (-365)) ((-718 $) -2811 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-727) . 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T) ((-647 |#1|) . T) ((-647 |#2|) |has| |#1| (-365)) ((-647 $) . T) ((-649 #1#) -2836 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-649 |#1|) . T) ((-649 |#2|) |has| |#1| (-365)) ((-649 $) . T) ((-641 #1#) -2836 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-641 |#1|) |has| |#1| (-172)) ((-641 |#2|) |has| |#1| (-365)) ((-641 $) -2836 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-640 (-567)) -12 (|has| |#1| (-365)) (|has| |#2| (-640 (-567)))) ((-640 |#2|) |has| |#1| (-365)) ((-718 #1#) -2836 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-718 |#1|) |has| |#1| (-172)) ((-718 |#2|) |has| |#1| (-365)) ((-718 $) -2836 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-727) . 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T) ((-922) |has| |#1| (-365)) ((-994 |#2|) |has| |#1| (-365)) ((-1004) |has| |#1| (-38 (-410 (-567)))) ((-1024) -12 (|has| |#1| (-365)) (|has| |#2| (-1024))) ((-1040 (-410 (-567))) -12 (|has| |#1| (-365)) (|has| |#2| (-1040 (-567)))) ((-1040 (-567)) -12 (|has| |#1| (-365)) (|has| |#2| (-1040 (-567)))) ((-1040 #2#) -12 (|has| |#1| (-365)) (|has| |#2| (-1040 (-1179)))) ((-1040 |#2|) . T) ((-1053 #1#) -2836 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-1053 |#1|) . T) ((-1053 |#2|) |has| |#1| (-365)) ((-1053 $) -2836 (|has| |#1| (-559)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1058 #1#) -2836 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-1058 |#1|) . T) ((-1058 |#2|) |has| |#1| (-365)) ((-1058 $) -2836 (|has| |#1| (-559)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1051) . T) ((-1060) . T) ((-1114) . T) ((-1102) . 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T) ((-23) . T) ((-47 |#1| #0=(-772)) . T) ((-25) . T) ((-38 #1=(-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-410 (-567)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-617 #1#) -2811 (|has| |#1| (-1040 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567))))) ((-617 (-567)) . T) ((-617 #2=(-1084)) . T) ((-617 |#1|) . T) ((-617 $) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-614 (-863)) . T) ((-172) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-615 (-539)) -12 (|has| (-1084) (-615 (-539))) (|has| |#1| (-615 (-539)))) ((-615 (-894 (-381))) -12 (|has| (-1084) (-615 (-894 (-381)))) (|has| |#1| (-615 (-894 (-381))))) ((-615 (-894 (-567))) -12 (|has| (-1084) (-615 (-894 (-567)))) (|has| |#1| (-615 (-894 (-567))))) ((-231 |#1|) . T) ((-233) . T) ((-287 (-410 $) (-410 $)) |has| |#1| (-559)) ((-287 |#1| |#1|) . T) ((-287 $ $) . T) ((-291) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-308) |has| |#1| (-365)) ((-310 $) . T) ((-327 |#1| #0#) . T) ((-379 |#1|) . T) ((-414 |#1|) . T) ((-455) -2811 (|has| |#1| (-911)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-517 #2# |#1|) . T) ((-517 #2# $) . T) ((-517 $ $) . T) ((-559) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-647 #1#) |has| |#1| (-38 (-410 (-567)))) ((-647 (-567)) . T) ((-647 |#1|) . T) ((-647 $) . T) ((-649 #1#) |has| |#1| (-38 (-410 (-567)))) ((-649 |#1|) . T) ((-649 $) . T) ((-641 #1#) |has| |#1| (-38 (-410 (-567)))) ((-641 |#1|) |has| |#1| (-172)) ((-641 $) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-640 (-567)) |has| |#1| (-640 (-567))) ((-640 |#1|) . T) ((-718 #1#) |has| |#1| (-38 (-410 (-567)))) ((-718 |#1|) |has| |#1| (-172)) ((-718 $) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-727) . T) ((-902 #2#) . T) ((-902 (-1179)) |has| |#1| (-902 (-1179))) ((-888 (-381)) -12 (|has| (-1084) (-888 (-381))) (|has| |#1| (-888 (-381)))) ((-888 (-567)) -12 (|has| (-1084) (-888 (-567))) (|has| |#1| (-888 (-567)))) ((-951 |#1| #0# #2#) . T) ((-911) |has| |#1| (-911)) ((-922) |has| |#1| (-365)) ((-1040 (-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) ((-1040 (-567)) |has| |#1| (-1040 (-567))) ((-1040 #2#) . T) ((-1040 |#1|) . T) ((-1053 #1#) |has| |#1| (-38 (-410 (-567)))) ((-1053 |#1|) . T) ((-1053 $) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1058 #1#) |has| |#1| (-38 (-410 (-567)))) ((-1058 |#1|) . T) ((-1058 $) -2811 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1051) . T) ((-1060) . T) ((-1114) . T) ((-1102) . T) ((-1154) |has| |#1| (-1154)) ((-1223) |has| |#1| (-911))) -((-2859 (((-645 (-1084)) $) 34)) (-3023 (($ $) 31)) (-2836 (($ |#2| |#3|) NIL) (($ $ (-1084) |#3|) 28) (($ $ (-645 (-1084)) (-645 |#3|)) 27)) (-2985 (($ $) 14)) (-2996 ((|#2| $) 12)) (-3104 ((|#3| $) 10))) -(((-1246 |#1| |#2| |#3|) (-10 -8 (-15 -2859 ((-645 (-1084)) |#1|)) (-15 -2836 (|#1| |#1| (-645 (-1084)) (-645 |#3|))) (-15 -2836 (|#1| |#1| (-1084) |#3|)) (-15 -3023 (|#1| |#1|)) (-15 -2836 (|#1| |#2| |#3|)) (-15 -3104 (|#3| |#1|)) (-15 -2985 (|#1| |#1|)) (-15 -2996 (|#2| |#1|))) (-1247 |#2| |#3|) (-1051) (-793)) (T -1246)) -NIL -(-10 -8 (-15 -2859 ((-645 (-1084)) |#1|)) (-15 -2836 (|#1| |#1| (-645 (-1084)) (-645 |#3|))) (-15 -2836 (|#1| |#1| (-1084) |#3|)) (-15 -3023 (|#1| |#1|)) (-15 -2836 (|#1| |#2| |#3|)) (-15 -3104 (|#3| |#1|)) (-15 -2985 (|#1| |#1|)) (-15 -2996 (|#2| |#1|))) -((-2412 (((-112) $ $) 7)) (-3791 (((-112) $) 17)) (-2859 (((-645 (-1084)) $) 86)) (-3653 (((-1179) $) 115)) (-1489 (((-2 (|:| -4369 $) (|:| 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(-410 (-567))))))) +(-13 (-951 |t#1| (-772) (-1084)) (-287 |t#1| |t#1|) (-287 $ $) (-233) (-231 |t#1|) (-10 -8 (-15 -1995 ((-1269 |t#1|) $ (-772))) (-15 -4163 ((-1175 |t#1|) $)) (-15 -3678 ($ (-1175 |t#1|))) (-15 -2240 ($ $ (-772))) (-15 -2462 ((-3 $ "failed") $ (-772))) (-15 -2177 ((-2 (|:| -3693 $) (|:| -2642 $)) $ $)) (-15 -3287 ((-2 (|:| -3693 $) (|:| -2642 $)) $ (-772))) (-15 -1863 ($ $ (-772))) (-15 -1751 ($ $ (-772))) (-15 -2497 ($ $ $)) (-15 -3592 ($ $ (-1 |t#1| |t#1|) $)) (IF (|has| |t#1| (-1154)) (-6 (-1154)) |%noBranch|) (IF (|has| |t#1| (-172)) (PROGN (-15 -2254 (|t#1| $)) (-15 -2304 (|t#1| $ $))) |%noBranch|) (IF (|has| |t#1| (-559)) (PROGN (-6 (-287 (-410 $) (-410 $))) (-15 -1882 ((-410 $) (-410 $) (-410 $))) (-15 -3905 ((-772) $ $)) (-15 -2717 ($ $ $)) (-15 -2557 ((-3 $ "failed") $ $)) (-15 -2557 ((-3 (-410 $) "failed") (-410 $) $)) (-15 -4228 ($ $ $)) (-15 -3207 ((-2 (|:| -1344 |t#1|) (|:| -3693 $) (|:| -2642 $)) $ $))) |%noBranch|) (IF (|has| |t#1| (-455)) (-15 -2170 ((-2 (|:| |primePart| $) (|:| |commonPart| $)) $ $)) |%noBranch|) (IF (|has| |t#1| (-365)) (PROGN (-6 (-308)) (-6 -4418) (-15 -1882 (|t#1| (-410 $) |t#1|))) |%noBranch|) (IF (|has| |t#1| (-38 (-410 (-567)))) (-15 -3670 ($ $)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-772)) . T) ((-25) . T) ((-38 #1=(-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-410 (-567)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-617 #1#) -2836 (|has| |#1| (-1040 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567))))) ((-617 (-567)) . T) ((-617 #2=(-1084)) . T) ((-617 |#1|) . T) ((-617 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-614 (-863)) . T) ((-172) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-615 (-539)) -12 (|has| (-1084) (-615 (-539))) (|has| |#1| (-615 (-539)))) ((-615 (-894 (-381))) -12 (|has| (-1084) (-615 (-894 (-381)))) (|has| |#1| (-615 (-894 (-381))))) ((-615 (-894 (-567))) -12 (|has| (-1084) (-615 (-894 (-567)))) (|has| |#1| (-615 (-894 (-567))))) ((-231 |#1|) . T) ((-233) . T) ((-287 (-410 $) (-410 $)) |has| |#1| (-559)) ((-287 |#1| |#1|) . T) ((-287 $ $) . T) ((-291) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-308) |has| |#1| (-365)) ((-310 $) . T) ((-327 |#1| #0#) . T) ((-379 |#1|) . T) ((-414 |#1|) . T) ((-455) -2836 (|has| |#1| (-911)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-517 #2# |#1|) . T) ((-517 #2# $) . T) ((-517 $ $) . T) ((-559) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-647 #1#) |has| |#1| (-38 (-410 (-567)))) ((-647 (-567)) . T) ((-647 |#1|) . T) ((-647 $) . T) ((-649 #1#) |has| |#1| (-38 (-410 (-567)))) ((-649 |#1|) . T) ((-649 $) . T) ((-641 #1#) |has| |#1| (-38 (-410 (-567)))) ((-641 |#1|) |has| |#1| (-172)) ((-641 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-640 (-567)) |has| |#1| (-640 (-567))) ((-640 |#1|) . T) ((-718 #1#) |has| |#1| (-38 (-410 (-567)))) ((-718 |#1|) |has| |#1| (-172)) ((-718 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-727) . T) ((-902 #2#) . T) ((-902 (-1179)) |has| |#1| (-902 (-1179))) ((-888 (-381)) -12 (|has| (-1084) (-888 (-381))) (|has| |#1| (-888 (-381)))) ((-888 (-567)) -12 (|has| (-1084) (-888 (-567))) (|has| |#1| (-888 (-567)))) ((-951 |#1| #0# #2#) . T) ((-911) |has| |#1| (-911)) ((-922) |has| |#1| (-365)) ((-1040 (-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) ((-1040 (-567)) |has| |#1| (-1040 (-567))) ((-1040 #2#) . T) ((-1040 |#1|) . T) ((-1053 #1#) |has| |#1| (-38 (-410 (-567)))) ((-1053 |#1|) . T) ((-1053 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1058 #1#) |has| |#1| (-38 (-410 (-567)))) ((-1058 |#1|) . T) ((-1058 $) -2836 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1051) . T) ((-1060) . T) ((-1114) . T) ((-1102) . T) ((-1154) |has| |#1| (-1154)) ((-1223) |has| |#1| (-911))) +((-3783 (((-645 (-1084)) $) 34)) (-1833 (($ $) 31)) (-3764 (($ |#2| |#3|) NIL) (($ $ (-1084) |#3|) 28) (($ $ (-645 (-1084)) (-645 |#3|)) 27)) (-1796 (($ $) 14)) (-1809 ((|#2| $) 12)) (-3380 ((|#3| $) 10))) +(((-1246 |#1| |#2| |#3|) (-10 -8 (-15 -3783 ((-645 (-1084)) |#1|)) (-15 -3764 (|#1| |#1| (-645 (-1084)) (-645 |#3|))) (-15 -3764 (|#1| |#1| (-1084) |#3|)) (-15 -1833 (|#1| |#1|)) (-15 -3764 (|#1| |#2| |#3|)) (-15 -3380 (|#3| |#1|)) (-15 -1796 (|#1| |#1|)) (-15 -1809 (|#2| |#1|))) (-1247 |#2| |#3|) (-1051) (-793)) (T -1246)) +NIL +(-10 -8 (-15 -3783 ((-645 (-1084)) |#1|)) (-15 -3764 (|#1| |#1| (-645 (-1084)) (-645 |#3|))) (-15 -3764 (|#1| |#1| (-1084) |#3|)) (-15 -1833 (|#1| |#1|)) (-15 -3764 (|#1| |#2| |#3|)) (-15 -3380 (|#3| |#1|)) (-15 -1796 (|#1| |#1|)) (-15 -1809 (|#2| |#1|))) +((-2487 (((-112) $ $) 7)) (-2684 (((-112) $) 17)) (-3783 (((-645 (-1084)) $) 86)) (-2722 (((-1179) $) 115)) (-2054 (((-2 (|:| -3414 $) (|:| 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) |has| |#1| (-559)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-410 (-567)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2811 (|has| |#1| (-559)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-617 #0#) |has| |#1| (-38 (-410 (-567)))) ((-617 (-567)) . T) ((-617 |#1|) |has| |#1| (-172)) ((-617 $) |has| |#1| (-559)) ((-614 (-863)) . T) ((-172) -2811 (|has| |#1| (-559)) (|has| |#1| (-172))) ((-233) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-287 $ $) |has| |#2| (-1114)) ((-291) |has| |#1| (-559)) ((-559) |has| |#1| (-559)) ((-647 #0#) |has| |#1| (-38 (-410 (-567)))) ((-647 (-567)) . T) ((-647 |#1|) . T) ((-647 $) . T) ((-649 #0#) |has| |#1| (-38 (-410 (-567)))) ((-649 |#1|) . T) ((-649 $) . T) ((-641 #0#) |has| |#1| (-38 (-410 (-567)))) ((-641 |#1|) |has| |#1| (-172)) ((-641 $) |has| |#1| (-559)) ((-718 #0#) |has| |#1| (-38 (-410 (-567)))) ((-718 |#1|) |has| |#1| (-172)) ((-718 $) |has| |#1| (-559)) ((-727) . T) ((-902 (-1179)) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-902 (-1179)))) ((-975 |#1| |#2| (-1084)) . T) ((-1053 #0#) |has| |#1| (-38 (-410 (-567)))) ((-1053 |#1|) . T) ((-1053 $) -2811 (|has| |#1| (-559)) (|has| |#1| (-172))) ((-1058 #0#) |has| |#1| (-38 (-410 (-567)))) ((-1058 |#1|) . T) ((-1058 $) -2811 (|has| |#1| (-559)) (|has| |#1| (-172))) ((-1051) . T) ((-1060) . T) ((-1114) . T) ((-1102) . 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T) ((-23) . T) ((-47 |#1| #0=(-410 (-567))) . T) ((-25) . T) ((-38 #1=(-410 (-567))) -2811 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2811 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-35) |has| |#1| (-38 (-410 (-567)))) ((-95) |has| |#1| (-38 (-410 (-567)))) ((-102) . T) ((-111 #1# #1#) -2811 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2811 (|has| |#1| (-559)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-617 #1#) -2811 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-617 (-567)) . T) ((-617 |#1|) |has| |#1| (-172)) ((-617 |#2|) . T) ((-617 $) -2811 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-614 (-863)) . 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NIL) (-1268 3139017 3139276 3139594 "VECTOR2" 3140170 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1267 3132491 3136798 3136841 "VECTCAT" 3137836 NIL VECTCAT (NIL T) -9 NIL 3138423 NIL) (-1266 3131505 3131759 3132149 "VECTCAT-" 3132154 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1265 3130959 3131156 3131276 "VARIABLE" 3131420 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1264 3130892 3130897 3130927 "UTYPE" 3130932 T UTYPE (NIL) -9 NIL NIL NIL) (-1263 3129722 3129876 3130138 "UTSODETL" 3130718 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1262 3127162 3127622 3128146 "UTSODE" 3129263 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1261 3118999 3124788 3125277 "UTS" 3126731 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1260 3109873 3115240 3115283 "UTSCAT" 3116395 NIL UTSCAT (NIL T) -9 NIL 3117153 NIL) (-1259 3107220 3107943 3108932 "UTSCAT-" 3108937 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1258 3106847 3106890 3107023 "UTS2" 3107171 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1257 3101073 3103685 3103728 "URAGG" 3105798 NIL URAGG (NIL T) -9 NIL 3106521 NIL) (-1256 3098012 3098875 3099998 "URAGG-" 3100003 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1255 3093721 3096647 3097112 "UPXSSING" 3097676 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1254 3085787 3092968 3093241 "UPXS" 3093506 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1253 3078860 3085691 3085763 "UPXSCONS" 3085768 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1252 3068605 3075398 3075460 "UPXSCCA" 3076034 NIL UPXSCCA (NIL T T) -9 NIL 3076267 NIL) (-1251 3068243 3068328 3068502 "UPXSCCA-" 3068507 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1250 3057840 3064406 3064449 "UPXSCAT" 3065097 NIL UPXSCAT (NIL T) -9 NIL 3065706 NIL) (-1249 3057270 3057349 3057528 "UPXS2" 3057755 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1248 3055924 3056177 3056528 "UPSQFREE" 3057013 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1247 3049345 3052402 3052457 "UPSCAT" 3053618 NIL UPSCAT (NIL T T) -9 NIL 3054392 NIL) (-1246 3048549 3048756 3049083 "UPSCAT-" 3049088 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1245 3034204 3041972 3042015 "UPOLYC" 3044116 NIL UPOLYC (NIL T) -9 NIL 3045337 NIL) (-1244 3025532 3027958 3031105 "UPOLYC-" 3031110 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1243 3025159 3025202 3025335 "UPOLYC2" 3025483 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1242 3016970 3024842 3024971 "UP" 3025078 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1241 3016309 3016416 3016580 "UPMP" 3016859 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1240 3015862 3015943 3016082 "UPDIVP" 3016222 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1239 3014430 3014679 3014995 "UPDECOMP" 3015611 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1238 3013665 3013777 3013962 "UPCDEN" 3014314 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1237 3013184 3013253 3013402 "UP2" 3013590 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1236 3011651 3012388 3012665 "UNISEG" 3012942 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1235 3010866 3010993 3011198 "UNISEG2" 3011494 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1234 3009926 3010106 3010332 "UNIFACT" 3010682 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1233 2993858 3009103 3009354 "ULS" 3009733 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1232 2981856 2993762 2993834 "ULSCONS" 2993839 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1231 2963875 2975860 2975922 "ULSCCAT" 2976560 NIL ULSCCAT (NIL T T) -9 NIL 2976848 NIL) (-1230 2962925 2963170 2963558 "ULSCCAT-" 2963563 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1229 2952299 2958779 2958822 "ULSCAT" 2959685 NIL ULSCAT (NIL T) -9 NIL 2960416 NIL) (-1228 2951729 2951808 2951987 "ULS2" 2952214 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1227 2950856 2951366 2951473 "UINT8" 2951584 T UINT8 (NIL) -8 NIL NIL 2951669) (-1226 2949982 2950492 2950599 "UINT64" 2950710 T UINT64 (NIL) -8 NIL NIL 2950795) (-1225 2949108 2949618 2949725 "UINT32" 2949836 T UINT32 (NIL) -8 NIL NIL 2949921) (-1224 2948234 2948744 2948851 "UINT16" 2948962 T UINT16 (NIL) -8 NIL NIL 2949047) (-1223 2946537 2947494 2947524 "UFD" 2947736 T UFD (NIL) -9 NIL 2947850 NIL) (-1222 2946331 2946377 2946472 "UFD-" 2946477 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1221 2945413 2945596 2945812 "UDVO" 2946137 T UDVO (NIL) -7 NIL NIL NIL) (-1220 2943229 2943638 2944109 "UDPO" 2944977 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1219 2943162 2943167 2943197 "TYPE" 2943202 T TYPE (NIL) -9 NIL NIL NIL) (-1218 2942922 2943117 2943148 "TYPEAST" 2943153 T TYPEAST (NIL) -8 NIL NIL NIL) (-1217 2941893 2942095 2942335 "TWOFACT" 2942716 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1216 2940916 2941302 2941537 "TUPLE" 2941693 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1215 2938607 2939126 2939665 "TUBETOOL" 2940399 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1214 2937456 2937661 2937902 "TUBE" 2938400 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1213 2932185 2936428 2936711 "TS" 2937208 NIL TS (NIL T) -8 NIL NIL NIL) (-1212 2920825 2924944 2925041 "TSETCAT" 2930310 NIL TSETCAT (NIL T T T T) -9 NIL 2931841 NIL) (-1211 2915557 2917157 2919048 "TSETCAT-" 2919053 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1210 2910196 2911043 2911972 "TRMANIP" 2914693 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1209 2909637 2909700 2909863 "TRIMAT" 2910128 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1208 2907503 2907740 2908097 "TRIGMNIP" 2909386 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1207 2907023 2907136 2907166 "TRIGCAT" 2907379 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1206 2906692 2906771 2906912 "TRIGCAT-" 2906917 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1205 2903537 2905550 2905831 "TREE" 2906446 NIL TREE (NIL T) -8 NIL NIL NIL) (-1204 2902811 2903339 2903369 "TRANFUN" 2903404 T TRANFUN (NIL) -9 NIL 2903470 NIL) (-1203 2902090 2902281 2902561 "TRANFUN-" 2902566 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1202 2901894 2901926 2901987 "TOPSP" 2902051 T TOPSP (NIL) -7 NIL NIL NIL) (-1201 2901242 2901357 2901511 "TOOLSIGN" 2901775 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1200 2899876 2900419 2900658 "TEXTFILE" 2901025 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1199 2897788 2898329 2898758 "TEX" 2899469 T TEX (NIL) -8 NIL NIL NIL) (-1198 2897569 2897600 2897672 "TEX1" 2897751 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1197 2897217 2897280 2897370 "TEMUTL" 2897501 T TEMUTL (NIL) -7 NIL NIL NIL) (-1196 2895371 2895651 2895976 "TBCMPPK" 2896940 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1195 2887148 2893531 2893587 "TBAGG" 2893987 NIL TBAGG (NIL T T) -9 NIL 2894198 NIL) (-1194 2882218 2883706 2885460 "TBAGG-" 2885465 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1193 2881602 2881709 2881854 "TANEXP" 2882107 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1192 2874992 2881459 2881552 "TABLE" 2881557 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1191 2874404 2874503 2874641 "TABLEAU" 2874889 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1190 2869012 2870232 2871480 "TABLBUMP" 2873190 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1189 2868234 2868381 2868562 "SYSTEM" 2868853 T SYSTEM (NIL) -8 NIL NIL NIL) (-1188 2864693 2865392 2866175 "SYSSOLP" 2867485 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1187 2864491 2864648 2864679 "SYSPTR" 2864684 T SYSPTR (NIL) -8 NIL NIL NIL) (-1186 2863535 2864040 2864159 "SYSNNI" 2864345 NIL SYSNNI (NIL NIL) -8 NIL NIL 2864430) (-1185 2862842 2863301 2863380 "SYSINT" 2863440 NIL SYSINT (NIL NIL) -8 NIL NIL 2863485) (-1184 2859174 2860120 2860830 "SYNTAX" 2862154 T SYNTAX (NIL) -8 NIL NIL NIL) (-1183 2856332 2856934 2857566 "SYMTAB" 2858564 T SYMTAB (NIL) -8 NIL NIL NIL) (-1182 2851581 2852483 2853466 "SYMS" 2855371 T SYMS (NIL) -8 NIL NIL NIL) (-1181 2848816 2851039 2851269 "SYMPOLY" 2851386 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1180 2848333 2848408 2848531 "SYMFUNC" 2848728 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1179 2844352 2845645 2846458 "SYMBOL" 2847542 T SYMBOL (NIL) -8 NIL NIL NIL) (-1178 2837891 2839580 2841300 "SWITCH" 2842654 T SWITCH (NIL) -8 NIL NIL NIL) (-1177 2831125 2836712 2837015 "SUTS" 2837646 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2823191 2830372 2830645 "SUPXS" 2830910 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1175 2814950 2822809 2822935 "SUP" 2823100 NIL SUP (NIL T) -8 NIL NIL NIL) (-1174 2814109 2814236 2814453 "SUPFRACF" 2814818 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1173 2813730 2813789 2813902 "SUP2" 2814044 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1172 2812178 2812452 2812808 "SUMRF" 2813429 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1171 2811513 2811579 2811771 "SUMFS" 2812099 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1170 2795480 2810690 2810941 "SULS" 2811320 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1169 2795082 2795302 2795372 "SUCHTAST" 2795432 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1168 2794377 2794607 2794747 "SUCH" 2794990 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1167 2788243 2789283 2790242 "SUBSPACE" 2793465 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1166 2787673 2787763 2787927 "SUBRESP" 2788131 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1165 2781038 2782338 2783649 "STTF" 2786409 NIL STTF (NIL T) -7 NIL NIL NIL) (-1164 2775211 2776331 2777478 "STTFNC" 2779938 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1163 2766521 2768393 2770187 "STTAYLOR" 2773452 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1162 2759651 2766385 2766468 "STRTBL" 2766473 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1161 2755015 2759606 2759637 "STRING" 2759642 T STRING (NIL) -8 NIL NIL NIL) (-1160 2749876 2754388 2754418 "STRICAT" 2754477 T STRICAT (NIL) -9 NIL 2754539 NIL) (-1159 2742629 2747495 2748106 "STREAM" 2749300 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1158 2742139 2742216 2742360 "STREAM3" 2742546 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1157 2741121 2741304 2741539 "STREAM2" 2741952 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1156 2740809 2740861 2740954 "STREAM1" 2741063 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1155 2739825 2740006 2740237 "STINPROD" 2740625 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1154 2739377 2739587 2739617 "STEP" 2739697 T STEP (NIL) -9 NIL 2739775 NIL) (-1153 2738564 2738866 2739014 "STEPAST" 2739251 T STEPAST (NIL) -8 NIL NIL NIL) (-1152 2731996 2738463 2738540 "STBL" 2738545 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1151 2727122 2731217 2731260 "STAGG" 2731413 NIL STAGG (NIL T) -9 NIL 2731502 NIL) (-1150 2724824 2725426 2726298 "STAGG-" 2726303 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1149 2722971 2724594 2724686 "STACK" 2724767 NIL STACK (NIL T) -8 NIL NIL NIL) (-1148 2715666 2721112 2721568 "SREGSET" 2722601 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1147 2708091 2709460 2710973 "SRDCMPK" 2714272 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1146 2701008 2705531 2705561 "SRAGG" 2706864 T SRAGG (NIL) -9 NIL 2707472 NIL) (-1145 2700025 2700280 2700659 "SRAGG-" 2700664 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1144 2694485 2698972 2699393 "SQMATRIX" 2699651 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1143 2688170 2691203 2691930 "SPLTREE" 2693830 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1142 2684133 2684826 2685472 "SPLNODE" 2687596 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1141 2683180 2683413 2683443 "SPFCAT" 2683887 T SPFCAT (NIL) -9 NIL NIL NIL) (-1140 2681917 2682127 2682391 "SPECOUT" 2682938 T SPECOUT (NIL) -7 NIL NIL NIL) (-1139 2673282 2675104 2675134 "SPADXPT" 2679669 T SPADXPT (NIL) -9 NIL 2681769 NIL) (-1138 2673043 2673083 2673152 "SPADPRSR" 2673235 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1137 2671144 2672998 2673029 "SPADAST" 2673034 T SPADAST (NIL) -8 NIL NIL NIL) (-1136 2663089 2664862 2664905 "SPACEC" 2669278 NIL SPACEC (NIL T) -9 NIL 2671094 NIL) (-1135 2661219 2663021 2663070 "SPACE3" 2663075 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1134 2659971 2660142 2660433 "SORTPAK" 2661024 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1133 2658063 2658366 2658778 "SOLVETRA" 2659635 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1132 2657113 2657335 2657596 "SOLVESER" 2657836 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1131 2652417 2653305 2654300 "SOLVERAD" 2656165 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1130 2648232 2648841 2649570 "SOLVEFOR" 2651784 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1129 2642502 2647581 2647678 "SNTSCAT" 2647683 NIL SNTSCAT (NIL T T T T) -9 NIL 2647753 NIL) (-1128 2636608 2640825 2641216 "SMTS" 2642192 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1127 2631292 2636496 2636573 "SMP" 2636578 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1126 2629451 2629752 2630150 "SMITH" 2630989 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1125 2622164 2626360 2626463 "SMATCAT" 2627814 NIL SMATCAT (NIL NIL T T T) -9 NIL 2628364 NIL) (-1124 2619104 2619927 2621105 "SMATCAT-" 2621110 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1123 2616770 2618340 2618383 "SKAGG" 2618644 NIL SKAGG (NIL T) -9 NIL 2618779 NIL) (-1122 2613081 2616186 2616381 "SINT" 2616568 T SINT (NIL) -8 NIL NIL 2616741) (-1121 2612853 2612891 2612957 "SIMPAN" 2613037 T SIMPAN (NIL) -7 NIL NIL NIL) (-1120 2612132 2612388 2612528 "SIG" 2612735 T SIG (NIL) -8 NIL NIL NIL) (-1119 2610970 2611191 2611466 "SIGNRF" 2611891 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1118 2609803 2609954 2610238 "SIGNEF" 2610799 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1117 2609109 2609386 2609510 "SIGAST" 2609701 T SIGAST (NIL) -8 NIL NIL NIL) (-1116 2606798 2607253 2607759 "SHP" 2608650 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1115 2600650 2606699 2606775 "SHDP" 2606780 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1114 2600223 2600415 2600445 "SGROUP" 2600538 T SGROUP (NIL) -9 NIL 2600600 NIL) (-1113 2600081 2600107 2600180 "SGROUP-" 2600185 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1112 2596916 2597614 2598337 "SGCF" 2599380 T SGCF (NIL) -7 NIL NIL NIL) (-1111 2591284 2596363 2596460 "SFRTCAT" 2596465 NIL SFRTCAT (NIL T T T T) -9 NIL 2596504 NIL) (-1110 2584705 2585723 2586859 "SFRGCD" 2590267 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1109 2577831 2578904 2580090 "SFQCMPK" 2583638 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1108 2577451 2577540 2577651 "SFORT" 2577772 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1107 2576569 2577291 2577412 "SEXOF" 2577417 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1106 2575676 2576450 2576518 "SEX" 2576523 T SEX (NIL) -8 NIL NIL NIL) (-1105 2571189 2571904 2571999 "SEXCAT" 2574936 NIL SEXCAT (NIL T T T T T) -9 NIL 2575514 NIL) (-1104 2568342 2571123 2571171 "SET" 2571176 NIL SET (NIL T) -8 NIL NIL NIL) (-1103 2566566 2567055 2567360 "SETMN" 2568083 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1102 2566062 2566214 2566244 "SETCAT" 2566420 T SETCAT (NIL) -9 NIL 2566530 NIL) (-1101 2565754 2565832 2565962 "SETCAT-" 2565967 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1100 2562115 2564215 2564258 "SETAGG" 2565128 NIL SETAGG (NIL T) -9 NIL 2565468 NIL) (-1099 2561573 2561689 2561926 "SETAGG-" 2561931 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1098 2561016 2561269 2561370 "SEQAST" 2561494 T SEQAST (NIL) -8 NIL NIL NIL) (-1097 2560215 2560509 2560570 "SEGXCAT" 2560856 NIL SEGXCAT (NIL T T) -9 NIL 2560976 NIL) (-1096 2559221 2559881 2560063 "SEG" 2560068 NIL SEG (NIL T) -8 NIL NIL NIL) (-1095 2558200 2558414 2558457 "SEGCAT" 2558979 NIL SEGCAT (NIL T) -9 NIL 2559200 NIL) (-1094 2557132 2557563 2557771 "SEGBIND" 2558027 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1093 2556753 2556812 2556925 "SEGBIND2" 2557067 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1092 2556326 2556554 2556631 "SEGAST" 2556698 T SEGAST (NIL) -8 NIL NIL NIL) (-1091 2555545 2555671 2555875 "SEG2" 2556170 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1090 2554955 2555480 2555527 "SDVAR" 2555532 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1089 2547482 2554725 2554855 "SDPOL" 2554860 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1088 2546075 2546341 2546660 "SCPKG" 2547197 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1087 2545239 2545411 2545603 "SCOPE" 2545905 T SCOPE (NIL) -8 NIL NIL NIL) (-1086 2544459 2544593 2544772 "SCACHE" 2545094 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1085 2544105 2544291 2544321 "SASTCAT" 2544326 T SASTCAT (NIL) -9 NIL 2544339 NIL) (-1084 2543592 2543940 2544016 "SAOS" 2544051 T SAOS (NIL) -8 NIL NIL NIL) (-1083 2543157 2543192 2543365 "SAERFFC" 2543551 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1082 2537096 2543054 2543134 "SAE" 2543139 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1081 2536689 2536724 2536883 "SAEFACT" 2537055 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1080 2535010 2535324 2535725 "RURPK" 2536355 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1079 2533647 2533953 2534258 "RULESET" 2534844 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1078 2530870 2531400 2531858 "RULE" 2533328 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1077 2530482 2530664 2530747 "RULECOLD" 2530822 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1076 2530272 2530300 2530371 "RTVALUE" 2530433 T RTVALUE (NIL) -8 NIL NIL NIL) (-1075 2529743 2529989 2530083 "RSTRCAST" 2530200 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1074 2524591 2525386 2526306 "RSETGCD" 2528942 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1073 2513821 2518900 2518997 "RSETCAT" 2523116 NIL RSETCAT (NIL T T T T) -9 NIL 2524213 NIL) (-1072 2511748 2512287 2513111 "RSETCAT-" 2513116 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1071 2504133 2505510 2507030 "RSDCMPK" 2510347 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1070 2502112 2502579 2502653 "RRCC" 2503739 NIL RRCC (NIL T T) -9 NIL 2504083 NIL) (-1069 2501463 2501637 2501916 "RRCC-" 2501921 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1068 2500906 2501159 2501260 "RPTAST" 2501384 T RPTAST (NIL) -8 NIL NIL NIL) (-1067 2474757 2484114 2484181 "RPOLCAT" 2494845 NIL RPOLCAT (NIL T T T) -9 NIL 2498004 NIL) (-1066 2466255 2468595 2471717 "RPOLCAT-" 2471722 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1065 2457186 2464466 2464948 "ROUTINE" 2465795 T ROUTINE (NIL) -8 NIL NIL NIL) (-1064 2453984 2456812 2456952 "ROMAN" 2457068 T ROMAN (NIL) -8 NIL NIL NIL) (-1063 2452228 2452844 2453104 "ROIRC" 2453789 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1062 2448460 2450744 2450774 "RNS" 2451078 T RNS (NIL) -9 NIL 2451352 NIL) (-1061 2446969 2447352 2447886 "RNS-" 2447961 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1060 2446372 2446780 2446810 "RNG" 2446815 T RNG (NIL) -9 NIL 2446836 NIL) (-1059 2445375 2445737 2445939 "RNGBIND" 2446223 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1058 2444774 2445162 2445205 "RMODULE" 2445210 NIL RMODULE (NIL T) -9 NIL 2445237 NIL) (-1057 2443610 2443704 2444040 "RMCAT2" 2444675 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1056 2440460 2442956 2443253 "RMATRIX" 2443372 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1055 2433287 2435547 2435662 "RMATCAT" 2439021 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2440003 NIL) (-1054 2432662 2432809 2433116 "RMATCAT-" 2433121 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1053 2432063 2432284 2432327 "RLINSET" 2432521 NIL RLINSET (NIL T) -9 NIL 2432612 NIL) (-1052 2431630 2431705 2431833 "RINTERP" 2431982 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1051 2430688 2431242 2431272 "RING" 2431328 T RING (NIL) -9 NIL 2431420 NIL) (-1050 2430480 2430524 2430621 "RING-" 2430626 NIL RING- (NIL T) -8 NIL NIL NIL) (-1049 2429321 2429558 2429816 "RIDIST" 2430244 T RIDIST (NIL) -7 NIL NIL NIL) (-1048 2420610 2428789 2428995 "RGCHAIN" 2429169 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1047 2419960 2420366 2420407 "RGBCSPC" 2420465 NIL RGBCSPC (NIL T) -9 NIL 2420517 NIL) (-1046 2419118 2419499 2419540 "RGBCMDL" 2419772 NIL RGBCMDL (NIL T) -9 NIL 2419886 NIL) (-1045 2416112 2416726 2417396 "RF" 2418482 NIL RF (NIL T) -7 NIL NIL NIL) (-1044 2415758 2415821 2415924 "RFFACTOR" 2416043 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1043 2415483 2415518 2415615 "RFFACT" 2415717 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1042 2413600 2413964 2414346 "RFDIST" 2415123 T RFDIST (NIL) -7 NIL NIL NIL) (-1041 2413053 2413145 2413308 "RETSOL" 2413502 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1040 2412689 2412769 2412812 "RETRACT" 2412945 NIL RETRACT (NIL T) -9 NIL 2413032 NIL) (-1039 2412538 2412563 2412650 "RETRACT-" 2412655 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1038 2412140 2412360 2412430 "RETAST" 2412490 T RETAST (NIL) -8 NIL NIL NIL) (-1037 2404878 2411793 2411920 "RESULT" 2412035 T RESULT (NIL) -8 NIL NIL NIL) (-1036 2403469 2404147 2404346 "RESRING" 2404781 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1035 2403105 2403154 2403252 "RESLATC" 2403406 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1034 2402810 2402845 2402952 "REPSQ" 2403064 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1033 2400232 2400812 2401414 "REP" 2402230 T REP (NIL) -7 NIL NIL NIL) (-1032 2399929 2399964 2400075 "REPDB" 2400191 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1031 2393829 2395218 2396441 "REP2" 2398741 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1030 2390206 2390887 2391695 "REP1" 2393056 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1029 2382902 2388347 2388803 "REGSET" 2389836 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1028 2381667 2382050 2382300 "REF" 2382687 NIL REF (NIL T) -8 NIL NIL NIL) (-1027 2381044 2381147 2381314 "REDORDER" 2381551 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1026 2377012 2380257 2380484 "RECLOS" 2380872 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1025 2376064 2376245 2376460 "REALSOLV" 2376819 T REALSOLV (NIL) -7 NIL NIL NIL) (-1024 2375910 2375951 2375981 "REAL" 2375986 T REAL (NIL) -9 NIL 2376021 NIL) (-1023 2372393 2373195 2374079 "REAL0Q" 2375075 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1022 2367994 2368982 2370043 "REAL0" 2371374 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1021 2367465 2367711 2367805 "RDUCEAST" 2367922 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1020 2366870 2366942 2367149 "RDIV" 2367387 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1019 2365938 2366112 2366325 "RDIST" 2366692 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1018 2364535 2364822 2365194 "RDETRS" 2365646 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1017 2362347 2362801 2363339 "RDETR" 2364077 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1016 2360972 2361250 2361647 "RDEEFS" 2362063 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1015 2359481 2359787 2360212 "RDEEF" 2360660 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1014 2353542 2356462 2356492 "RCFIELD" 2357787 T RCFIELD (NIL) -9 NIL 2358518 NIL) (-1013 2351606 2352110 2352806 "RCFIELD-" 2352881 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1012 2347875 2349707 2349750 "RCAGG" 2350834 NIL RCAGG (NIL T) -9 NIL 2351299 NIL) (-1011 2347503 2347597 2347760 "RCAGG-" 2347765 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1010 2346838 2346950 2347115 "RATRET" 2347387 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1009 2346391 2346458 2346579 "RATFACT" 2346766 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1008 2345699 2345819 2345971 "RANDSRC" 2346261 T RANDSRC (NIL) -7 NIL NIL NIL) (-1007 2345433 2345477 2345550 "RADUTIL" 2345648 T RADUTIL (NIL) -7 NIL NIL NIL) (-1006 2338549 2344266 2344576 "RADIX" 2345157 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1005 2330168 2338391 2338521 "RADFF" 2338526 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1004 2329815 2329890 2329920 "RADCAT" 2330080 T RADCAT (NIL) -9 NIL NIL NIL) (-1003 2329597 2329645 2329745 "RADCAT-" 2329750 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1002 2327697 2329369 2329460 "QUEUE" 2329541 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1001 2324236 2327632 2327679 "QUAT" 2327684 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1000 2323871 2323914 2324043 "QUATCT2" 2324187 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-999 2317333 2320678 2320718 "QUATCAT" 2321498 NIL QUATCAT (NIL T) -9 NIL 2322264 NIL) (-998 2313477 2314514 2315901 "QUATCAT-" 2315995 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-997 2310950 2312561 2312602 "QUAGG" 2312977 NIL QUAGG (NIL T) -9 NIL 2313152 NIL) (-996 2310555 2310775 2310843 "QQUTAST" 2310902 T QQUTAST (NIL) -8 NIL NIL NIL) (-995 2309453 2309953 2310125 "QFORM" 2310427 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-994 2300458 2305697 2305737 "QFCAT" 2306395 NIL QFCAT (NIL T) -9 NIL 2307396 NIL) (-993 2296030 2297231 2298822 "QFCAT-" 2298916 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-992 2295668 2295711 2295838 "QFCAT2" 2295981 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-991 2295128 2295238 2295368 "QEQUAT" 2295558 T QEQUAT (NIL) -8 NIL NIL NIL) (-990 2288274 2289347 2290531 "QCMPACK" 2294061 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-989 2285823 2286271 2286699 "QALGSET" 2287929 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-988 2285068 2285242 2285474 "QALGSET2" 2285643 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-987 2283758 2283982 2284299 "PWFFINTB" 2284841 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-986 2281940 2282108 2282462 "PUSHVAR" 2283572 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-985 2277858 2278912 2278953 "PTRANFN" 2280837 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-984 2276260 2276551 2276873 "PTPACK" 2277569 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-983 2275892 2275949 2276058 "PTFUNC2" 2276197 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-982 2270369 2274764 2274805 "PTCAT" 2275101 NIL PTCAT (NIL T) -9 NIL 2275254 NIL) (-981 2270027 2270062 2270186 "PSQFR" 2270328 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-980 2268622 2268920 2269254 "PSEUDLIN" 2269725 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-979 2255385 2257756 2260080 "PSETPK" 2266382 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-978 2248403 2251143 2251239 "PSETCAT" 2254260 NIL PSETCAT (NIL T T T T) -9 NIL 2255074 NIL) (-977 2246239 2246873 2247694 "PSETCAT-" 2247699 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-976 2245588 2245753 2245781 "PSCURVE" 2246049 T PSCURVE (NIL) -9 NIL 2246216 NIL) (-975 2241586 2243102 2243167 "PSCAT" 2244011 NIL PSCAT (NIL T T T) -9 NIL 2244251 NIL) (-974 2240649 2240865 2241265 "PSCAT-" 2241270 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-973 2239354 2240014 2240219 "PRTITION" 2240464 T PRTITION (NIL) -8 NIL NIL NIL) (-972 2238829 2239075 2239167 "PRTDAST" 2239282 T PRTDAST (NIL) -8 NIL NIL NIL) (-971 2227918 2230133 2232321 "PRS" 2236691 NIL PRS (NIL T T) -7 NIL NIL NIL) (-970 2225729 2227268 2227308 "PRQAGG" 2227491 NIL PRQAGG (NIL T) -9 NIL 2227593 NIL) (-969 2224933 2225238 2225266 "PROPLOG" 2225513 T PROPLOG (NIL) -9 NIL 2225679 NIL) (-968 2223363 2223884 2224141 "PROPFRML" 2224709 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-967 2222832 2222939 2223067 "PROPERTY" 2223255 T PROPERTY (NIL) -8 NIL NIL NIL) (-966 2216890 2220998 2221818 "PRODUCT" 2222058 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-965 2214168 2216348 2216582 "PR" 2216701 NIL PR (NIL T T) -8 NIL NIL NIL) (-964 2213964 2213996 2214055 "PRINT" 2214129 T PRINT (NIL) -7 NIL NIL NIL) (-963 2213304 2213421 2213573 "PRIMES" 2213844 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-962 2211369 2211770 2212236 "PRIMELT" 2212883 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-961 2211098 2211147 2211175 "PRIMCAT" 2211299 T PRIMCAT (NIL) -9 NIL NIL NIL) (-960 2207213 2211036 2211081 "PRIMARR" 2211086 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-959 2206220 2206398 2206626 "PRIMARR2" 2207031 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-958 2205863 2205919 2206030 "PREASSOC" 2206158 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-957 2205338 2205471 2205499 "PPCURVE" 2205704 T PPCURVE (NIL) -9 NIL 2205840 NIL) (-956 2204933 2205133 2205216 "PORTNUM" 2205275 T PORTNUM (NIL) -8 NIL NIL NIL) (-955 2202292 2202691 2203283 "POLYROOT" 2204514 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-954 2196474 2201896 2202056 "POLY" 2202165 NIL POLY (NIL T) -8 NIL NIL NIL) (-953 2195857 2195915 2196149 "POLYLIFT" 2196410 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-952 2192132 2192581 2193210 "POLYCATQ" 2195402 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-951 2178844 2183972 2184037 "POLYCAT" 2187551 NIL POLYCAT (NIL T T T) -9 NIL 2189429 NIL) (-950 2172293 2174155 2176539 "POLYCAT-" 2176544 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-949 2171880 2171948 2172068 "POLY2UP" 2172219 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-948 2171512 2171569 2171678 "POLY2" 2171817 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-947 2170197 2170436 2170712 "POLUTIL" 2171286 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-946 2168552 2168829 2169160 "POLTOPOL" 2169919 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-945 2164017 2168488 2168534 "POINT" 2168539 NIL POINT (NIL T) -8 NIL NIL NIL) (-944 2162204 2162561 2162936 "PNTHEORY" 2163662 T PNTHEORY (NIL) -7 NIL NIL NIL) (-943 2160662 2160959 2161358 "PMTOOLS" 2161902 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-942 2160255 2160333 2160450 "PMSYM" 2160578 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-941 2159765 2159834 2160008 "PMQFCAT" 2160180 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-940 2159120 2159230 2159386 "PMPRED" 2159642 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-939 2158513 2158599 2158761 "PMPREDFS" 2159021 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-938 2157177 2157385 2157763 "PMPLCAT" 2158275 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-937 2156709 2156788 2156940 "PMLSAGG" 2157092 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-936 2156182 2156258 2156440 "PMKERNEL" 2156627 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-935 2155799 2155874 2155987 "PMINS" 2156101 NIL PMINS (NIL T) -7 NIL NIL NIL) (-934 2155241 2155310 2155519 "PMFS" 2155724 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-933 2154469 2154587 2154792 "PMDOWN" 2155118 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-932 2153636 2153794 2153975 "PMASS" 2154308 T PMASS (NIL) -7 NIL NIL NIL) (-931 2152909 2153019 2153182 "PMASSFS" 2153523 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-930 2152564 2152632 2152726 "PLOTTOOL" 2152835 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-929 2147171 2148375 2149523 "PLOT" 2151436 T PLOT (NIL) -8 NIL NIL NIL) (-928 2142975 2144019 2144940 "PLOT3D" 2146270 T PLOT3D (NIL) -8 NIL NIL NIL) (-927 2141887 2142064 2142299 "PLOT1" 2142779 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-926 2117276 2121953 2126804 "PLEQN" 2137153 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-925 2116594 2116716 2116896 "PINTERP" 2117141 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-924 2116287 2116334 2116437 "PINTERPA" 2116541 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-923 2115508 2116056 2116143 "PI" 2116183 T PI (NIL) -8 NIL NIL 2116250) (-922 2113805 2114780 2114808 "PID" 2114990 T PID (NIL) -9 NIL 2115124 NIL) (-921 2113556 2113593 2113668 "PICOERCE" 2113762 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-920 2112876 2113015 2113191 "PGROEB" 2113412 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-919 2108463 2109277 2110182 "PGE" 2111991 T PGE (NIL) -7 NIL NIL NIL) (-918 2106586 2106833 2107199 "PGCD" 2108180 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-917 2105924 2106027 2106188 "PFRPAC" 2106470 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-916 2102564 2104472 2104825 "PFR" 2105603 NIL PFR (NIL T) -8 NIL NIL NIL) (-915 2100953 2101197 2101522 "PFOTOOLS" 2102311 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-914 2099486 2099725 2100076 "PFOQ" 2100710 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-913 2097987 2098199 2098555 "PFO" 2099270 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-912 2094540 2097876 2097945 "PF" 2097950 NIL PF (NIL NIL) -8 NIL NIL NIL) (-911 2091874 2093145 2093173 "PFECAT" 2093758 T PFECAT (NIL) -9 NIL 2094142 NIL) (-910 2091319 2091473 2091687 "PFECAT-" 2091692 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-909 2089922 2090174 2090475 "PFBRU" 2091068 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-908 2087788 2088140 2088572 "PFBR" 2089573 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-907 2083670 2085164 2085840 "PERM" 2087145 NIL PERM (NIL T) -8 NIL NIL NIL) (-906 2078904 2079877 2080747 "PERMGRP" 2082833 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-905 2077010 2077967 2078008 "PERMCAT" 2078454 NIL PERMCAT (NIL T) -9 NIL 2078759 NIL) (-904 2076663 2076704 2076828 "PERMAN" 2076963 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-903 2074151 2076328 2076450 "PENDTREE" 2076574 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-902 2072175 2072943 2072984 "PDRING" 2073641 NIL PDRING (NIL T) -9 NIL 2073927 NIL) (-901 2071278 2071496 2071858 "PDRING-" 2071863 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-900 2068493 2069271 2069939 "PDEPROB" 2070630 T PDEPROB (NIL) -8 NIL NIL NIL) (-899 2066038 2066542 2067097 "PDEPACK" 2067958 T PDEPACK (NIL) -7 NIL NIL NIL) (-898 2064950 2065140 2065391 "PDECOMP" 2065837 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-897 2062529 2063372 2063400 "PDECAT" 2064187 T PDECAT (NIL) -9 NIL 2064900 NIL) (-896 2062280 2062313 2062403 "PCOMP" 2062490 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-895 2060458 2061081 2061378 "PBWLB" 2062009 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-894 2052931 2054531 2055869 "PATTERN" 2059141 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-893 2052563 2052620 2052729 "PATTERN2" 2052868 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-892 2050320 2050708 2051165 "PATTERN1" 2052152 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-891 2047688 2048269 2048750 "PATRES" 2049885 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-890 2047252 2047319 2047451 "PATRES2" 2047615 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-889 2045135 2045540 2045947 "PATMATCH" 2046919 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-888 2044645 2044854 2044895 "PATMAB" 2045002 NIL PATMAB (NIL T) -9 NIL 2045085 NIL) (-887 2043163 2043499 2043757 "PATLRES" 2044450 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-886 2042709 2042832 2042873 "PATAB" 2042878 NIL PATAB (NIL T) -9 NIL 2043050 NIL) (-885 2040190 2040722 2041295 "PARTPERM" 2042156 T PARTPERM (NIL) -7 NIL NIL NIL) (-884 2039811 2039874 2039976 "PARSURF" 2040121 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-883 2039443 2039500 2039609 "PARSU2" 2039748 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-882 2039207 2039247 2039314 "PARSER" 2039396 T PARSER (NIL) -7 NIL NIL NIL) (-881 2038828 2038891 2038993 "PARSCURV" 2039138 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-880 2038460 2038517 2038626 "PARSC2" 2038765 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-879 2038099 2038157 2038254 "PARPCURV" 2038396 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-878 2037731 2037788 2037897 "PARPC2" 2038036 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-877 2036792 2037104 2037286 "PARAMAST" 2037569 T PARAMAST (NIL) -8 NIL NIL NIL) (-876 2036312 2036398 2036517 "PAN2EXPR" 2036693 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-875 2035089 2035433 2035661 "PALETTE" 2036104 T PALETTE (NIL) -8 NIL NIL NIL) (-874 2033482 2034094 2034454 "PAIR" 2034775 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-873 2027352 2032741 2032935 "PADICRC" 2033337 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-872 2020581 2026698 2026882 "PADICRAT" 2027200 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-871 2018896 2020518 2020563 "PADIC" 2020568 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-870 2016006 2017570 2017610 "PADICCT" 2018191 NIL PADICCT (NIL NIL) -9 NIL 2018473 NIL) (-869 2014963 2015163 2015431 "PADEPAC" 2015793 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-868 2014175 2014308 2014514 "PADE" 2014825 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-867 2012562 2013383 2013663 "OWP" 2013979 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-866 2012055 2012268 2012365 "OVERSET" 2012485 T OVERSET (NIL) -8 NIL NIL NIL) (-865 2011101 2011660 2011832 "OVAR" 2011923 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-864 2010365 2010486 2010647 "OUT" 2010960 T OUT (NIL) -7 NIL NIL NIL) (-863 1999237 2001474 2003674 "OUTFORM" 2008185 T OUTFORM (NIL) -8 NIL NIL NIL) (-862 1998573 1998834 1998961 "OUTBFILE" 1999130 T OUTBFILE (NIL) -8 NIL NIL NIL) (-861 1997880 1998045 1998073 "OUTBCON" 1998391 T OUTBCON (NIL) -9 NIL 1998557 NIL) (-860 1997481 1997593 1997750 "OUTBCON-" 1997755 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-859 1996861 1997210 1997299 "OSI" 1997412 T OSI (NIL) -8 NIL NIL NIL) (-858 1996391 1996729 1996757 "OSGROUP" 1996762 T OSGROUP (NIL) -9 NIL 1996784 NIL) (-857 1995136 1995363 1995648 "ORTHPOL" 1996138 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-856 1992687 1994971 1995092 "OREUP" 1995097 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-855 1990090 1992378 1992505 "ORESUP" 1992629 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-854 1987618 1988118 1988679 "OREPCTO" 1989579 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-853 1981304 1983505 1983546 "OREPCAT" 1985894 NIL OREPCAT (NIL T) -9 NIL 1986998 NIL) (-852 1978451 1979233 1980291 "OREPCAT-" 1980296 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-851 1977602 1977900 1977928 "ORDSET" 1978237 T ORDSET (NIL) -9 NIL 1978401 NIL) (-850 1977033 1977181 1977405 "ORDSET-" 1977410 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-849 1975598 1976389 1976417 "ORDRING" 1976619 T ORDRING (NIL) -9 NIL 1976744 NIL) (-848 1975243 1975337 1975481 "ORDRING-" 1975486 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-847 1974623 1975086 1975114 "ORDMON" 1975119 T ORDMON (NIL) -9 NIL 1975140 NIL) (-846 1973785 1973932 1974127 "ORDFUNS" 1974472 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-845 1973123 1973542 1973570 "ORDFIN" 1973635 T ORDFIN (NIL) -9 NIL 1973709 NIL) (-844 1969682 1971709 1972118 "ORDCOMP" 1972747 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-843 1968948 1969075 1969261 "ORDCOMP2" 1969542 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-842 1965529 1966439 1967253 "OPTPROB" 1968154 T OPTPROB (NIL) -8 NIL NIL NIL) (-841 1962331 1962970 1963674 "OPTPACK" 1964845 T OPTPACK (NIL) -7 NIL NIL NIL) (-840 1960018 1960784 1960812 "OPTCAT" 1961631 T OPTCAT (NIL) -9 NIL 1962281 NIL) (-839 1959402 1959695 1959800 "OPSIG" 1959933 T OPSIG (NIL) -8 NIL NIL NIL) (-838 1959170 1959209 1959275 "OPQUERY" 1959356 T OPQUERY (NIL) -7 NIL NIL NIL) (-837 1956301 1957481 1957985 "OP" 1958699 NIL OP (NIL T) -8 NIL NIL NIL) (-836 1955675 1955901 1955942 "OPERCAT" 1956154 NIL OPERCAT (NIL T) -9 NIL 1956251 NIL) (-835 1955430 1955486 1955603 "OPERCAT-" 1955608 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-834 1952243 1954227 1954596 "ONECOMP" 1955094 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-833 1951548 1951663 1951837 "ONECOMP2" 1952115 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-832 1950967 1951073 1951203 "OMSERVER" 1951438 T OMSERVER (NIL) -7 NIL NIL NIL) (-831 1947829 1950407 1950447 "OMSAGG" 1950508 NIL OMSAGG (NIL T) -9 NIL 1950572 NIL) (-830 1946452 1946715 1946997 "OMPKG" 1947567 T OMPKG (NIL) -7 NIL NIL NIL) (-829 1945882 1945985 1946013 "OM" 1946312 T OM (NIL) -9 NIL NIL NIL) (-828 1944429 1945431 1945600 "OMLO" 1945763 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-827 1943389 1943536 1943756 "OMEXPR" 1944255 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-826 1942680 1942935 1943071 "OMERR" 1943273 T OMERR (NIL) -8 NIL NIL NIL) (-825 1941831 1942101 1942261 "OMERRK" 1942540 T OMERRK (NIL) -8 NIL NIL NIL) (-824 1941282 1941508 1941616 "OMENC" 1941743 T OMENC (NIL) -8 NIL NIL NIL) (-823 1935177 1936362 1937533 "OMDEV" 1940131 T OMDEV (NIL) -8 NIL NIL NIL) (-822 1934246 1934417 1934611 "OMCONN" 1935003 T OMCONN (NIL) -8 NIL NIL NIL) (-821 1932767 1933743 1933771 "OINTDOM" 1933776 T OINTDOM (NIL) -9 NIL 1933797 NIL) (-820 1930105 1931455 1931792 "OFMONOID" 1932462 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-819 1929516 1930042 1930087 "ODVAR" 1930092 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-818 1926939 1929261 1929416 "ODR" 1929421 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-817 1919520 1926715 1926841 "ODPOL" 1926846 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-816 1913342 1919392 1919497 "ODP" 1919502 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-815 1912108 1912323 1912598 "ODETOOLS" 1913116 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-814 1909075 1909733 1910449 "ODESYS" 1911441 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-813 1903957 1904865 1905890 "ODERTRIC" 1908150 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-812 1903383 1903465 1903659 "ODERED" 1903869 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-811 1900271 1900819 1901496 "ODERAT" 1902806 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-810 1897228 1897695 1898292 "ODEPRRIC" 1899800 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-809 1895171 1895767 1896253 "ODEPROB" 1896762 T ODEPROB (NIL) -8 NIL NIL NIL) (-808 1891691 1892176 1892823 "ODEPRIM" 1894650 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-807 1890940 1891042 1891302 "ODEPAL" 1891583 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-806 1887102 1887893 1888757 "ODEPACK" 1890096 T ODEPACK (NIL) -7 NIL NIL NIL) (-805 1886163 1886270 1886492 "ODEINT" 1886991 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-804 1880264 1881689 1883136 "ODEIFTBL" 1884736 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-803 1875662 1876448 1877400 "ODEEF" 1879423 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-802 1875011 1875100 1875323 "ODECONST" 1875567 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-801 1873136 1873797 1873825 "ODECAT" 1874430 T ODECAT (NIL) -9 NIL 1874961 NIL) (-800 1869991 1872841 1872963 "OCT" 1873046 NIL OCT (NIL T) -8 NIL NIL NIL) (-799 1869629 1869672 1869799 "OCTCT2" 1869942 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-798 1864278 1866713 1866753 "OC" 1867850 NIL OC (NIL T) -9 NIL 1868708 NIL) (-797 1861505 1862253 1863243 "OC-" 1863337 NIL OC- (NIL T T) -8 NIL NIL NIL) (-796 1860857 1861325 1861353 "OCAMON" 1861358 T OCAMON (NIL) -9 NIL 1861379 NIL) (-795 1860388 1860729 1860757 "OASGP" 1860762 T OASGP (NIL) -9 NIL 1860782 NIL) (-794 1859649 1860138 1860166 "OAMONS" 1860206 T OAMONS (NIL) -9 NIL 1860249 NIL) (-793 1859063 1859496 1859524 "OAMON" 1859529 T OAMON (NIL) -9 NIL 1859549 NIL) (-792 1858321 1858839 1858867 "OAGROUP" 1858872 T OAGROUP (NIL) -9 NIL 1858892 NIL) (-791 1858011 1858061 1858149 "NUMTUBE" 1858265 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-790 1851584 1853102 1854638 "NUMQUAD" 1856495 T NUMQUAD (NIL) -7 NIL NIL NIL) (-789 1847340 1848328 1849353 "NUMODE" 1850579 T NUMODE (NIL) -7 NIL NIL NIL) (-788 1844695 1845575 1845603 "NUMINT" 1846526 T NUMINT (NIL) -9 NIL 1847290 NIL) (-787 1843643 1843840 1844058 "NUMFMT" 1844497 T NUMFMT (NIL) -7 NIL NIL NIL) (-786 1830002 1832947 1835479 "NUMERIC" 1841150 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-785 1824372 1829451 1829546 "NTSCAT" 1829551 NIL NTSCAT (NIL T T T T) -9 NIL 1829590 NIL) (-784 1823566 1823731 1823924 "NTPOLFN" 1824211 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-783 1811643 1820391 1821203 "NSUP" 1822787 NIL NSUP (NIL T) -8 NIL NIL NIL) (-782 1811275 1811332 1811441 "NSUP2" 1811580 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-781 1801503 1811049 1811182 "NSMP" 1811187 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-780 1799935 1800236 1800593 "NREP" 1801191 NIL NREP (NIL T) -7 NIL NIL NIL) (-779 1798526 1798778 1799136 "NPCOEF" 1799678 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-778 1797592 1797707 1797923 "NORMRETR" 1798407 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-777 1795633 1795923 1796332 "NORMPK" 1797300 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-776 1795318 1795346 1795470 "NORMMA" 1795599 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-775 1795118 1795275 1795304 "NONE" 1795309 T NONE (NIL) -8 NIL NIL NIL) (-774 1794907 1794936 1795005 "NONE1" 1795082 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-773 1794404 1794466 1794645 "NODE1" 1794839 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-772 1792689 1793540 1793795 "NNI" 1794142 T NNI (NIL) -8 NIL NIL 1794377) (-771 1791109 1791422 1791786 "NLINSOL" 1792357 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-770 1787350 1788345 1789244 "NIPROB" 1790230 T NIPROB (NIL) -8 NIL NIL NIL) (-769 1786107 1786341 1786643 "NFINTBAS" 1787112 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-768 1785281 1785757 1785798 "NETCLT" 1785970 NIL NETCLT (NIL T) -9 NIL 1786052 NIL) (-767 1783989 1784220 1784501 "NCODIV" 1785049 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-766 1783751 1783788 1783863 "NCNTFRAC" 1783946 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-765 1781931 1782295 1782715 "NCEP" 1783376 NIL NCEP (NIL T) -7 NIL NIL NIL) (-764 1780782 1781555 1781583 "NASRING" 1781693 T NASRING (NIL) -9 NIL 1781773 NIL) (-763 1780577 1780621 1780715 "NASRING-" 1780720 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-762 1779684 1780209 1780237 "NARNG" 1780354 T NARNG (NIL) -9 NIL 1780445 NIL) (-761 1779376 1779443 1779577 "NARNG-" 1779582 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-760 1778255 1778462 1778697 "NAGSP" 1779161 T NAGSP (NIL) -7 NIL NIL NIL) (-759 1769527 1771211 1772884 "NAGS" 1776602 T NAGS (NIL) -7 NIL NIL NIL) (-758 1768075 1768383 1768714 "NAGF07" 1769216 T NAGF07 (NIL) -7 NIL NIL NIL) (-757 1762613 1763904 1765211 "NAGF04" 1766788 T NAGF04 (NIL) -7 NIL NIL NIL) (-756 1755581 1757195 1758828 "NAGF02" 1761000 T NAGF02 (NIL) -7 NIL NIL NIL) (-755 1750805 1751905 1753022 "NAGF01" 1754484 T NAGF01 (NIL) -7 NIL NIL NIL) (-754 1744433 1745999 1747584 "NAGE04" 1749240 T NAGE04 (NIL) -7 NIL NIL NIL) (-753 1735602 1737723 1739853 "NAGE02" 1742323 T NAGE02 (NIL) -7 NIL NIL NIL) (-752 1731555 1732502 1733466 "NAGE01" 1734658 T NAGE01 (NIL) -7 NIL NIL NIL) (-751 1729350 1729884 1730442 "NAGD03" 1731017 T NAGD03 (NIL) -7 NIL NIL NIL) (-750 1721100 1723028 1724982 "NAGD02" 1727416 T NAGD02 (NIL) -7 NIL NIL NIL) (-749 1714911 1716336 1717776 "NAGD01" 1719680 T NAGD01 (NIL) -7 NIL NIL NIL) (-748 1711120 1711942 1712779 "NAGC06" 1714094 T NAGC06 (NIL) -7 NIL NIL NIL) (-747 1709585 1709917 1710273 "NAGC05" 1710784 T NAGC05 (NIL) -7 NIL NIL NIL) (-746 1708961 1709080 1709224 "NAGC02" 1709461 T NAGC02 (NIL) -7 NIL NIL NIL) (-745 1707920 1708503 1708543 "NAALG" 1708622 NIL NAALG (NIL T) -9 NIL 1708683 NIL) (-744 1707755 1707784 1707874 "NAALG-" 1707879 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-743 1701705 1702813 1704000 "MULTSQFR" 1706651 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-742 1701024 1701099 1701283 "MULTFACT" 1701617 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-741 1693748 1697661 1697714 "MTSCAT" 1698784 NIL MTSCAT (NIL T T) -9 NIL 1699299 NIL) (-740 1693460 1693514 1693606 "MTHING" 1693688 NIL MTHING (NIL T) -7 NIL NIL NIL) (-739 1693252 1693285 1693345 "MSYSCMD" 1693420 T MSYSCMD (NIL) -7 NIL NIL NIL) (-738 1689334 1692007 1692327 "MSET" 1692965 NIL MSET (NIL T) -8 NIL NIL NIL) (-737 1686403 1688895 1688936 "MSETAGG" 1688941 NIL MSETAGG (NIL T) -9 NIL 1688975 NIL) (-736 1682244 1683782 1684527 "MRING" 1685703 NIL MRING (NIL T T) -8 NIL NIL NIL) (-735 1681810 1681877 1682008 "MRF2" 1682171 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-734 1681428 1681463 1681607 "MRATFAC" 1681769 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-733 1679040 1679335 1679766 "MPRFF" 1681133 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-732 1673337 1678894 1678991 "MPOLY" 1678996 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-731 1672827 1672862 1673070 "MPCPF" 1673296 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-730 1672341 1672384 1672568 "MPC3" 1672778 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-729 1671536 1671617 1671838 "MPC2" 1672256 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-728 1669837 1670174 1670564 "MONOTOOL" 1671196 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-727 1669062 1669379 1669407 "MONOID" 1669626 T MONOID (NIL) -9 NIL 1669773 NIL) (-726 1668608 1668727 1668908 "MONOID-" 1668913 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-725 1659083 1665034 1665093 "MONOGEN" 1665767 NIL MONOGEN (NIL T T) -9 NIL 1666223 NIL) (-724 1656301 1657036 1658036 "MONOGEN-" 1658155 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-723 1655134 1655580 1655608 "MONADWU" 1656000 T MONADWU (NIL) -9 NIL 1656238 NIL) (-722 1654506 1654665 1654913 "MONADWU-" 1654918 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-721 1653865 1654109 1654137 "MONAD" 1654344 T MONAD (NIL) -9 NIL 1654456 NIL) (-720 1653550 1653628 1653760 "MONAD-" 1653765 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-719 1651839 1652463 1652742 "MOEBIUS" 1653303 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-718 1651117 1651521 1651561 "MODULE" 1651566 NIL MODULE (NIL T) -9 NIL 1651605 NIL) (-717 1650685 1650781 1650971 "MODULE-" 1650976 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-716 1648365 1649049 1649376 "MODRING" 1650509 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-715 1645309 1646470 1646991 "MODOP" 1647894 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-714 1643897 1644376 1644653 "MODMONOM" 1645172 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-713 1633938 1642188 1642602 "MODMON" 1643534 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-712 1631094 1632782 1633058 "MODFIELD" 1633813 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-711 1630071 1630375 1630565 "MMLFORM" 1630924 T MMLFORM (NIL) -8 NIL NIL NIL) (-710 1629597 1629640 1629819 "MMAP" 1630022 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-709 1627676 1628443 1628484 "MLO" 1628907 NIL MLO (NIL T) -9 NIL 1629149 NIL) (-708 1625042 1625558 1626160 "MLIFT" 1627157 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-707 1624433 1624517 1624671 "MKUCFUNC" 1624953 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-706 1624032 1624102 1624225 "MKRECORD" 1624356 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-705 1623079 1623241 1623469 "MKFUNC" 1623843 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-704 1622467 1622571 1622727 "MKFLCFN" 1622962 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-703 1621744 1621846 1622031 "MKBCFUNC" 1622360 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-702 1618451 1621298 1621434 "MINT" 1621628 T MINT (NIL) -8 NIL NIL NIL) (-701 1617263 1617506 1617783 "MHROWRED" 1618206 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-700 1612642 1615798 1616203 "MFLOAT" 1616878 T MFLOAT (NIL) -8 NIL NIL NIL) (-699 1611999 1612075 1612246 "MFINFACT" 1612554 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-698 1608314 1609162 1610046 "MESH" 1611135 T MESH (NIL) -7 NIL NIL NIL) (-697 1606704 1607016 1607369 "MDDFACT" 1608001 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-696 1603499 1605863 1605904 "MDAGG" 1606159 NIL MDAGG (NIL T) -9 NIL 1606302 NIL) (-695 1593239 1602792 1602999 "MCMPLX" 1603312 T MCMPLX (NIL) -8 NIL NIL NIL) (-694 1592380 1592526 1592726 "MCDEN" 1593088 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-693 1590270 1590540 1590920 "MCALCFN" 1592110 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-692 1589195 1589435 1589668 "MAYBE" 1590076 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-691 1586807 1587330 1587892 "MATSTOR" 1588666 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-690 1582764 1586179 1586427 "MATRIX" 1586592 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-689 1578528 1579237 1579973 "MATLIN" 1582121 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-688 1568634 1571820 1571897 "MATCAT" 1576777 NIL MATCAT (NIL T T T) -9 NIL 1578194 NIL) (-687 1564990 1566011 1567367 "MATCAT-" 1567372 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-686 1563584 1563737 1564070 "MATCAT2" 1564825 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-685 1561696 1562020 1562404 "MAPPKG3" 1563259 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-684 1560677 1560850 1561072 "MAPPKG2" 1561520 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-683 1559176 1559460 1559787 "MAPPKG1" 1560383 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-682 1558255 1558582 1558759 "MAPPAST" 1559019 T MAPPAST (NIL) -8 NIL NIL NIL) (-681 1557866 1557924 1558047 "MAPHACK3" 1558191 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-680 1557458 1557519 1557633 "MAPHACK2" 1557798 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-679 1556895 1556999 1557141 "MAPHACK1" 1557349 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-678 1554974 1555595 1555899 "MAGMA" 1556623 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-677 1554453 1554698 1554789 "MACROAST" 1554903 T MACROAST (NIL) -8 NIL NIL NIL) (-676 1550871 1552692 1553153 "M3D" 1554025 NIL M3D (NIL T) -8 NIL NIL NIL) (-675 1544977 1549240 1549281 "LZSTAGG" 1550063 NIL LZSTAGG (NIL T) -9 NIL 1550358 NIL) (-674 1540934 1542108 1543565 "LZSTAGG-" 1543570 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-673 1538021 1538825 1539312 "LWORD" 1540479 NIL LWORD (NIL T) -8 NIL NIL NIL) (-672 1537597 1537825 1537900 "LSTAST" 1537966 T LSTAST (NIL) -8 NIL NIL NIL) (-671 1530763 1537368 1537502 "LSQM" 1537507 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-670 1529987 1530126 1530354 "LSPP" 1530618 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-669 1527799 1528100 1528556 "LSMP" 1529676 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-668 1524578 1525252 1525982 "LSMP1" 1527101 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-667 1518455 1523745 1523786 "LSAGG" 1523848 NIL LSAGG (NIL T) -9 NIL 1523926 NIL) (-666 1515150 1516074 1517287 "LSAGG-" 1517292 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-665 1512749 1514294 1514543 "LPOLY" 1514945 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-664 1512331 1512416 1512539 "LPEFRAC" 1512658 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-663 1510652 1511425 1511678 "LO" 1512163 NIL LO (NIL T T T) -8 NIL NIL NIL) (-662 1510304 1510416 1510444 "LOGIC" 1510555 T LOGIC (NIL) -9 NIL 1510636 NIL) (-661 1510166 1510189 1510260 "LOGIC-" 1510265 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-660 1509359 1509499 1509692 "LODOOPS" 1510022 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-659 1506782 1509275 1509341 "LODO" 1509346 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-658 1505320 1505555 1505908 "LODOF" 1506529 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-657 1501538 1503969 1504010 "LODOCAT" 1504448 NIL LODOCAT (NIL T) -9 NIL 1504659 NIL) (-656 1501271 1501329 1501456 "LODOCAT-" 1501461 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-655 1498591 1501112 1501230 "LODO2" 1501235 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-654 1496026 1498528 1498573 "LODO1" 1498578 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-653 1494907 1495072 1495377 "LODEEF" 1495849 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-652 1490146 1493037 1493078 "LNAGG" 1494025 NIL LNAGG (NIL T) -9 NIL 1494469 NIL) (-651 1489293 1489507 1489849 "LNAGG-" 1489854 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-650 1485429 1486218 1486857 "LMOPS" 1488708 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-649 1484832 1485220 1485261 "LMODULE" 1485266 NIL LMODULE (NIL T) -9 NIL 1485292 NIL) (-648 1482030 1484477 1484600 "LMDICT" 1484742 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-647 1481436 1481657 1481698 "LLINSET" 1481889 NIL LLINSET (NIL T) -9 NIL 1481980 NIL) (-646 1481135 1481344 1481404 "LITERAL" 1481409 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-645 1474298 1480069 1480373 "LIST" 1480864 NIL LIST (NIL T) -8 NIL NIL NIL) (-644 1473823 1473897 1474036 "LIST3" 1474218 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-643 1472830 1473008 1473236 "LIST2" 1473641 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-642 1470964 1471276 1471675 "LIST2MAP" 1472477 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-641 1470560 1470797 1470838 "LINSET" 1470843 NIL LINSET (NIL T) -9 NIL 1470877 NIL) (-640 1469221 1469891 1469932 "LINEXP" 1470187 NIL LINEXP (NIL T) -9 NIL 1470336 NIL) (-639 1467868 1468128 1468425 "LINDEP" 1468973 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-638 1464635 1465354 1466131 "LIMITRF" 1467123 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-637 1462938 1463234 1463643 "LIMITPS" 1464330 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-636 1457366 1462449 1462677 "LIE" 1462759 NIL LIE (NIL T T) -8 NIL NIL NIL) (-635 1456314 1456783 1456823 "LIECAT" 1456963 NIL LIECAT (NIL T) -9 NIL 1457114 NIL) (-634 1456155 1456182 1456270 "LIECAT-" 1456275 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-633 1448651 1455604 1455769 "LIB" 1456010 T LIB (NIL) -8 NIL NIL NIL) (-632 1444286 1445169 1446104 "LGROBP" 1447768 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-631 1442284 1442558 1442908 "LF" 1444007 NIL LF (NIL T T) -7 NIL NIL NIL) (-630 1441124 1441816 1441844 "LFCAT" 1442051 T LFCAT (NIL) -9 NIL 1442190 NIL) (-629 1438026 1438656 1439344 "LEXTRIPK" 1440488 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-628 1434770 1435596 1436099 "LEXP" 1437606 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-627 1434246 1434491 1434583 "LETAST" 1434698 T LETAST (NIL) -8 NIL NIL NIL) (-626 1432644 1432957 1433358 "LEADCDET" 1433928 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-625 1431834 1431908 1432137 "LAZM3PK" 1432565 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-624 1426751 1429911 1430449 "LAUPOL" 1431346 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-623 1426330 1426374 1426535 "LAPLACE" 1426701 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-622 1424269 1425431 1425682 "LA" 1426163 NIL LA (NIL T T T) -8 NIL NIL NIL) (-621 1423263 1423847 1423888 "LALG" 1423950 NIL LALG (NIL T) -9 NIL 1424009 NIL) (-620 1422977 1423036 1423172 "LALG-" 1423177 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-619 1422812 1422836 1422877 "KVTFROM" 1422939 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-618 1421735 1422179 1422364 "KTVLOGIC" 1422647 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-617 1421570 1421594 1421635 "KRCFROM" 1421697 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-616 1420474 1420661 1420960 "KOVACIC" 1421370 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-615 1420309 1420333 1420374 "KONVERT" 1420436 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-614 1420144 1420168 1420209 "KOERCE" 1420271 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-613 1417974 1418737 1419114 "KERNEL" 1419800 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-612 1417470 1417551 1417683 "KERNEL2" 1417888 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-611 1411240 1416009 1416063 "KDAGG" 1416440 NIL KDAGG (NIL T T) -9 NIL 1416646 NIL) (-610 1410769 1410893 1411098 "KDAGG-" 1411103 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-609 1403917 1410430 1410585 "KAFILE" 1410647 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-608 1398345 1403428 1403656 "JORDAN" 1403738 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-607 1397724 1397994 1398115 "JOINAST" 1398244 T JOINAST (NIL) -8 NIL NIL NIL) (-606 1397570 1397629 1397684 "JAVACODE" 1397689 T JAVACODE (NIL) -8 NIL NIL NIL) (-605 1393822 1395775 1395829 "IXAGG" 1396758 NIL IXAGG (NIL T T) -9 NIL 1397217 NIL) (-604 1392741 1393047 1393466 "IXAGG-" 1393471 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-603 1388271 1392663 1392722 "IVECTOR" 1392727 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-602 1387037 1387274 1387540 "ITUPLE" 1388038 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-601 1385539 1385716 1386011 "ITRIGMNP" 1386859 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-600 1384284 1384488 1384771 "ITFUN3" 1385315 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-599 1383916 1383973 1384082 "ITFUN2" 1384221 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-598 1381877 1382936 1383214 "ITAYLOR" 1383671 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-597 1370822 1376014 1377177 "ISUPS" 1380747 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-596 1369926 1370066 1370302 "ISUMP" 1370669 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-595 1365301 1369871 1369912 "ISTRING" 1369917 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-594 1364777 1365022 1365114 "ISAST" 1365229 T ISAST (NIL) -8 NIL NIL NIL) (-593 1363986 1364068 1364284 "IRURPK" 1364691 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-592 1362922 1363123 1363363 "IRSN" 1363766 T IRSN (NIL) -7 NIL NIL NIL) (-591 1360993 1361348 1361777 "IRRF2F" 1362560 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-590 1360740 1360778 1360854 "IRREDFFX" 1360949 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-589 1359355 1359614 1359913 "IROOT" 1360473 NIL IROOT (NIL T) -7 NIL NIL NIL) (-588 1355959 1357039 1357731 "IR" 1358695 NIL IR (NIL T) -8 NIL NIL NIL) (-587 1353572 1354067 1354633 "IR2" 1355437 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-586 1352672 1352785 1352999 "IR2F" 1353455 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-585 1352463 1352497 1352557 "IPRNTPK" 1352632 T IPRNTPK (NIL) -7 NIL NIL NIL) (-584 1349044 1352352 1352421 "IPF" 1352426 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-583 1347371 1348969 1349026 "IPADIC" 1349031 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-582 1346683 1346931 1347061 "IP4ADDR" 1347261 T IP4ADDR (NIL) -8 NIL NIL NIL) (-581 1346156 1346387 1346497 "IOMODE" 1346593 T IOMODE (NIL) -8 NIL NIL NIL) (-580 1345229 1345753 1345880 "IOBFILE" 1346049 T IOBFILE (NIL) -8 NIL NIL NIL) (-579 1344717 1345133 1345161 "IOBCON" 1345166 T IOBCON (NIL) -9 NIL 1345187 NIL) (-578 1344228 1344286 1344469 "INVLAPLA" 1344653 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-577 1333876 1336230 1338616 "INTTR" 1341892 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-576 1330211 1330953 1331818 "INTTOOLS" 1333061 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-575 1329797 1329888 1330005 "INTSLPE" 1330114 T INTSLPE (NIL) -7 NIL NIL NIL) (-574 1327750 1329720 1329779 "INTRVL" 1329784 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-573 1325352 1325864 1326439 "INTRF" 1327235 NIL INTRF (NIL T) -7 NIL NIL NIL) (-572 1324763 1324860 1325002 "INTRET" 1325250 NIL INTRET (NIL T) -7 NIL NIL NIL) (-571 1322760 1323149 1323619 "INTRAT" 1324371 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-570 1320023 1320606 1321225 "INTPM" 1322245 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-569 1316768 1317367 1318105 "INTPAF" 1319409 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-568 1311947 1312909 1313960 "INTPACK" 1315737 T INTPACK (NIL) -7 NIL NIL NIL) (-567 1308895 1311744 1311853 "INT" 1311858 T INT (NIL) -8 NIL NIL NIL) (-566 1308147 1308299 1308507 "INTHERTR" 1308737 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-565 1307586 1307666 1307854 "INTHERAL" 1308061 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-564 1305432 1305875 1306332 "INTHEORY" 1307149 T INTHEORY (NIL) -7 NIL NIL NIL) (-563 1296838 1298459 1300231 "INTG0" 1303784 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-562 1277411 1282201 1287011 "INTFTBL" 1292048 T INTFTBL (NIL) -8 NIL NIL NIL) (-561 1276660 1276798 1276971 "INTFACT" 1277270 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-560 1274087 1274533 1275090 "INTEF" 1276214 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-559 1272454 1273193 1273221 "INTDOM" 1273522 T INTDOM (NIL) -9 NIL 1273729 NIL) (-558 1271823 1271997 1272239 "INTDOM-" 1272244 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-557 1268211 1270139 1270193 "INTCAT" 1270992 NIL INTCAT (NIL T) -9 NIL 1271313 NIL) (-556 1267683 1267786 1267914 "INTBIT" 1268103 T INTBIT (NIL) -7 NIL NIL NIL) (-555 1266382 1266536 1266843 "INTALG" 1267528 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-554 1265865 1265955 1266112 "INTAF" 1266286 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-553 1259208 1265675 1265815 "INTABL" 1265820 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-552 1258549 1259015 1259080 "INT8" 1259114 T INT8 (NIL) -8 NIL NIL 1259159) (-551 1257889 1258355 1258420 "INT64" 1258454 T INT64 (NIL) -8 NIL NIL 1258499) (-550 1257229 1257695 1257760 "INT32" 1257794 T INT32 (NIL) -8 NIL NIL 1257839) (-549 1256569 1257035 1257100 "INT16" 1257134 T INT16 (NIL) -8 NIL NIL 1257179) (-548 1251479 1254192 1254220 "INS" 1255154 T INS (NIL) -9 NIL 1255819 NIL) (-547 1248719 1249490 1250464 "INS-" 1250537 NIL INS- (NIL T) -8 NIL NIL NIL) (-546 1247494 1247721 1248019 "INPSIGN" 1248472 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-545 1246612 1246729 1246926 "INPRODPF" 1247374 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-544 1245506 1245623 1245860 "INPRODFF" 1246492 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-543 1244506 1244658 1244918 "INNMFACT" 1245342 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-542 1243703 1243800 1243988 "INMODGCD" 1244405 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-541 1242211 1242456 1242780 "INFSP" 1243448 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-540 1241395 1241512 1241695 "INFPROD0" 1242091 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-539 1238250 1239460 1239975 "INFORM" 1240888 T INFORM (NIL) -8 NIL NIL NIL) (-538 1237860 1237920 1238018 "INFORM1" 1238185 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-537 1237383 1237472 1237586 "INFINITY" 1237766 T INFINITY (NIL) -7 NIL NIL NIL) (-536 1236559 1237103 1237204 "INETCLTS" 1237302 T INETCLTS (NIL) -8 NIL NIL NIL) (-535 1235175 1235425 1235746 "INEP" 1236307 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-534 1234424 1235072 1235137 "INDE" 1235142 NIL INDE (NIL T) -8 NIL NIL NIL) (-533 1233988 1234056 1234173 "INCRMAPS" 1234351 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-532 1232806 1233257 1233463 "INBFILE" 1233802 T INBFILE (NIL) -8 NIL NIL NIL) (-531 1228105 1229042 1229986 "INBFF" 1231894 NIL INBFF (NIL T) -7 NIL NIL NIL) (-530 1227013 1227282 1227310 "INBCON" 1227823 T INBCON (NIL) -9 NIL 1228089 NIL) (-529 1226265 1226488 1226764 "INBCON-" 1226769 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-528 1225744 1225989 1226080 "INAST" 1226194 T INAST (NIL) -8 NIL NIL NIL) (-527 1225171 1225423 1225529 "IMPTAST" 1225658 T IMPTAST (NIL) -8 NIL NIL NIL) (-526 1221617 1225015 1225119 "IMATRIX" 1225124 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-525 1220329 1220452 1220767 "IMATQF" 1221473 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-524 1218549 1218776 1219113 "IMATLIN" 1220085 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-523 1213127 1218473 1218531 "ILIST" 1218536 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-522 1211032 1212987 1213100 "IIARRAY2" 1213105 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-521 1206430 1210943 1211007 "IFF" 1211012 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-520 1205777 1206047 1206163 "IFAST" 1206334 T IFAST (NIL) -8 NIL NIL NIL) (-519 1200772 1205069 1205257 "IFARRAY" 1205634 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-518 1199952 1200676 1200749 "IFAMON" 1200754 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-517 1199536 1199601 1199655 "IEVALAB" 1199862 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-516 1199211 1199279 1199439 "IEVALAB-" 1199444 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-515 1198842 1199125 1199188 "IDPO" 1199193 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-514 1198092 1198731 1198806 "IDPOAMS" 1198811 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-513 1197399 1197981 1198056 "IDPOAM" 1198061 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-512 1196458 1196734 1196787 "IDPC" 1197200 NIL IDPC (NIL T T) -9 NIL 1197349 NIL) (-511 1195927 1196350 1196423 "IDPAM" 1196428 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-510 1195303 1195819 1195892 "IDPAG" 1195897 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-509 1194948 1195139 1195214 "IDENT" 1195248 T IDENT (NIL) -8 NIL NIL NIL) (-508 1191203 1192051 1192946 "IDECOMP" 1194105 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-507 1184041 1185126 1186173 "IDEAL" 1190239 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-506 1183205 1183317 1183516 "ICDEN" 1183925 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-505 1182276 1182685 1182832 "ICARD" 1183078 T ICARD (NIL) -8 NIL NIL NIL) (-504 1180336 1180649 1181054 "IBPTOOLS" 1181953 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-503 1175943 1179956 1180069 "IBITS" 1180255 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-502 1172666 1173242 1173937 "IBATOOL" 1175360 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-501 1170445 1170907 1171440 "IBACHIN" 1172201 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-500 1168274 1170291 1170394 "IARRAY2" 1170399 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-499 1164380 1168200 1168257 "IARRAY1" 1168262 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-498 1158489 1162792 1163273 "IAN" 1163919 T IAN (NIL) -8 NIL NIL NIL) (-497 1158000 1158057 1158230 "IALGFACT" 1158426 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-496 1157528 1157641 1157669 "HYPCAT" 1157876 T HYPCAT (NIL) -9 NIL NIL NIL) (-495 1157066 1157183 1157369 "HYPCAT-" 1157374 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-494 1156661 1156861 1156944 "HOSTNAME" 1157003 T HOSTNAME (NIL) -8 NIL NIL NIL) (-493 1156506 1156543 1156584 "HOMOTOP" 1156589 NIL HOMOTOP (NIL T) -9 NIL 1156622 NIL) (-492 1153138 1154516 1154557 "HOAGG" 1155538 NIL HOAGG (NIL T) -9 NIL 1156217 NIL) (-491 1151732 1152131 1152657 "HOAGG-" 1152662 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-490 1145736 1151327 1151476 "HEXADEC" 1151603 T HEXADEC (NIL) -8 NIL NIL NIL) (-489 1144483 1144706 1144969 "HEUGCD" 1145513 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-488 1143559 1144320 1144450 "HELLFDIV" 1144455 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-487 1141738 1143336 1143424 "HEAP" 1143503 NIL HEAP (NIL T) -8 NIL NIL NIL) (-486 1141001 1141290 1141424 "HEADAST" 1141624 T HEADAST (NIL) -8 NIL NIL NIL) (-485 1134867 1140916 1140978 "HDP" 1140983 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-484 1128855 1134502 1134654 "HDMP" 1134768 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-483 1128179 1128319 1128483 "HB" 1128711 T HB (NIL) -7 NIL NIL NIL) (-482 1121565 1128025 1128129 "HASHTBL" 1128134 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-481 1121041 1121286 1121378 "HASAST" 1121493 T HASAST (NIL) -8 NIL NIL NIL) (-480 1118819 1120663 1120845 "HACKPI" 1120879 T HACKPI (NIL) -8 NIL NIL NIL) (-479 1114487 1118672 1118785 "GTSET" 1118790 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-478 1107902 1114365 1114463 "GSTBL" 1114468 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-477 1100180 1106933 1107198 "GSERIES" 1107693 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-476 1099321 1099738 1099766 "GROUP" 1099969 T GROUP (NIL) -9 NIL 1100103 NIL) (-475 1098687 1098846 1099097 "GROUP-" 1099102 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-474 1097054 1097375 1097762 "GROEBSOL" 1098364 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-473 1095968 1096256 1096307 "GRMOD" 1096836 NIL GRMOD (NIL T T) -9 NIL 1097004 NIL) (-472 1095736 1095772 1095900 "GRMOD-" 1095905 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-471 1091026 1092090 1093090 "GRIMAGE" 1094756 T GRIMAGE (NIL) -8 NIL NIL NIL) (-470 1089492 1089753 1090077 "GRDEF" 1090722 T GRDEF (NIL) -7 NIL NIL NIL) (-469 1088936 1089052 1089193 "GRAY" 1089371 T GRAY (NIL) -7 NIL NIL NIL) (-468 1088123 1088529 1088580 "GRALG" 1088733 NIL GRALG (NIL T T) -9 NIL 1088826 NIL) (-467 1087784 1087857 1088020 "GRALG-" 1088025 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-466 1084561 1087369 1087547 "GPOLSET" 1087691 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-465 1083915 1083972 1084230 "GOSPER" 1084498 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-464 1079647 1080353 1080879 "GMODPOL" 1083614 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-463 1078652 1078836 1079074 "GHENSEL" 1079459 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-462 1072808 1073651 1074671 "GENUPS" 1077736 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-461 1072505 1072556 1072645 "GENUFACT" 1072751 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-460 1071917 1071994 1072159 "GENPGCD" 1072423 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-459 1071391 1071426 1071639 "GENMFACT" 1071876 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-458 1069957 1070214 1070521 "GENEEZ" 1071134 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-457 1064103 1069568 1069730 "GDMP" 1069880 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-456 1053445 1057874 1058980 "GCNAALG" 1063086 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-455 1051772 1052634 1052662 "GCDDOM" 1052917 T GCDDOM (NIL) -9 NIL 1053074 NIL) (-454 1051242 1051369 1051584 "GCDDOM-" 1051589 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-453 1049914 1050099 1050403 "GB" 1051021 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-452 1038530 1040860 1043252 "GBINTERN" 1047605 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-451 1036367 1036659 1037080 "GBF" 1038205 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-450 1035148 1035313 1035580 "GBEUCLID" 1036183 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-449 1034497 1034622 1034771 "GAUSSFAC" 1035019 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-448 1032864 1033166 1033480 "GALUTIL" 1034216 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-447 1031172 1031446 1031770 "GALPOLYU" 1032591 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-446 1028537 1028827 1029234 "GALFACTU" 1030869 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-445 1020342 1021842 1023450 "GALFACT" 1026969 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-444 1017730 1018388 1018416 "FVFUN" 1019572 T FVFUN (NIL) -9 NIL 1020292 NIL) (-443 1016996 1017178 1017206 "FVC" 1017497 T FVC (NIL) -9 NIL 1017680 NIL) (-442 1016639 1016821 1016889 "FUNDESC" 1016948 T FUNDESC (NIL) -8 NIL NIL NIL) (-441 1016254 1016436 1016517 "FUNCTION" 1016591 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-440 1013998 1014576 1015042 "FT" 1015808 T FT (NIL) -8 NIL NIL NIL) (-439 1012789 1013299 1013502 "FTEM" 1013815 T FTEM (NIL) -8 NIL NIL NIL) (-438 1011080 1011369 1011766 "FSUPFACT" 1012480 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-437 1009477 1009766 1010098 "FST" 1010768 T FST (NIL) -8 NIL NIL NIL) (-436 1008676 1008782 1008970 "FSRED" 1009359 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-435 1007375 1007631 1007978 "FSPRMELT" 1008391 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-434 1004681 1005119 1005605 "FSPECF" 1006938 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-433 986319 994650 994691 "FS" 998575 NIL FS (NIL T) -9 NIL 1000864 NIL) (-432 974962 977955 982012 "FS-" 982312 NIL FS- (NIL T T) -8 NIL NIL NIL) (-431 974490 974544 974714 "FSINT" 974903 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-430 972782 973483 973786 "FSERIES" 974269 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-429 971824 971940 972164 "FSCINT" 972662 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-428 968032 970768 970809 "FSAGG" 971179 NIL FSAGG (NIL T) -9 NIL 971438 NIL) (-427 965794 966395 967191 "FSAGG-" 967286 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-426 964836 964979 965206 "FSAGG2" 965647 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-425 962518 962798 963345 "FS2UPS" 964554 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-424 962152 962195 962324 "FS2" 962469 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-423 961030 961201 961503 "FS2EXPXP" 961977 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-422 960456 960571 960723 "FRUTIL" 960910 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-421 951869 955951 957309 "FR" 959130 NIL FR (NIL T) -8 NIL NIL NIL) (-420 946838 949512 949552 "FRNAALG" 950948 NIL FRNAALG (NIL T) -9 NIL 951555 NIL) (-419 942511 943587 944862 "FRNAALG-" 945612 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-418 942149 942192 942319 "FRNAAF2" 942462 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-417 940529 941003 941298 "FRMOD" 941961 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-416 938280 938912 939229 "FRIDEAL" 940320 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-415 937475 937562 937851 "FRIDEAL2" 938187 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-414 936608 937022 937063 "FRETRCT" 937068 NIL FRETRCT (NIL T) -9 NIL 937244 NIL) (-413 935720 935951 936302 "FRETRCT-" 936307 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-412 932808 934018 934077 "FRAMALG" 934959 NIL FRAMALG (NIL T T) -9 NIL 935251 NIL) (-411 930942 931397 932027 "FRAMALG-" 932250 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-410 924863 930417 930693 "FRAC" 930698 NIL FRAC (NIL T) -8 NIL NIL NIL) (-409 924499 924556 924663 "FRAC2" 924800 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-408 924135 924192 924299 "FR2" 924436 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-407 918648 921541 921569 "FPS" 922688 T FPS (NIL) -9 NIL 923245 NIL) (-406 918097 918206 918370 "FPS-" 918516 NIL FPS- (NIL T) -8 NIL NIL NIL) (-405 915399 917068 917096 "FPC" 917321 T FPC (NIL) -9 NIL 917463 NIL) (-404 915192 915232 915329 "FPC-" 915334 NIL FPC- (NIL T) -8 NIL NIL NIL) (-403 913982 914680 914721 "FPATMAB" 914726 NIL FPATMAB (NIL T) -9 NIL 914878 NIL) (-402 911655 912158 912584 "FPARFRAC" 913619 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-401 907048 907547 908229 "FORTRAN" 911087 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-400 904764 905264 905803 "FORT" 906529 T FORT (NIL) -7 NIL NIL NIL) (-399 902440 903002 903030 "FORTFN" 904090 T FORTFN (NIL) -9 NIL 904714 NIL) (-398 902204 902254 902282 "FORTCAT" 902341 T FORTCAT (NIL) -9 NIL 902403 NIL) (-397 900310 900820 901210 "FORMULA" 901834 T FORMULA (NIL) -8 NIL NIL NIL) (-396 900098 900128 900197 "FORMULA1" 900274 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-395 899621 899673 899846 "FORDER" 900040 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-394 898717 898881 899074 "FOP" 899448 T FOP (NIL) -7 NIL NIL NIL) (-393 897298 897997 898171 "FNLA" 898599 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-392 896027 896442 896470 "FNCAT" 896930 T FNCAT (NIL) -9 NIL 897190 NIL) (-391 895566 895986 896014 "FNAME" 896019 T FNAME (NIL) -8 NIL NIL NIL) (-390 894129 895092 895120 "FMTC" 895125 T FMTC (NIL) -9 NIL 895161 NIL) (-389 892875 894065 894111 "FMONOID" 894116 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-388 889703 890871 890912 "FMONCAT" 892129 NIL FMONCAT (NIL T) -9 NIL 892734 NIL) (-387 888895 889445 889594 "FM" 889599 NIL FM (NIL T T) -8 NIL NIL NIL) (-386 886319 886965 886993 "FMFUN" 888137 T FMFUN (NIL) -9 NIL 888845 NIL) (-385 885588 885769 885797 "FMC" 886087 T FMC (NIL) -9 NIL 886269 NIL) (-384 882667 883527 883581 "FMCAT" 884776 NIL FMCAT (NIL T T) -9 NIL 885271 NIL) (-383 881533 882433 882533 "FM1" 882612 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-382 879307 879723 880217 "FLOATRP" 881084 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-381 872882 877036 877657 "FLOAT" 878706 T FLOAT (NIL) -8 NIL NIL NIL) (-380 870320 870820 871398 "FLOATCP" 872349 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-379 869060 869898 869939 "FLINEXP" 869944 NIL FLINEXP (NIL T) -9 NIL 870037 NIL) (-378 868214 868449 868777 "FLINEXP-" 868782 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-377 867290 867434 867658 "FLASORT" 868066 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-376 864406 865274 865326 "FLALG" 866553 NIL FLALG (NIL T T) -9 NIL 867020 NIL) (-375 858142 861892 861933 "FLAGG" 863195 NIL FLAGG (NIL T) -9 NIL 863847 NIL) (-374 856868 857207 857697 "FLAGG-" 857702 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-373 855910 856053 856280 "FLAGG2" 856721 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-372 852761 853769 853828 "FINRALG" 854956 NIL FINRALG (NIL T T) -9 NIL 855464 NIL) (-371 851921 852150 852489 "FINRALG-" 852494 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-370 851301 851540 851568 "FINITE" 851764 T FINITE (NIL) -9 NIL 851871 NIL) (-369 843658 845845 845885 "FINAALG" 849552 NIL FINAALG (NIL T) -9 NIL 851005 NIL) (-368 838990 840040 841184 "FINAALG-" 842563 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-367 838358 838745 838848 "FILE" 838920 NIL FILE (NIL T) -8 NIL NIL NIL) (-366 837016 837354 837408 "FILECAT" 838092 NIL FILECAT (NIL T T) -9 NIL 838308 NIL) (-365 834732 836260 836288 "FIELD" 836328 T FIELD (NIL) -9 NIL 836408 NIL) (-364 833352 833737 834248 "FIELD-" 834253 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-363 831202 831987 832334 "FGROUP" 833038 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-362 830292 830456 830676 "FGLMICPK" 831034 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-361 826124 830217 830274 "FFX" 830279 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-360 825725 825786 825921 "FFSLPE" 826057 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-359 821714 822497 823293 "FFPOLY" 824961 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-358 821218 821254 821463 "FFPOLY2" 821672 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-357 817061 821137 821200 "FFP" 821205 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-356 812459 816972 817036 "FF" 817041 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-355 807585 811802 811992 "FFNBX" 812313 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-354 802514 806720 806978 "FFNBP" 807439 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-353 797147 801798 802009 "FFNB" 802347 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-352 795979 796177 796492 "FFINTBAS" 796944 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-351 792048 794268 794296 "FFIELDC" 794916 T FFIELDC (NIL) -9 NIL 795292 NIL) (-350 790710 791081 791578 "FFIELDC-" 791583 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-349 790279 790325 790449 "FFHOM" 790652 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-348 787974 788461 788978 "FFF" 789794 NIL FFF (NIL T) -7 NIL NIL NIL) (-347 783592 787716 787817 "FFCGX" 787917 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-346 779213 783324 783431 "FFCGP" 783535 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-345 774396 778940 779048 "FFCG" 779149 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-344 755792 764873 764959 "FFCAT" 770124 NIL FFCAT (NIL T T T) -9 NIL 771575 NIL) (-343 750990 752037 753351 "FFCAT-" 754581 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-342 750401 750444 750679 "FFCAT2" 750941 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 739722 743373 744593 "FEXPR" 749253 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-340 738722 739157 739198 "FEVALAB" 739282 NIL FEVALAB (NIL T) -9 NIL 739543 NIL) (-339 737881 738091 738429 "FEVALAB-" 738434 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-338 736447 737264 737467 "FDIV" 737780 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-337 733467 734208 734323 "FDIVCAT" 735891 NIL FDIVCAT (NIL T T T T) -9 NIL 736328 NIL) (-336 733229 733256 733426 "FDIVCAT-" 733431 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-335 732449 732536 732813 "FDIV2" 733136 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-334 731423 731744 731946 "FCTRDATA" 732267 T FCTRDATA (NIL) -8 NIL NIL NIL) (-333 730109 730368 730657 "FCPAK1" 731154 T FCPAK1 (NIL) -7 NIL NIL NIL) (-332 729208 729609 729750 "FCOMP" 730000 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-331 712910 716358 719896 "FC" 725690 T FC (NIL) -8 NIL NIL NIL) (-330 705273 709301 709341 "FAXF" 711143 NIL FAXF (NIL T) -9 NIL 711835 NIL) (-329 702549 703207 704032 "FAXF-" 704497 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-328 697601 701925 702101 "FARRAY" 702406 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-327 692495 694562 694615 "FAMR" 695638 NIL FAMR (NIL T T) -9 NIL 696098 NIL) (-326 691385 691687 692122 "FAMR-" 692127 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-325 690554 691307 691360 "FAMONOID" 691365 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-324 688340 689050 689103 "FAMONC" 690044 NIL FAMONC (NIL T T) -9 NIL 690430 NIL) (-323 687004 688094 688231 "FAGROUP" 688236 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-322 684799 685118 685521 "FACUTIL" 686685 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-321 683898 684083 684305 "FACTFUNC" 684609 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-320 676320 683201 683400 "EXPUPXS" 683754 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-319 673803 674343 674929 "EXPRTUBE" 675754 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-318 670074 670666 671396 "EXPRODE" 673142 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-317 655559 668723 669152 "EXPR" 669678 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 650113 650700 651506 "EXPR2UPS" 654857 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-315 649745 649802 649911 "EXPR2" 650050 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-314 641135 648898 649188 "EXPEXPAN" 649582 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-313 640935 641092 641121 "EXIT" 641126 T EXIT (NIL) -8 NIL NIL NIL) (-312 640415 640659 640750 "EXITAST" 640864 T EXITAST (NIL) -8 NIL NIL NIL) (-311 640042 640104 640217 "EVALCYC" 640347 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-310 639583 639701 639742 "EVALAB" 639912 NIL EVALAB (NIL T) -9 NIL 640016 NIL) (-309 639064 639186 639407 "EVALAB-" 639412 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-308 636432 637734 637762 "EUCDOM" 638317 T EUCDOM (NIL) -9 NIL 638667 NIL) (-307 634837 635279 635869 "EUCDOM-" 635874 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-306 622375 625135 627885 "ESTOOLS" 632107 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 622007 622064 622173 "ESTOOLS2" 622312 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-304 621758 621800 621880 "ESTOOLS1" 621959 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-303 615795 617403 617431 "ES" 620199 T ES (NIL) -9 NIL 621609 NIL) (-302 610742 612029 613846 "ES-" 614010 NIL ES- (NIL T) -8 NIL NIL NIL) (-301 607116 607877 608657 "ESCONT" 609982 T ESCONT (NIL) -7 NIL NIL NIL) (-300 606861 606893 606975 "ESCONT1" 607078 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-299 606536 606586 606686 "ES2" 606805 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-298 606166 606224 606333 "ES1" 606472 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-297 605382 605511 605687 "ERROR" 606010 T ERROR (NIL) -7 NIL NIL NIL) (-296 598774 605241 605332 "EQTBL" 605337 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-295 591277 594088 595537 "EQ" 597358 NIL -2109 (NIL T) -8 NIL NIL NIL) (-294 590909 590966 591075 "EQ2" 591214 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-293 586198 587247 588340 "EP" 589848 NIL EP (NIL T) -7 NIL NIL NIL) (-292 584798 585089 585395 "ENV" 585912 T ENV (NIL) -8 NIL NIL NIL) (-291 583892 584446 584474 "ENTIRER" 584479 T ENTIRER (NIL) -9 NIL 584525 NIL) (-290 580359 581847 582217 "EMR" 583691 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-289 579503 579688 579742 "ELTAGG" 580122 NIL ELTAGG (NIL T T) -9 NIL 580333 NIL) (-288 579222 579284 579425 "ELTAGG-" 579430 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-287 579011 579040 579094 "ELTAB" 579178 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-286 578137 578283 578482 "ELFUTS" 578862 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-285 577879 577935 577963 "ELEMFUN" 578068 T ELEMFUN (NIL) -9 NIL NIL NIL) (-284 577749 577770 577838 "ELEMFUN-" 577843 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-283 572593 575849 575890 "ELAGG" 576830 NIL ELAGG (NIL T) -9 NIL 577293 NIL) (-282 570878 571312 571975 "ELAGG-" 571980 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-281 569539 569818 570112 "ELABEXPR" 570604 T ELABEXPR (NIL) -8 NIL NIL NIL) (-280 562403 564206 565033 "EFUPXS" 568815 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-279 555853 557654 558464 "EFULS" 561679 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-278 553338 553696 554168 "EFSTRUC" 555485 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-277 543129 544695 546243 "EF" 551853 NIL EF (NIL T T) -7 NIL NIL NIL) (-276 542203 542614 542763 "EAB" 543000 T EAB (NIL) -8 NIL NIL NIL) (-275 541385 542162 542190 "E04UCFA" 542195 T E04UCFA (NIL) -8 NIL NIL NIL) (-274 540567 541344 541372 "E04NAFA" 541377 T E04NAFA (NIL) -8 NIL NIL NIL) (-273 539749 540526 540554 "E04MBFA" 540559 T E04MBFA (NIL) -8 NIL NIL NIL) (-272 538931 539708 539736 "E04JAFA" 539741 T E04JAFA (NIL) -8 NIL NIL NIL) (-271 538115 538890 538918 "E04GCFA" 538923 T E04GCFA (NIL) -8 NIL NIL NIL) (-270 537299 538074 538102 "E04FDFA" 538107 T E04FDFA (NIL) -8 NIL NIL NIL) (-269 536481 537258 537286 "E04DGFA" 537291 T E04DGFA (NIL) -8 NIL NIL NIL) (-268 530654 532006 533370 "E04AGNT" 535137 T E04AGNT (NIL) -7 NIL NIL NIL) (-267 529334 529840 529880 "DVARCAT" 530355 NIL DVARCAT (NIL T) -9 NIL 530554 NIL) (-266 528538 528750 529064 "DVARCAT-" 529069 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-265 521675 528337 528466 "DSMP" 528471 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-264 516456 517620 518688 "DROPT" 520627 T DROPT (NIL) -8 NIL NIL NIL) (-263 516121 516180 516278 "DROPT1" 516391 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-262 511236 512362 513499 "DROPT0" 515004 T DROPT0 (NIL) -7 NIL NIL NIL) (-261 509581 509906 510292 "DRAWPT" 510870 T DRAWPT (NIL) -7 NIL NIL NIL) (-260 504168 505091 506170 "DRAW" 508555 NIL DRAW (NIL T) -7 NIL NIL NIL) (-259 503801 503854 503972 "DRAWHACK" 504109 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-258 502532 502801 503092 "DRAWCX" 503530 T DRAWCX (NIL) -7 NIL NIL NIL) (-257 502047 502116 502267 "DRAWCURV" 502458 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-256 492515 494477 496592 "DRAWCFUN" 499952 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-255 489281 491210 491251 "DQAGG" 491880 NIL DQAGG (NIL T) -9 NIL 492153 NIL) (-254 477405 483874 483957 "DPOLCAT" 485809 NIL DPOLCAT (NIL T T T T) -9 NIL 486354 NIL) (-253 472241 473590 475548 "DPOLCAT-" 475553 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-252 465363 472102 472200 "DPMO" 472205 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-251 458388 465143 465310 "DPMM" 465315 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-250 457866 458080 458178 "DOMTMPLT" 458310 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-249 457299 457668 457748 "DOMCTOR" 457806 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456511 456779 456930 "DOMAIN" 457168 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450499 456146 456298 "DMP" 456412 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450099 450155 450299 "DLP" 450437 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 443921 449426 449616 "DLIST" 449941 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 440718 442774 442815 "DLAGG" 443365 NIL DLAGG (NIL T) -9 NIL 443595 NIL) (-243 439394 440058 440086 "DIVRING" 440178 T DIVRING (NIL) -9 NIL 440261 NIL) (-242 438631 438821 439121 "DIVRING-" 439126 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 436733 437090 437496 "DISPLAY" 438245 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430621 436647 436710 "DIRPROD" 436715 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429469 429672 429937 "DIRPROD2" 430414 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418244 424250 424303 "DIRPCAT" 424713 NIL DIRPCAT (NIL NIL T) -9 NIL 425553 NIL) (-237 415570 416212 417093 "DIRPCAT-" 417430 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 414857 415017 415203 "DIOSP" 415404 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411512 413769 413810 "DIOPS" 414244 NIL DIOPS (NIL T) -9 NIL 414473 NIL) (-234 411061 411175 411366 "DIOPS-" 411371 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 409884 410512 410540 "DIFRING" 410727 T DIFRING (NIL) -9 NIL 410837 NIL) (-232 409530 409607 409759 "DIFRING-" 409764 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407266 408538 408579 "DIFEXT" 408942 NIL DIFEXT (NIL T) -9 NIL 409236 NIL) (-230 405551 405979 406645 "DIFEXT-" 406650 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 402826 405083 405124 "DIAGG" 405129 NIL DIAGG (NIL T) -9 NIL 405149 NIL) (-228 402210 402367 402619 "DIAGG-" 402624 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397627 401169 401446 "DHMATRIX" 401979 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393239 394148 395158 "DFSFUN" 396637 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388317 392170 392482 "DFLOAT" 392947 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386580 386861 387250 "DFINTTLS" 388025 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383609 384601 385001 "DERHAM" 386246 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381410 383384 383473 "DEQUEUE" 383553 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 380664 380797 380980 "DEGRED" 381272 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 377094 377839 378685 "DEFINTRF" 379892 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 374649 375118 375710 "DEFINTEF" 376613 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373999 374269 374384 "DEFAST" 374554 T DEFAST (NIL) -8 NIL NIL NIL) (-217 368003 373594 373743 "DECIMAL" 373870 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365515 365973 366479 "DDFACT" 367547 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 365111 365154 365305 "DBLRESP" 365466 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362983 363344 363704 "DBASE" 364878 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362225 362463 362609 "DATAARY" 362882 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361331 362184 362212 "D03FAFA" 362217 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360438 361290 361318 "D03EEFA" 361323 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358388 358854 359343 "D03AGNT" 359969 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 357677 358347 358375 "D02EJFA" 358380 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356966 357636 357664 "D02CJFA" 357669 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356255 356925 356953 "D02BHFA" 356958 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355544 356214 356242 "D02BBFA" 356247 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 348741 350330 351936 "D02AGNT" 353958 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346509 347032 347578 "D01WGTS" 348215 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345576 346468 346496 "D01TRNS" 346501 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 344644 345535 345563 "D01GBFA" 345568 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 343712 344603 344631 "D01FCFA" 344636 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 342780 343671 343699 "D01ASFA" 343704 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 341848 342739 342767 "D01AQFA" 342772 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340916 341807 341835 "D01APFA" 341840 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339984 340875 340903 "D01ANFA" 340908 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 339052 339943 339971 "D01AMFA" 339976 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 338120 339011 339039 "D01ALFA" 339044 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337188 338079 338107 "D01AKFA" 338112 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336256 337147 337175 "D01AJFA" 337180 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329551 331104 332665 "D01AGNT" 334715 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 328888 329016 329168 "CYCLOTOM" 329419 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325622 326336 327063 "CYCLES" 328181 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324934 325068 325239 "CVMP" 325483 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 322775 323033 323402 "CTRIGMNP" 324662 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322211 322569 322642 "CTOR" 322722 T CTOR (NIL) -8 NIL NIL NIL) (-186 321720 321942 322043 "CTORKIND" 322130 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 321011 321327 321355 "CTORCAT" 321537 T CTORCAT (NIL) -9 NIL 321650 NIL) (-184 320609 320720 320879 "CTORCAT-" 320884 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 320071 320283 320391 "CTORCALL" 320533 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-182 319445 319544 319697 "CSTTOOLS" 319968 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315244 315901 316659 "CRFP" 318757 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 314719 314965 315057 "CRCEAST" 315172 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 313766 313951 314179 "CRAPACK" 314523 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313150 313251 313455 "CPMATCH" 313642 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312875 312903 313009 "CPIMA" 313116 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309223 309895 310614 "COORDSYS" 312210 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 308635 308756 308898 "CONTOUR" 309101 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304526 306638 307130 "CONTFRAC" 308175 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304406 304427 304455 "CONDUIT" 304492 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303494 304048 304076 "COMRING" 304081 T COMRING (NIL) -9 NIL 304133 NIL) (-171 302548 302852 303036 "COMPPROP" 303330 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302209 302244 302372 "COMPLPAT" 302507 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 292500 302018 302127 "COMPLEX" 302132 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 292136 292193 292300 "COMPLEX2" 292437 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 291854 291889 291987 "COMPFACT" 292095 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275934 285928 285968 "COMPCAT" 286972 NIL COMPCAT (NIL T) -9 NIL 288320 NIL) (-165 265446 268373 272000 "COMPCAT-" 272356 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265175 265203 265306 "COMMUPC" 265412 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264969 265003 265062 "COMMONOP" 265136 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264525 264720 264807 "COMM" 264902 T COMM (NIL) -8 NIL NIL NIL) (-161 264101 264329 264404 "COMMAAST" 264470 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263350 263544 263572 "COMBOPC" 263910 T COMBOPC (NIL) -9 NIL 264085 NIL) (-159 262246 262456 262698 "COMBINAT" 263140 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258703 259277 259904 "COMBF" 261668 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257461 257819 258054 "COLOR" 258488 T COLOR (NIL) -8 NIL NIL NIL) (-156 256937 257182 257274 "COLONAST" 257389 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256577 256624 256749 "CMPLXRT" 256884 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256025 256277 256376 "CLLCTAST" 256498 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251523 252555 253635 "CLIP" 254965 T CLIP (NIL) -7 NIL NIL NIL) (-152 249869 250629 250868 "CLIF" 251350 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246044 248015 248056 "CLAGG" 248985 NIL CLAGG (NIL T) -9 NIL 249521 NIL) (-150 244466 244923 245506 "CLAGG-" 245511 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244010 244095 244235 "CINTSLPE" 244375 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241511 241982 242530 "CHVAR" 243538 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240685 241239 241267 "CHARZ" 241272 T CHARZ (NIL) -9 NIL 241287 NIL) (-146 240439 240479 240557 "CHARPOL" 240639 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239497 240084 240112 "CHARNZ" 240159 T CHARNZ (NIL) -9 NIL 240215 NIL) (-144 237403 238151 238504 "CHAR" 239164 T CHAR (NIL) -8 NIL NIL NIL) (-143 237129 237190 237218 "CFCAT" 237329 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236374 236485 236667 "CDEN" 237013 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232339 235527 235807 "CCLASS" 236114 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231590 231747 231924 "CATEGORY" 232182 T -10 (NIL) -8 NIL NIL NIL) (-139 231163 231509 231557 "CATCTOR" 231562 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230614 230866 230964 "CATAST" 231085 T CATAST (NIL) -8 NIL NIL NIL) (-137 230090 230335 230427 "CASEAST" 230542 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225099 226119 226872 "CARTEN" 229393 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224207 224355 224576 "CARTEN2" 224946 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222523 223357 223614 "CARD" 223970 T CARD (NIL) -8 NIL NIL NIL) (-133 222099 222327 222402 "CAPSLAST" 222468 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221603 221811 221839 "CACHSET" 221971 T CACHSET (NIL) -9 NIL 222049 NIL) (-131 221073 221395 221423 "CABMON" 221473 T CABMON (NIL) -9 NIL 221529 NIL) (-130 220546 220777 220887 "BYTEORD" 220983 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219529 220080 220222 "BYTE" 220385 T BYTE (NIL) -8 NIL NIL 220507) (-128 214879 219034 219206 "BYTEBUF" 219377 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212388 214571 214678 "BTREE" 214805 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209837 212036 212158 "BTOURN" 212298 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207207 209307 209348 "BTCAT" 209416 NIL BTCAT (NIL T) -9 NIL 209493 NIL) (-124 206874 206954 207103 "BTCAT-" 207108 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202139 206017 206045 "BTAGG" 206267 T BTAGG (NIL) -9 NIL 206428 NIL) (-122 201629 201754 201960 "BTAGG-" 201965 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198624 200907 201122 "BSTREE" 201446 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197762 197888 198072 "BRILL" 198480 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194414 196488 196529 "BRAGG" 197178 NIL BRAGG (NIL T) -9 NIL 197436 NIL) (-118 192943 193349 193904 "BRAGG-" 193909 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186172 192289 192473 "BPADICRT" 192791 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184487 186109 186154 "BPADIC" 186159 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184185 184215 184329 "BOUNDZRO" 184451 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179413 180611 181523 "BOP" 183293 T BOP (NIL) -8 NIL NIL NIL) (-113 177194 177598 178073 "BOP1" 178971 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176019 176768 176917 "BOOLEAN" 177065 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175298 175702 175756 "BMODULE" 175761 NIL BMODULE (NIL T T) -9 NIL 175826 NIL) (-110 171099 175096 175169 "BITS" 175245 T BITS (NIL) -8 NIL NIL NIL) (-109 170520 170639 170779 "BINDING" 170979 T BINDING (NIL) -8 NIL NIL NIL) (-108 164527 170117 170265 "BINARY" 170392 T BINARY (NIL) -8 NIL NIL NIL) (-107 162307 163782 163823 "BGAGG" 164083 NIL BGAGG (NIL T) -9 NIL 164220 NIL) (-106 162138 162170 162261 "BGAGG-" 162266 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161209 161522 161727 "BFUNCT" 161953 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159899 160077 160365 "BEZOUT" 161033 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156368 158751 159081 "BBTREE" 159602 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156102 156155 156183 "BASTYPE" 156302 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155954 155983 156056 "BASTYPE-" 156061 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155388 155464 155616 "BALFACT" 155865 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154244 154803 154989 "AUTOMOR" 155233 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153970 153975 154001 "ATTREG" 154006 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152222 152667 153019 "ATTRBUT" 153636 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151830 152050 152116 "ATTRAST" 152174 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151366 151479 151505 "ATRIG" 151706 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151175 151216 151303 "ATRIG-" 151308 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150820 151006 151032 "ASTCAT" 151037 T ASTCAT (NIL) -9 NIL 151067 NIL) (-92 150547 150606 150725 "ASTCAT-" 150730 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148696 150323 150411 "ASTACK" 150490 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147201 147498 147863 "ASSOCEQ" 148378 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146233 146860 146984 "ASP9" 147108 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145996 146181 146220 "ASP8" 146225 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144864 145601 145743 "ASP80" 145885 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143762 144499 144631 "ASP7" 144763 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142716 143439 143557 "ASP78" 143675 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141685 142396 142513 "ASP77" 142630 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140597 141323 141454 "ASP74" 141585 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139497 140232 140364 "ASP73" 140496 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138601 139323 139423 "ASP6" 139428 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137545 138278 138396 "ASP55" 138514 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136494 137219 137338 "ASP50" 137457 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135582 136195 136305 "ASP4" 136415 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134670 135283 135393 "ASP49" 135503 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133454 134209 134377 "ASP42" 134559 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132230 132987 133157 "ASP41" 133341 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131180 131907 132025 "ASP35" 132143 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130945 131128 131167 "ASP34" 131172 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130682 130749 130825 "ASP33" 130900 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129575 130317 130449 "ASP31" 130581 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129340 129523 129562 "ASP30" 129567 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129075 129144 129220 "ASP29" 129295 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128840 129023 129062 "ASP28" 129067 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128605 128788 128827 "ASP27" 128832 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127689 128303 128414 "ASP24" 128525 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126765 127491 127603 "ASP20" 127608 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125853 126466 126576 "ASP1" 126686 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124795 125527 125646 "ASP19" 125765 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124532 124599 124675 "ASP12" 124750 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123384 124131 124275 "ASP10" 124419 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121235 123228 123319 "ARRAY2" 123324 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117000 120883 120997 "ARRAY1" 121152 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116032 116205 116426 "ARRAY12" 116823 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110344 112262 112337 "ARR2CAT" 114967 NIL ARR2CAT (NIL T T T) -9 NIL 115725 NIL) (-56 107778 108522 109476 "ARR2CAT-" 109481 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107095 107405 107530 "ARITY" 107671 T ARITY (NIL) -8 NIL NIL NIL) (-54 105871 106023 106322 "APPRULE" 106931 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105522 105570 105689 "APPLYORE" 105817 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104876 105115 105235 "ANY" 105420 T ANY (NIL) -8 NIL NIL NIL) (-51 104154 104277 104434 "ANY1" 104750 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101684 102591 102918 "ANTISYM" 103878 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101176 101391 101487 "ANON" 101606 T ANON (NIL) -8 NIL NIL NIL) (-48 95425 99715 100169 "AN" 100740 T AN (NIL) -8 NIL NIL NIL) (-47 91323 92711 92762 "AMR" 93510 NIL AMR (NIL T T) -9 NIL 94110 NIL) (-46 90435 90656 91019 "AMR-" 91024 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74874 90352 90413 "ALIST" 90418 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71676 74468 74637 "ALGSC" 74792 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68231 68786 69393 "ALGPKG" 71116 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67508 67609 67793 "ALGMFACT" 68117 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63543 64122 64716 "ALGMANIP" 67092 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54913 63169 63319 "ALGFF" 63476 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54109 54240 54419 "ALGFACT" 54771 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53050 53650 53688 "ALGEBRA" 53693 NIL ALGEBRA (NIL T) -9 NIL 53734 NIL) (-37 52768 52827 52959 "ALGEBRA-" 52964 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34861 50770 50822 "ALAGG" 50958 NIL ALAGG (NIL T T) -9 NIL 51119 NIL) (-35 34397 34510 34536 "AHYP" 34737 T AHYP (NIL) -9 NIL NIL NIL) (-34 33328 33576 33602 "AGG" 34101 T AGG (NIL) -9 NIL 34380 NIL) (-33 32762 32924 33138 "AGG-" 33143 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30568 30991 31396 "AF" 32404 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30048 30293 30383 "ADDAST" 30496 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29316 29575 29731 "ACPLOT" 29910 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18639 26443 26481 "ACFS" 27088 NIL ACFS (NIL T) -9 NIL 27327 NIL) (-28 16666 17156 17918 "ACFS-" 17923 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14713 14739 "ACF" 15618 T ACF (NIL) -9 NIL 16031 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3223634 3223639 3223644 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3223619 3223624 3223629 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3223604 3223609 3223614 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3223589 3223594 3223599 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1297 3222732 3223464 3223541 "ZMOD" 3223546 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1296 3221842 3222006 3222215 "ZLINDEP" 3222564 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1295 3211142 3212910 3214882 "ZDSOLVE" 3219972 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1294 3210388 3210529 3210718 "YSTREAM" 3210988 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1293 3208162 3209689 3209893 "XRPOLY" 3210231 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1292 3204715 3206033 3206608 "XPR" 3207634 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1291 3202436 3204046 3204250 "XPOLY" 3204546 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1290 3200089 3201457 3201512 "XPOLYC" 3201800 NIL XPOLYC (NIL T T) -9 NIL 3201913 NIL) (-1289 3196464 3198606 3198994 "XPBWPOLY" 3199747 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1288 3192159 3194454 3194496 "XF" 3195117 NIL XF (NIL T) -9 NIL 3195517 NIL) (-1287 3191780 3191868 3192037 "XF-" 3192042 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1286 3186976 3188265 3188320 "XFALG" 3190492 NIL XFALG (NIL T T) -9 NIL 3191281 NIL) (-1285 3186109 3186213 3186418 "XEXPPKG" 3186868 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1284 3184218 3185959 3186055 "XDPOLY" 3186060 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1283 3183025 3183625 3183668 "XALG" 3183673 NIL XALG (NIL T) -9 NIL 3183784 NIL) (-1282 3176467 3181002 3181496 "WUTSET" 3182617 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1281 3174723 3175519 3175842 "WP" 3176278 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1280 3174325 3174545 3174615 "WHILEAST" 3174675 T WHILEAST (NIL) -8 NIL NIL NIL) (-1279 3173797 3174042 3174136 "WHEREAST" 3174253 T WHEREAST (NIL) -8 NIL NIL NIL) (-1278 3172683 3172881 3173176 "WFFINTBS" 3173594 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1277 3170587 3171014 3171476 "WEIER" 3172255 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1276 3169633 3170083 3170125 "VSPACE" 3170261 NIL VSPACE (NIL T) -9 NIL 3170335 NIL) (-1275 3169471 3169498 3169589 "VSPACE-" 3169594 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1274 3169280 3169322 3169390 "VOID" 3169425 T VOID (NIL) -8 NIL NIL NIL) (-1273 3167416 3167775 3168181 "VIEW" 3168896 T VIEW (NIL) -7 NIL NIL NIL) (-1272 3163840 3164479 3165216 "VIEWDEF" 3166701 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1271 3153144 3155388 3157561 "VIEW3D" 3161689 T VIEW3D (NIL) -8 NIL NIL NIL) (-1270 3145395 3147055 3148634 "VIEW2D" 3151587 T VIEW2D (NIL) -8 NIL NIL NIL) (-1269 3140747 3145165 3145257 "VECTOR" 3145338 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1268 3139324 3139583 3139901 "VECTOR2" 3140477 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1267 3132798 3137105 3137148 "VECTCAT" 3138143 NIL VECTCAT (NIL T) -9 NIL 3138730 NIL) (-1266 3131812 3132066 3132456 "VECTCAT-" 3132461 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1265 3131266 3131463 3131583 "VARIABLE" 3131727 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1264 3131199 3131204 3131234 "UTYPE" 3131239 T UTYPE (NIL) -9 NIL NIL NIL) (-1263 3130029 3130183 3130445 "UTSODETL" 3131025 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1262 3127469 3127929 3128453 "UTSODE" 3129570 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1261 3119306 3125095 3125584 "UTS" 3127038 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1260 3110180 3115547 3115590 "UTSCAT" 3116702 NIL UTSCAT (NIL T) -9 NIL 3117460 NIL) (-1259 3107527 3108250 3109239 "UTSCAT-" 3109244 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1258 3107154 3107197 3107330 "UTS2" 3107478 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1257 3101380 3103992 3104035 "URAGG" 3106105 NIL URAGG (NIL T) -9 NIL 3106828 NIL) (-1256 3098319 3099182 3100305 "URAGG-" 3100310 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1255 3094028 3096954 3097419 "UPXSSING" 3097983 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1254 3086094 3093275 3093548 "UPXS" 3093813 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1253 3079167 3085998 3086070 "UPXSCONS" 3086075 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1252 3068912 3075705 3075767 "UPXSCCA" 3076341 NIL UPXSCCA (NIL T T) -9 NIL 3076574 NIL) (-1251 3068550 3068635 3068809 "UPXSCCA-" 3068814 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1250 3058147 3064713 3064756 "UPXSCAT" 3065404 NIL UPXSCAT (NIL T) -9 NIL 3066013 NIL) (-1249 3057577 3057656 3057835 "UPXS2" 3058062 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1248 3056231 3056484 3056835 "UPSQFREE" 3057320 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1247 3049652 3052709 3052764 "UPSCAT" 3053925 NIL UPSCAT (NIL T T) -9 NIL 3054699 NIL) (-1246 3048856 3049063 3049390 "UPSCAT-" 3049395 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1245 3034511 3042279 3042322 "UPOLYC" 3044423 NIL UPOLYC (NIL T) -9 NIL 3045644 NIL) (-1244 3025839 3028265 3031412 "UPOLYC-" 3031417 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1243 3025466 3025509 3025642 "UPOLYC2" 3025790 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1242 3017277 3025149 3025278 "UP" 3025385 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1241 3016616 3016723 3016887 "UPMP" 3017166 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1240 3016169 3016250 3016389 "UPDIVP" 3016529 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1239 3014737 3014986 3015302 "UPDECOMP" 3015918 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1238 3013972 3014084 3014269 "UPCDEN" 3014621 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1237 3013491 3013560 3013709 "UP2" 3013897 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1236 3011958 3012695 3012972 "UNISEG" 3013249 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1235 3011173 3011300 3011505 "UNISEG2" 3011801 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1234 3010233 3010413 3010639 "UNIFACT" 3010989 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1233 2994165 3009410 3009661 "ULS" 3010040 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1232 2982163 2994069 2994141 "ULSCONS" 2994146 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1231 2964182 2976167 2976229 "ULSCCAT" 2976867 NIL ULSCCAT (NIL T T) -9 NIL 2977155 NIL) (-1230 2963232 2963477 2963865 "ULSCCAT-" 2963870 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1229 2952606 2959086 2959129 "ULSCAT" 2959992 NIL ULSCAT (NIL T) -9 NIL 2960723 NIL) (-1228 2952036 2952115 2952294 "ULS2" 2952521 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1227 2951163 2951673 2951780 "UINT8" 2951891 T UINT8 (NIL) -8 NIL NIL 2951976) (-1226 2950289 2950799 2950906 "UINT64" 2951017 T UINT64 (NIL) -8 NIL NIL 2951102) (-1225 2949415 2949925 2950032 "UINT32" 2950143 T UINT32 (NIL) -8 NIL NIL 2950228) (-1224 2948541 2949051 2949158 "UINT16" 2949269 T UINT16 (NIL) -8 NIL NIL 2949354) (-1223 2946844 2947801 2947831 "UFD" 2948043 T UFD (NIL) -9 NIL 2948157 NIL) (-1222 2946638 2946684 2946779 "UFD-" 2946784 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1221 2945720 2945903 2946119 "UDVO" 2946444 T UDVO (NIL) -7 NIL NIL NIL) (-1220 2943536 2943945 2944416 "UDPO" 2945284 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1219 2943469 2943474 2943504 "TYPE" 2943509 T TYPE (NIL) -9 NIL NIL NIL) (-1218 2943229 2943424 2943455 "TYPEAST" 2943460 T TYPEAST (NIL) -8 NIL NIL NIL) (-1217 2942200 2942402 2942642 "TWOFACT" 2943023 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1216 2941223 2941609 2941844 "TUPLE" 2942000 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1215 2938914 2939433 2939972 "TUBETOOL" 2940706 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1214 2937763 2937968 2938209 "TUBE" 2938707 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1213 2932492 2936735 2937018 "TS" 2937515 NIL TS (NIL T) -8 NIL NIL NIL) (-1212 2921132 2925251 2925348 "TSETCAT" 2930617 NIL TSETCAT (NIL T T T T) -9 NIL 2932148 NIL) (-1211 2915864 2917464 2919355 "TSETCAT-" 2919360 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1210 2910503 2911350 2912279 "TRMANIP" 2915000 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1209 2909944 2910007 2910170 "TRIMAT" 2910435 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1208 2907810 2908047 2908404 "TRIGMNIP" 2909693 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1207 2907330 2907443 2907473 "TRIGCAT" 2907686 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1206 2906999 2907078 2907219 "TRIGCAT-" 2907224 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1205 2903844 2905857 2906138 "TREE" 2906753 NIL TREE (NIL T) -8 NIL NIL NIL) (-1204 2903118 2903646 2903676 "TRANFUN" 2903711 T TRANFUN (NIL) -9 NIL 2903777 NIL) (-1203 2902397 2902588 2902868 "TRANFUN-" 2902873 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1202 2902201 2902233 2902294 "TOPSP" 2902358 T TOPSP (NIL) -7 NIL NIL NIL) (-1201 2901549 2901664 2901818 "TOOLSIGN" 2902082 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1200 2900183 2900726 2900965 "TEXTFILE" 2901332 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1199 2898095 2898636 2899065 "TEX" 2899776 T TEX (NIL) -8 NIL NIL NIL) (-1198 2897876 2897907 2897979 "TEX1" 2898058 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1197 2897524 2897587 2897677 "TEMUTL" 2897808 T TEMUTL (NIL) -7 NIL NIL NIL) (-1196 2895678 2895958 2896283 "TBCMPPK" 2897247 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1195 2887455 2893838 2893894 "TBAGG" 2894294 NIL TBAGG (NIL T T) -9 NIL 2894505 NIL) (-1194 2882525 2884013 2885767 "TBAGG-" 2885772 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1193 2881909 2882016 2882161 "TANEXP" 2882414 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1192 2875299 2881766 2881859 "TABLE" 2881864 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1191 2874711 2874810 2874948 "TABLEAU" 2875196 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1190 2869319 2870539 2871787 "TABLBUMP" 2873497 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1189 2868541 2868688 2868869 "SYSTEM" 2869160 T SYSTEM (NIL) -8 NIL NIL NIL) (-1188 2865000 2865699 2866482 "SYSSOLP" 2867792 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1187 2864798 2864955 2864986 "SYSPTR" 2864991 T SYSPTR (NIL) -8 NIL NIL NIL) (-1186 2863842 2864347 2864466 "SYSNNI" 2864652 NIL SYSNNI (NIL NIL) -8 NIL NIL 2864737) (-1185 2863149 2863608 2863687 "SYSINT" 2863747 NIL SYSINT (NIL NIL) -8 NIL NIL 2863792) (-1184 2859481 2860427 2861137 "SYNTAX" 2862461 T SYNTAX (NIL) -8 NIL NIL NIL) (-1183 2856639 2857241 2857873 "SYMTAB" 2858871 T SYMTAB (NIL) -8 NIL NIL NIL) (-1182 2851888 2852790 2853773 "SYMS" 2855678 T SYMS (NIL) -8 NIL NIL NIL) (-1181 2849123 2851346 2851576 "SYMPOLY" 2851693 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1180 2848640 2848715 2848838 "SYMFUNC" 2849035 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1179 2844659 2845952 2846765 "SYMBOL" 2847849 T SYMBOL (NIL) -8 NIL NIL NIL) (-1178 2838198 2839887 2841607 "SWITCH" 2842961 T SWITCH (NIL) -8 NIL NIL NIL) (-1177 2831432 2837019 2837322 "SUTS" 2837953 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2823498 2830679 2830952 "SUPXS" 2831217 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1175 2815257 2823116 2823242 "SUP" 2823407 NIL SUP (NIL T) -8 NIL NIL NIL) (-1174 2814416 2814543 2814760 "SUPFRACF" 2815125 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1173 2814037 2814096 2814209 "SUP2" 2814351 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1172 2812485 2812759 2813115 "SUMRF" 2813736 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1171 2811820 2811886 2812078 "SUMFS" 2812406 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1170 2795787 2810997 2811248 "SULS" 2811627 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1169 2795389 2795609 2795679 "SUCHTAST" 2795739 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1168 2794684 2794914 2795054 "SUCH" 2795297 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1167 2788550 2789590 2790549 "SUBSPACE" 2793772 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1166 2787980 2788070 2788234 "SUBRESP" 2788438 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1165 2781345 2782645 2783956 "STTF" 2786716 NIL STTF (NIL T) -7 NIL NIL NIL) (-1164 2775518 2776638 2777785 "STTFNC" 2780245 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1163 2766828 2768700 2770494 "STTAYLOR" 2773759 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1162 2759958 2766692 2766775 "STRTBL" 2766780 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1161 2755322 2759913 2759944 "STRING" 2759949 T STRING (NIL) -8 NIL NIL NIL) (-1160 2750183 2754695 2754725 "STRICAT" 2754784 T STRICAT (NIL) -9 NIL 2754846 NIL) (-1159 2742936 2747802 2748413 "STREAM" 2749607 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1158 2742446 2742523 2742667 "STREAM3" 2742853 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1157 2741428 2741611 2741846 "STREAM2" 2742259 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1156 2741116 2741168 2741261 "STREAM1" 2741370 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1155 2740132 2740313 2740544 "STINPROD" 2740932 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1154 2739684 2739894 2739924 "STEP" 2740004 T STEP (NIL) -9 NIL 2740082 NIL) (-1153 2738871 2739173 2739321 "STEPAST" 2739558 T STEPAST (NIL) -8 NIL NIL NIL) (-1152 2732303 2738770 2738847 "STBL" 2738852 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1151 2727429 2731524 2731567 "STAGG" 2731720 NIL STAGG (NIL T) -9 NIL 2731809 NIL) (-1150 2725131 2725733 2726605 "STAGG-" 2726610 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1149 2723278 2724901 2724993 "STACK" 2725074 NIL STACK (NIL T) -8 NIL NIL NIL) (-1148 2715973 2721419 2721875 "SREGSET" 2722908 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1147 2708398 2709767 2711280 "SRDCMPK" 2714579 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1146 2701315 2705838 2705868 "SRAGG" 2707171 T SRAGG (NIL) -9 NIL 2707779 NIL) (-1145 2700332 2700587 2700966 "SRAGG-" 2700971 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1144 2694792 2699279 2699700 "SQMATRIX" 2699958 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1143 2688477 2691510 2692237 "SPLTREE" 2694137 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1142 2684440 2685133 2685779 "SPLNODE" 2687903 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1141 2683487 2683720 2683750 "SPFCAT" 2684194 T SPFCAT (NIL) -9 NIL NIL NIL) (-1140 2682224 2682434 2682698 "SPECOUT" 2683245 T SPECOUT (NIL) -7 NIL NIL NIL) (-1139 2673334 2675206 2675236 "SPADXPT" 2679912 T SPADXPT (NIL) -9 NIL 2682076 NIL) (-1138 2673095 2673135 2673204 "SPADPRSR" 2673287 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1137 2671144 2673050 2673081 "SPADAST" 2673086 T SPADAST (NIL) -8 NIL NIL NIL) (-1136 2663089 2664862 2664905 "SPACEC" 2669278 NIL SPACEC (NIL T) -9 NIL 2671094 NIL) (-1135 2661219 2663021 2663070 "SPACE3" 2663075 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1134 2659971 2660142 2660433 "SORTPAK" 2661024 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1133 2658063 2658366 2658778 "SOLVETRA" 2659635 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1132 2657113 2657335 2657596 "SOLVESER" 2657836 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1131 2652417 2653305 2654300 "SOLVERAD" 2656165 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1130 2648232 2648841 2649570 "SOLVEFOR" 2651784 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1129 2642502 2647581 2647678 "SNTSCAT" 2647683 NIL SNTSCAT (NIL T T T T) -9 NIL 2647753 NIL) (-1128 2636608 2640825 2641216 "SMTS" 2642192 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1127 2631292 2636496 2636573 "SMP" 2636578 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1126 2629451 2629752 2630150 "SMITH" 2630989 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1125 2622164 2626360 2626463 "SMATCAT" 2627814 NIL SMATCAT (NIL NIL T T T) -9 NIL 2628364 NIL) (-1124 2619104 2619927 2621105 "SMATCAT-" 2621110 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1123 2616770 2618340 2618383 "SKAGG" 2618644 NIL SKAGG (NIL T) -9 NIL 2618779 NIL) (-1122 2613081 2616186 2616381 "SINT" 2616568 T SINT (NIL) -8 NIL NIL 2616741) (-1121 2612853 2612891 2612957 "SIMPAN" 2613037 T SIMPAN (NIL) -7 NIL NIL NIL) (-1120 2612132 2612388 2612528 "SIG" 2612735 T SIG (NIL) -8 NIL NIL NIL) (-1119 2610970 2611191 2611466 "SIGNRF" 2611891 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1118 2609803 2609954 2610238 "SIGNEF" 2610799 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1117 2609109 2609386 2609510 "SIGAST" 2609701 T SIGAST (NIL) -8 NIL NIL NIL) (-1116 2606798 2607253 2607759 "SHP" 2608650 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1115 2600650 2606699 2606775 "SHDP" 2606780 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1114 2600223 2600415 2600445 "SGROUP" 2600538 T SGROUP (NIL) -9 NIL 2600600 NIL) (-1113 2600081 2600107 2600180 "SGROUP-" 2600185 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1112 2596916 2597614 2598337 "SGCF" 2599380 T SGCF (NIL) -7 NIL NIL NIL) (-1111 2591284 2596363 2596460 "SFRTCAT" 2596465 NIL SFRTCAT (NIL T T T T) -9 NIL 2596504 NIL) (-1110 2584705 2585723 2586859 "SFRGCD" 2590267 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1109 2577831 2578904 2580090 "SFQCMPK" 2583638 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1108 2577451 2577540 2577651 "SFORT" 2577772 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1107 2576569 2577291 2577412 "SEXOF" 2577417 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1106 2575676 2576450 2576518 "SEX" 2576523 T SEX (NIL) -8 NIL NIL NIL) (-1105 2571189 2571904 2571999 "SEXCAT" 2574936 NIL SEXCAT (NIL T T T T T) -9 NIL 2575514 NIL) (-1104 2568342 2571123 2571171 "SET" 2571176 NIL SET (NIL T) -8 NIL NIL NIL) (-1103 2566566 2567055 2567360 "SETMN" 2568083 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1102 2566062 2566214 2566244 "SETCAT" 2566420 T SETCAT (NIL) -9 NIL 2566530 NIL) (-1101 2565754 2565832 2565962 "SETCAT-" 2565967 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1100 2562115 2564215 2564258 "SETAGG" 2565128 NIL SETAGG (NIL T) -9 NIL 2565468 NIL) (-1099 2561573 2561689 2561926 "SETAGG-" 2561931 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1098 2561016 2561269 2561370 "SEQAST" 2561494 T SEQAST (NIL) -8 NIL NIL NIL) (-1097 2560215 2560509 2560570 "SEGXCAT" 2560856 NIL SEGXCAT (NIL T T) -9 NIL 2560976 NIL) (-1096 2559221 2559881 2560063 "SEG" 2560068 NIL SEG (NIL T) -8 NIL NIL NIL) (-1095 2558200 2558414 2558457 "SEGCAT" 2558979 NIL SEGCAT (NIL T) -9 NIL 2559200 NIL) (-1094 2557132 2557563 2557771 "SEGBIND" 2558027 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1093 2556753 2556812 2556925 "SEGBIND2" 2557067 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1092 2556326 2556554 2556631 "SEGAST" 2556698 T SEGAST (NIL) -8 NIL NIL NIL) (-1091 2555545 2555671 2555875 "SEG2" 2556170 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1090 2554955 2555480 2555527 "SDVAR" 2555532 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1089 2547482 2554725 2554855 "SDPOL" 2554860 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1088 2546075 2546341 2546660 "SCPKG" 2547197 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1087 2545239 2545411 2545603 "SCOPE" 2545905 T SCOPE (NIL) -8 NIL NIL NIL) (-1086 2544459 2544593 2544772 "SCACHE" 2545094 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1085 2544105 2544291 2544321 "SASTCAT" 2544326 T SASTCAT (NIL) -9 NIL 2544339 NIL) (-1084 2543592 2543940 2544016 "SAOS" 2544051 T SAOS (NIL) -8 NIL NIL NIL) (-1083 2543157 2543192 2543365 "SAERFFC" 2543551 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1082 2537096 2543054 2543134 "SAE" 2543139 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1081 2536689 2536724 2536883 "SAEFACT" 2537055 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1080 2535010 2535324 2535725 "RURPK" 2536355 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1079 2533647 2533953 2534258 "RULESET" 2534844 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1078 2530870 2531400 2531858 "RULE" 2533328 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1077 2530482 2530664 2530747 "RULECOLD" 2530822 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1076 2530272 2530300 2530371 "RTVALUE" 2530433 T RTVALUE (NIL) -8 NIL NIL NIL) (-1075 2529743 2529989 2530083 "RSTRCAST" 2530200 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1074 2524591 2525386 2526306 "RSETGCD" 2528942 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1073 2513821 2518900 2518997 "RSETCAT" 2523116 NIL RSETCAT (NIL T T T T) -9 NIL 2524213 NIL) (-1072 2511748 2512287 2513111 "RSETCAT-" 2513116 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1071 2504133 2505510 2507030 "RSDCMPK" 2510347 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1070 2502112 2502579 2502653 "RRCC" 2503739 NIL RRCC (NIL T T) -9 NIL 2504083 NIL) (-1069 2501463 2501637 2501916 "RRCC-" 2501921 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1068 2500906 2501159 2501260 "RPTAST" 2501384 T RPTAST (NIL) -8 NIL NIL NIL) (-1067 2474757 2484114 2484181 "RPOLCAT" 2494845 NIL RPOLCAT (NIL T T T) -9 NIL 2498004 NIL) (-1066 2466255 2468595 2471717 "RPOLCAT-" 2471722 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1065 2457186 2464466 2464948 "ROUTINE" 2465795 T ROUTINE (NIL) -8 NIL NIL NIL) (-1064 2453984 2456812 2456952 "ROMAN" 2457068 T ROMAN (NIL) -8 NIL NIL NIL) (-1063 2452228 2452844 2453104 "ROIRC" 2453789 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1062 2448460 2450744 2450774 "RNS" 2451078 T RNS (NIL) -9 NIL 2451352 NIL) (-1061 2446969 2447352 2447886 "RNS-" 2447961 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1060 2446372 2446780 2446810 "RNG" 2446815 T RNG (NIL) -9 NIL 2446836 NIL) (-1059 2445375 2445737 2445939 "RNGBIND" 2446223 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1058 2444774 2445162 2445205 "RMODULE" 2445210 NIL RMODULE (NIL T) -9 NIL 2445237 NIL) (-1057 2443610 2443704 2444040 "RMCAT2" 2444675 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1056 2440460 2442956 2443253 "RMATRIX" 2443372 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1055 2433287 2435547 2435662 "RMATCAT" 2439021 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2440003 NIL) (-1054 2432662 2432809 2433116 "RMATCAT-" 2433121 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1053 2432063 2432284 2432327 "RLINSET" 2432521 NIL RLINSET (NIL T) -9 NIL 2432612 NIL) (-1052 2431630 2431705 2431833 "RINTERP" 2431982 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1051 2430688 2431242 2431272 "RING" 2431328 T RING (NIL) -9 NIL 2431420 NIL) (-1050 2430480 2430524 2430621 "RING-" 2430626 NIL RING- (NIL T) -8 NIL NIL NIL) (-1049 2429321 2429558 2429816 "RIDIST" 2430244 T RIDIST (NIL) -7 NIL NIL NIL) (-1048 2420610 2428789 2428995 "RGCHAIN" 2429169 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1047 2419960 2420366 2420407 "RGBCSPC" 2420465 NIL RGBCSPC (NIL T) -9 NIL 2420517 NIL) (-1046 2419118 2419499 2419540 "RGBCMDL" 2419772 NIL RGBCMDL (NIL T) -9 NIL 2419886 NIL) (-1045 2416112 2416726 2417396 "RF" 2418482 NIL RF (NIL T) -7 NIL NIL NIL) (-1044 2415758 2415821 2415924 "RFFACTOR" 2416043 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1043 2415483 2415518 2415615 "RFFACT" 2415717 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1042 2413600 2413964 2414346 "RFDIST" 2415123 T RFDIST (NIL) -7 NIL NIL NIL) (-1041 2413053 2413145 2413308 "RETSOL" 2413502 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1040 2412689 2412769 2412812 "RETRACT" 2412945 NIL RETRACT (NIL T) -9 NIL 2413032 NIL) (-1039 2412538 2412563 2412650 "RETRACT-" 2412655 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1038 2412140 2412360 2412430 "RETAST" 2412490 T RETAST (NIL) -8 NIL NIL NIL) (-1037 2404878 2411793 2411920 "RESULT" 2412035 T RESULT (NIL) -8 NIL NIL NIL) (-1036 2403469 2404147 2404346 "RESRING" 2404781 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1035 2403105 2403154 2403252 "RESLATC" 2403406 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1034 2402810 2402845 2402952 "REPSQ" 2403064 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1033 2400232 2400812 2401414 "REP" 2402230 T REP (NIL) -7 NIL NIL NIL) (-1032 2399929 2399964 2400075 "REPDB" 2400191 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1031 2393829 2395218 2396441 "REP2" 2398741 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1030 2390206 2390887 2391695 "REP1" 2393056 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1029 2382902 2388347 2388803 "REGSET" 2389836 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1028 2381667 2382050 2382300 "REF" 2382687 NIL REF (NIL T) -8 NIL NIL NIL) (-1027 2381044 2381147 2381314 "REDORDER" 2381551 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1026 2377012 2380257 2380484 "RECLOS" 2380872 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1025 2376064 2376245 2376460 "REALSOLV" 2376819 T REALSOLV (NIL) -7 NIL NIL NIL) (-1024 2375910 2375951 2375981 "REAL" 2375986 T REAL (NIL) -9 NIL 2376021 NIL) (-1023 2372393 2373195 2374079 "REAL0Q" 2375075 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1022 2367994 2368982 2370043 "REAL0" 2371374 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1021 2367465 2367711 2367805 "RDUCEAST" 2367922 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1020 2366870 2366942 2367149 "RDIV" 2367387 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1019 2365938 2366112 2366325 "RDIST" 2366692 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1018 2364535 2364822 2365194 "RDETRS" 2365646 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1017 2362347 2362801 2363339 "RDETR" 2364077 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1016 2360972 2361250 2361647 "RDEEFS" 2362063 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1015 2359481 2359787 2360212 "RDEEF" 2360660 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1014 2353542 2356462 2356492 "RCFIELD" 2357787 T RCFIELD (NIL) -9 NIL 2358518 NIL) (-1013 2351606 2352110 2352806 "RCFIELD-" 2352881 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1012 2347875 2349707 2349750 "RCAGG" 2350834 NIL RCAGG (NIL T) -9 NIL 2351299 NIL) (-1011 2347503 2347597 2347760 "RCAGG-" 2347765 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1010 2346838 2346950 2347115 "RATRET" 2347387 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1009 2346391 2346458 2346579 "RATFACT" 2346766 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1008 2345699 2345819 2345971 "RANDSRC" 2346261 T RANDSRC (NIL) -7 NIL NIL NIL) (-1007 2345433 2345477 2345550 "RADUTIL" 2345648 T RADUTIL (NIL) -7 NIL NIL NIL) (-1006 2338549 2344266 2344576 "RADIX" 2345157 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1005 2330168 2338391 2338521 "RADFF" 2338526 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1004 2329815 2329890 2329920 "RADCAT" 2330080 T RADCAT (NIL) -9 NIL NIL NIL) (-1003 2329597 2329645 2329745 "RADCAT-" 2329750 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1002 2327697 2329369 2329460 "QUEUE" 2329541 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1001 2324236 2327632 2327679 "QUAT" 2327684 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1000 2323871 2323914 2324043 "QUATCT2" 2324187 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-999 2317333 2320678 2320718 "QUATCAT" 2321498 NIL QUATCAT (NIL T) -9 NIL 2322264 NIL) (-998 2313477 2314514 2315901 "QUATCAT-" 2315995 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-997 2310950 2312561 2312602 "QUAGG" 2312977 NIL QUAGG (NIL T) -9 NIL 2313152 NIL) (-996 2310555 2310775 2310843 "QQUTAST" 2310902 T QQUTAST (NIL) -8 NIL NIL NIL) (-995 2309453 2309953 2310125 "QFORM" 2310427 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-994 2300458 2305697 2305737 "QFCAT" 2306395 NIL QFCAT (NIL T) -9 NIL 2307396 NIL) (-993 2296030 2297231 2298822 "QFCAT-" 2298916 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-992 2295668 2295711 2295838 "QFCAT2" 2295981 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-991 2295128 2295238 2295368 "QEQUAT" 2295558 T QEQUAT (NIL) -8 NIL NIL NIL) (-990 2288274 2289347 2290531 "QCMPACK" 2294061 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-989 2285823 2286271 2286699 "QALGSET" 2287929 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-988 2285068 2285242 2285474 "QALGSET2" 2285643 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-987 2283758 2283982 2284299 "PWFFINTB" 2284841 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-986 2281940 2282108 2282462 "PUSHVAR" 2283572 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-985 2277858 2278912 2278953 "PTRANFN" 2280837 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-984 2276260 2276551 2276873 "PTPACK" 2277569 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-983 2275892 2275949 2276058 "PTFUNC2" 2276197 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-982 2270369 2274764 2274805 "PTCAT" 2275101 NIL PTCAT (NIL T) -9 NIL 2275254 NIL) (-981 2270027 2270062 2270186 "PSQFR" 2270328 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-980 2268622 2268920 2269254 "PSEUDLIN" 2269725 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-979 2255385 2257756 2260080 "PSETPK" 2266382 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-978 2248403 2251143 2251239 "PSETCAT" 2254260 NIL PSETCAT (NIL T T T T) -9 NIL 2255074 NIL) (-977 2246239 2246873 2247694 "PSETCAT-" 2247699 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-976 2245588 2245753 2245781 "PSCURVE" 2246049 T PSCURVE (NIL) -9 NIL 2246216 NIL) (-975 2241586 2243102 2243167 "PSCAT" 2244011 NIL PSCAT (NIL T T T) -9 NIL 2244251 NIL) (-974 2240649 2240865 2241265 "PSCAT-" 2241270 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-973 2239354 2240014 2240219 "PRTITION" 2240464 T PRTITION (NIL) -8 NIL NIL NIL) (-972 2238829 2239075 2239167 "PRTDAST" 2239282 T PRTDAST (NIL) -8 NIL NIL NIL) (-971 2227918 2230133 2232321 "PRS" 2236691 NIL PRS (NIL T T) -7 NIL NIL NIL) (-970 2225729 2227268 2227308 "PRQAGG" 2227491 NIL PRQAGG (NIL T) -9 NIL 2227593 NIL) (-969 2224933 2225238 2225266 "PROPLOG" 2225513 T PROPLOG (NIL) -9 NIL 2225679 NIL) (-968 2223363 2223884 2224141 "PROPFRML" 2224709 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-967 2222832 2222939 2223067 "PROPERTY" 2223255 T PROPERTY (NIL) -8 NIL NIL NIL) (-966 2216890 2220998 2221818 "PRODUCT" 2222058 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-965 2214168 2216348 2216582 "PR" 2216701 NIL PR (NIL T T) -8 NIL NIL NIL) (-964 2213964 2213996 2214055 "PRINT" 2214129 T PRINT (NIL) -7 NIL NIL NIL) (-963 2213304 2213421 2213573 "PRIMES" 2213844 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-962 2211369 2211770 2212236 "PRIMELT" 2212883 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-961 2211098 2211147 2211175 "PRIMCAT" 2211299 T PRIMCAT (NIL) -9 NIL NIL NIL) (-960 2207213 2211036 2211081 "PRIMARR" 2211086 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-959 2206220 2206398 2206626 "PRIMARR2" 2207031 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-958 2205863 2205919 2206030 "PREASSOC" 2206158 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-957 2205338 2205471 2205499 "PPCURVE" 2205704 T PPCURVE (NIL) -9 NIL 2205840 NIL) (-956 2204933 2205133 2205216 "PORTNUM" 2205275 T PORTNUM (NIL) -8 NIL NIL NIL) (-955 2202292 2202691 2203283 "POLYROOT" 2204514 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-954 2196474 2201896 2202056 "POLY" 2202165 NIL POLY (NIL T) -8 NIL NIL NIL) (-953 2195857 2195915 2196149 "POLYLIFT" 2196410 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-952 2192132 2192581 2193210 "POLYCATQ" 2195402 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-951 2178844 2183972 2184037 "POLYCAT" 2187551 NIL POLYCAT (NIL T T T) -9 NIL 2189429 NIL) (-950 2172293 2174155 2176539 "POLYCAT-" 2176544 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-949 2171880 2171948 2172068 "POLY2UP" 2172219 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-948 2171512 2171569 2171678 "POLY2" 2171817 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-947 2170197 2170436 2170712 "POLUTIL" 2171286 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-946 2168552 2168829 2169160 "POLTOPOL" 2169919 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-945 2164017 2168488 2168534 "POINT" 2168539 NIL POINT (NIL T) -8 NIL NIL NIL) (-944 2162204 2162561 2162936 "PNTHEORY" 2163662 T PNTHEORY (NIL) -7 NIL NIL NIL) (-943 2160662 2160959 2161358 "PMTOOLS" 2161902 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-942 2160255 2160333 2160450 "PMSYM" 2160578 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-941 2159765 2159834 2160008 "PMQFCAT" 2160180 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-940 2159120 2159230 2159386 "PMPRED" 2159642 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-939 2158513 2158599 2158761 "PMPREDFS" 2159021 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-938 2157177 2157385 2157763 "PMPLCAT" 2158275 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-937 2156709 2156788 2156940 "PMLSAGG" 2157092 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-936 2156182 2156258 2156440 "PMKERNEL" 2156627 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-935 2155799 2155874 2155987 "PMINS" 2156101 NIL PMINS (NIL T) -7 NIL NIL NIL) (-934 2155241 2155310 2155519 "PMFS" 2155724 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-933 2154469 2154587 2154792 "PMDOWN" 2155118 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-932 2153636 2153794 2153975 "PMASS" 2154308 T PMASS (NIL) -7 NIL NIL NIL) (-931 2152909 2153019 2153182 "PMASSFS" 2153523 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-930 2152564 2152632 2152726 "PLOTTOOL" 2152835 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-929 2147171 2148375 2149523 "PLOT" 2151436 T PLOT (NIL) -8 NIL NIL NIL) (-928 2142975 2144019 2144940 "PLOT3D" 2146270 T PLOT3D (NIL) -8 NIL NIL NIL) (-927 2141887 2142064 2142299 "PLOT1" 2142779 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-926 2117276 2121953 2126804 "PLEQN" 2137153 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-925 2116594 2116716 2116896 "PINTERP" 2117141 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-924 2116287 2116334 2116437 "PINTERPA" 2116541 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-923 2115508 2116056 2116143 "PI" 2116183 T PI (NIL) -8 NIL NIL 2116250) (-922 2113805 2114780 2114808 "PID" 2114990 T PID (NIL) -9 NIL 2115124 NIL) (-921 2113556 2113593 2113668 "PICOERCE" 2113762 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-920 2112876 2113015 2113191 "PGROEB" 2113412 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-919 2108463 2109277 2110182 "PGE" 2111991 T PGE (NIL) -7 NIL NIL NIL) (-918 2106586 2106833 2107199 "PGCD" 2108180 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-917 2105924 2106027 2106188 "PFRPAC" 2106470 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-916 2102564 2104472 2104825 "PFR" 2105603 NIL PFR (NIL T) -8 NIL NIL NIL) (-915 2100953 2101197 2101522 "PFOTOOLS" 2102311 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-914 2099486 2099725 2100076 "PFOQ" 2100710 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-913 2097987 2098199 2098555 "PFO" 2099270 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-912 2094540 2097876 2097945 "PF" 2097950 NIL PF (NIL NIL) -8 NIL NIL NIL) (-911 2091874 2093145 2093173 "PFECAT" 2093758 T PFECAT (NIL) -9 NIL 2094142 NIL) (-910 2091319 2091473 2091687 "PFECAT-" 2091692 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-909 2089922 2090174 2090475 "PFBRU" 2091068 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-908 2087788 2088140 2088572 "PFBR" 2089573 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-907 2083670 2085164 2085840 "PERM" 2087145 NIL PERM (NIL T) -8 NIL NIL NIL) (-906 2078904 2079877 2080747 "PERMGRP" 2082833 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-905 2077010 2077967 2078008 "PERMCAT" 2078454 NIL PERMCAT (NIL T) -9 NIL 2078759 NIL) (-904 2076663 2076704 2076828 "PERMAN" 2076963 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-903 2074151 2076328 2076450 "PENDTREE" 2076574 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-902 2072175 2072943 2072984 "PDRING" 2073641 NIL PDRING (NIL T) -9 NIL 2073927 NIL) (-901 2071278 2071496 2071858 "PDRING-" 2071863 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-900 2068493 2069271 2069939 "PDEPROB" 2070630 T PDEPROB (NIL) -8 NIL NIL NIL) (-899 2066038 2066542 2067097 "PDEPACK" 2067958 T PDEPACK (NIL) -7 NIL NIL NIL) (-898 2064950 2065140 2065391 "PDECOMP" 2065837 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-897 2062529 2063372 2063400 "PDECAT" 2064187 T PDECAT (NIL) -9 NIL 2064900 NIL) (-896 2062280 2062313 2062403 "PCOMP" 2062490 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-895 2060458 2061081 2061378 "PBWLB" 2062009 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-894 2052931 2054531 2055869 "PATTERN" 2059141 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-893 2052563 2052620 2052729 "PATTERN2" 2052868 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-892 2050320 2050708 2051165 "PATTERN1" 2052152 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-891 2047688 2048269 2048750 "PATRES" 2049885 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-890 2047252 2047319 2047451 "PATRES2" 2047615 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-889 2045135 2045540 2045947 "PATMATCH" 2046919 NIL PATMATCH (NIL T T T) -7 NIL NIL 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NIL NIL NIL) (-876 2036312 2036398 2036517 "PAN2EXPR" 2036693 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-875 2035089 2035433 2035661 "PALETTE" 2036104 T PALETTE (NIL) -8 NIL NIL NIL) (-874 2033482 2034094 2034454 "PAIR" 2034775 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-873 2027352 2032741 2032935 "PADICRC" 2033337 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-872 2020581 2026698 2026882 "PADICRAT" 2027200 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-871 2018896 2020518 2020563 "PADIC" 2020568 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-870 2016006 2017570 2017610 "PADICCT" 2018191 NIL PADICCT (NIL NIL) -9 NIL 2018473 NIL) (-869 2014963 2015163 2015431 "PADEPAC" 2015793 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-868 2014175 2014308 2014514 "PADE" 2014825 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-867 2012562 2013383 2013663 "OWP" 2013979 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-866 2012055 2012268 2012365 "OVERSET" 2012485 T OVERSET (NIL) -8 NIL NIL NIL) (-865 2011101 2011660 2011832 "OVAR" 2011923 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-864 2010365 2010486 2010647 "OUT" 2010960 T OUT (NIL) -7 NIL NIL NIL) (-863 1999237 2001474 2003674 "OUTFORM" 2008185 T OUTFORM (NIL) -8 NIL NIL NIL) (-862 1998573 1998834 1998961 "OUTBFILE" 1999130 T OUTBFILE (NIL) -8 NIL NIL NIL) (-861 1997880 1998045 1998073 "OUTBCON" 1998391 T OUTBCON (NIL) -9 NIL 1998557 NIL) (-860 1997481 1997593 1997750 "OUTBCON-" 1997755 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-859 1996861 1997210 1997299 "OSI" 1997412 T OSI (NIL) -8 NIL NIL NIL) (-858 1996391 1996729 1996757 "OSGROUP" 1996762 T OSGROUP (NIL) -9 NIL 1996784 NIL) (-857 1995136 1995363 1995648 "ORTHPOL" 1996138 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-856 1992687 1994971 1995092 "OREUP" 1995097 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-855 1990090 1992378 1992505 "ORESUP" 1992629 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-854 1987618 1988118 1988679 "OREPCTO" 1989579 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-853 1981304 1983505 1983546 "OREPCAT" 1985894 NIL OREPCAT (NIL T) -9 NIL 1986998 NIL) (-852 1978451 1979233 1980291 "OREPCAT-" 1980296 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-851 1977602 1977900 1977928 "ORDSET" 1978237 T ORDSET (NIL) -9 NIL 1978401 NIL) (-850 1977033 1977181 1977405 "ORDSET-" 1977410 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-849 1975598 1976389 1976417 "ORDRING" 1976619 T ORDRING (NIL) -9 NIL 1976744 NIL) (-848 1975243 1975337 1975481 "ORDRING-" 1975486 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-847 1974623 1975086 1975114 "ORDMON" 1975119 T ORDMON (NIL) -9 NIL 1975140 NIL) (-846 1973785 1973932 1974127 "ORDFUNS" 1974472 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-845 1973123 1973542 1973570 "ORDFIN" 1973635 T ORDFIN (NIL) -9 NIL 1973709 NIL) (-844 1969682 1971709 1972118 "ORDCOMP" 1972747 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-843 1968948 1969075 1969261 "ORDCOMP2" 1969542 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-842 1965529 1966439 1967253 "OPTPROB" 1968154 T OPTPROB (NIL) -8 NIL NIL NIL) (-841 1962331 1962970 1963674 "OPTPACK" 1964845 T OPTPACK (NIL) -7 NIL NIL NIL) (-840 1960018 1960784 1960812 "OPTCAT" 1961631 T OPTCAT (NIL) -9 NIL 1962281 NIL) (-839 1959402 1959695 1959800 "OPSIG" 1959933 T OPSIG (NIL) -8 NIL NIL NIL) (-838 1959170 1959209 1959275 "OPQUERY" 1959356 T OPQUERY (NIL) -7 NIL NIL NIL) (-837 1956301 1957481 1957985 "OP" 1958699 NIL OP (NIL T) -8 NIL NIL NIL) (-836 1955675 1955901 1955942 "OPERCAT" 1956154 NIL OPERCAT (NIL T) -9 NIL 1956251 NIL) (-835 1955430 1955486 1955603 "OPERCAT-" 1955608 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-834 1952243 1954227 1954596 "ONECOMP" 1955094 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-833 1951548 1951663 1951837 "ONECOMP2" 1952115 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-832 1950967 1951073 1951203 "OMSERVER" 1951438 T OMSERVER (NIL) -7 NIL NIL NIL) (-831 1947829 1950407 1950447 "OMSAGG" 1950508 NIL OMSAGG (NIL T) -9 NIL 1950572 NIL) (-830 1946452 1946715 1946997 "OMPKG" 1947567 T OMPKG (NIL) -7 NIL NIL NIL) (-829 1945882 1945985 1946013 "OM" 1946312 T OM (NIL) -9 NIL NIL NIL) (-828 1944429 1945431 1945600 "OMLO" 1945763 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-827 1943389 1943536 1943756 "OMEXPR" 1944255 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-826 1942680 1942935 1943071 "OMERR" 1943273 T OMERR (NIL) -8 NIL NIL NIL) (-825 1941831 1942101 1942261 "OMERRK" 1942540 T OMERRK (NIL) -8 NIL NIL NIL) (-824 1941282 1941508 1941616 "OMENC" 1941743 T OMENC (NIL) -8 NIL NIL NIL) (-823 1935177 1936362 1937533 "OMDEV" 1940131 T OMDEV (NIL) -8 NIL NIL NIL) (-822 1934246 1934417 1934611 "OMCONN" 1935003 T OMCONN (NIL) -8 NIL NIL NIL) (-821 1932767 1933743 1933771 "OINTDOM" 1933776 T OINTDOM (NIL) -9 NIL 1933797 NIL) (-820 1930105 1931455 1931792 "OFMONOID" 1932462 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-819 1929516 1930042 1930087 "ODVAR" 1930092 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-818 1926939 1929261 1929416 "ODR" 1929421 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-817 1919520 1926715 1926841 "ODPOL" 1926846 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-816 1913342 1919392 1919497 "ODP" 1919502 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-815 1912108 1912323 1912598 "ODETOOLS" 1913116 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-814 1909075 1909733 1910449 "ODESYS" 1911441 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-813 1903957 1904865 1905890 "ODERTRIC" 1908150 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-812 1903383 1903465 1903659 "ODERED" 1903869 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-811 1900271 1900819 1901496 "ODERAT" 1902806 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-810 1897228 1897695 1898292 "ODEPRRIC" 1899800 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-809 1895171 1895767 1896253 "ODEPROB" 1896762 T ODEPROB (NIL) -8 NIL NIL NIL) (-808 1891691 1892176 1892823 "ODEPRIM" 1894650 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-807 1890940 1891042 1891302 "ODEPAL" 1891583 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-806 1887102 1887893 1888757 "ODEPACK" 1890096 T ODEPACK (NIL) -7 NIL NIL NIL) (-805 1886163 1886270 1886492 "ODEINT" 1886991 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-804 1880264 1881689 1883136 "ODEIFTBL" 1884736 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-803 1875662 1876448 1877400 "ODEEF" 1879423 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-802 1875011 1875100 1875323 "ODECONST" 1875567 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-801 1873136 1873797 1873825 "ODECAT" 1874430 T ODECAT (NIL) -9 NIL 1874961 NIL) (-800 1869991 1872841 1872963 "OCT" 1873046 NIL OCT (NIL T) -8 NIL NIL NIL) (-799 1869629 1869672 1869799 "OCTCT2" 1869942 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-798 1864278 1866713 1866753 "OC" 1867850 NIL OC (NIL T) -9 NIL 1868708 NIL) (-797 1861505 1862253 1863243 "OC-" 1863337 NIL OC- (NIL T T) -8 NIL NIL NIL) (-796 1860857 1861325 1861353 "OCAMON" 1861358 T OCAMON (NIL) -9 NIL 1861379 NIL) (-795 1860388 1860729 1860757 "OASGP" 1860762 T OASGP (NIL) -9 NIL 1860782 NIL) (-794 1859649 1860138 1860166 "OAMONS" 1860206 T OAMONS (NIL) -9 NIL 1860249 NIL) (-793 1859063 1859496 1859524 "OAMON" 1859529 T OAMON (NIL) -9 NIL 1859549 NIL) (-792 1858321 1858839 1858867 "OAGROUP" 1858872 T OAGROUP (NIL) -9 NIL 1858892 NIL) (-791 1858011 1858061 1858149 "NUMTUBE" 1858265 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-790 1851584 1853102 1854638 "NUMQUAD" 1856495 T NUMQUAD (NIL) -7 NIL NIL NIL) (-789 1847340 1848328 1849353 "NUMODE" 1850579 T NUMODE (NIL) -7 NIL NIL NIL) (-788 1844695 1845575 1845603 "NUMINT" 1846526 T NUMINT (NIL) -9 NIL 1847290 NIL) (-787 1843643 1843840 1844058 "NUMFMT" 1844497 T NUMFMT (NIL) -7 NIL NIL NIL) (-786 1830002 1832947 1835479 "NUMERIC" 1841150 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-785 1824372 1829451 1829546 "NTSCAT" 1829551 NIL NTSCAT (NIL T T T T) -9 NIL 1829590 NIL) (-784 1823566 1823731 1823924 "NTPOLFN" 1824211 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-783 1811643 1820391 1821203 "NSUP" 1822787 NIL NSUP (NIL T) -8 NIL NIL NIL) (-782 1811275 1811332 1811441 "NSUP2" 1811580 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-781 1801503 1811049 1811182 "NSMP" 1811187 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-780 1799935 1800236 1800593 "NREP" 1801191 NIL NREP (NIL T) -7 NIL NIL NIL) (-779 1798526 1798778 1799136 "NPCOEF" 1799678 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-778 1797592 1797707 1797923 "NORMRETR" 1798407 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-777 1795633 1795923 1796332 "NORMPK" 1797300 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-776 1795318 1795346 1795470 "NORMMA" 1795599 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-775 1795118 1795275 1795304 "NONE" 1795309 T NONE (NIL) -8 NIL NIL NIL) (-774 1794907 1794936 1795005 "NONE1" 1795082 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-773 1794404 1794466 1794645 "NODE1" 1794839 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-772 1792689 1793540 1793795 "NNI" 1794142 T NNI (NIL) -8 NIL NIL 1794377) (-771 1791109 1791422 1791786 "NLINSOL" 1792357 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-770 1787350 1788345 1789244 "NIPROB" 1790230 T NIPROB (NIL) -8 NIL NIL NIL) (-769 1786107 1786341 1786643 "NFINTBAS" 1787112 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-768 1785281 1785757 1785798 "NETCLT" 1785970 NIL NETCLT (NIL T) -9 NIL 1786052 NIL) (-767 1783989 1784220 1784501 "NCODIV" 1785049 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-766 1783751 1783788 1783863 "NCNTFRAC" 1783946 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-765 1781931 1782295 1782715 "NCEP" 1783376 NIL NCEP (NIL T) -7 NIL NIL NIL) (-764 1780782 1781555 1781583 "NASRING" 1781693 T NASRING (NIL) -9 NIL 1781773 NIL) (-763 1780577 1780621 1780715 "NASRING-" 1780720 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-762 1779684 1780209 1780237 "NARNG" 1780354 T NARNG (NIL) -9 NIL 1780445 NIL) (-761 1779376 1779443 1779577 "NARNG-" 1779582 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-760 1778255 1778462 1778697 "NAGSP" 1779161 T NAGSP (NIL) -7 NIL NIL NIL) (-759 1769527 1771211 1772884 "NAGS" 1776602 T NAGS (NIL) -7 NIL NIL NIL) (-758 1768075 1768383 1768714 "NAGF07" 1769216 T NAGF07 (NIL) -7 NIL NIL NIL) (-757 1762613 1763904 1765211 "NAGF04" 1766788 T NAGF04 (NIL) -7 NIL NIL NIL) (-756 1755581 1757195 1758828 "NAGF02" 1761000 T NAGF02 (NIL) -7 NIL NIL NIL) (-755 1750805 1751905 1753022 "NAGF01" 1754484 T NAGF01 (NIL) -7 NIL NIL NIL) (-754 1744433 1745999 1747584 "NAGE04" 1749240 T NAGE04 (NIL) -7 NIL NIL NIL) (-753 1735602 1737723 1739853 "NAGE02" 1742323 T NAGE02 (NIL) -7 NIL NIL NIL) (-752 1731555 1732502 1733466 "NAGE01" 1734658 T NAGE01 (NIL) -7 NIL NIL NIL) (-751 1729350 1729884 1730442 "NAGD03" 1731017 T NAGD03 (NIL) -7 NIL NIL NIL) (-750 1721100 1723028 1724982 "NAGD02" 1727416 T NAGD02 (NIL) -7 NIL NIL NIL) (-749 1714911 1716336 1717776 "NAGD01" 1719680 T NAGD01 (NIL) -7 NIL NIL NIL) (-748 1711120 1711942 1712779 "NAGC06" 1714094 T NAGC06 (NIL) -7 NIL NIL NIL) (-747 1709585 1709917 1710273 "NAGC05" 1710784 T NAGC05 (NIL) -7 NIL NIL NIL) (-746 1708961 1709080 1709224 "NAGC02" 1709461 T NAGC02 (NIL) -7 NIL NIL NIL) (-745 1707920 1708503 1708543 "NAALG" 1708622 NIL NAALG (NIL T) -9 NIL 1708683 NIL) (-744 1707755 1707784 1707874 "NAALG-" 1707879 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-743 1701705 1702813 1704000 "MULTSQFR" 1706651 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-742 1701024 1701099 1701283 "MULTFACT" 1701617 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-741 1693748 1697661 1697714 "MTSCAT" 1698784 NIL MTSCAT (NIL T T) -9 NIL 1699299 NIL) (-740 1693460 1693514 1693606 "MTHING" 1693688 NIL MTHING (NIL T) -7 NIL NIL NIL) (-739 1693252 1693285 1693345 "MSYSCMD" 1693420 T MSYSCMD (NIL) -7 NIL NIL NIL) (-738 1689334 1692007 1692327 "MSET" 1692965 NIL MSET (NIL T) -8 NIL NIL NIL) (-737 1686403 1688895 1688936 "MSETAGG" 1688941 NIL MSETAGG (NIL T) -9 NIL 1688975 NIL) (-736 1682244 1683782 1684527 "MRING" 1685703 NIL MRING (NIL T T) -8 NIL NIL NIL) (-735 1681810 1681877 1682008 "MRF2" 1682171 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-734 1681428 1681463 1681607 "MRATFAC" 1681769 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-733 1679040 1679335 1679766 "MPRFF" 1681133 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-732 1673337 1678894 1678991 "MPOLY" 1678996 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-731 1672827 1672862 1673070 "MPCPF" 1673296 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-730 1672341 1672384 1672568 "MPC3" 1672778 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-729 1671536 1671617 1671838 "MPC2" 1672256 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-728 1669837 1670174 1670564 "MONOTOOL" 1671196 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-727 1669062 1669379 1669407 "MONOID" 1669626 T MONOID (NIL) -9 NIL 1669773 NIL) (-726 1668608 1668727 1668908 "MONOID-" 1668913 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-725 1659083 1665034 1665093 "MONOGEN" 1665767 NIL MONOGEN (NIL T T) -9 NIL 1666223 NIL) (-724 1656301 1657036 1658036 "MONOGEN-" 1658155 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-723 1655134 1655580 1655608 "MONADWU" 1656000 T MONADWU (NIL) -9 NIL 1656238 NIL) (-722 1654506 1654665 1654913 "MONADWU-" 1654918 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-721 1653865 1654109 1654137 "MONAD" 1654344 T MONAD (NIL) -9 NIL 1654456 NIL) (-720 1653550 1653628 1653760 "MONAD-" 1653765 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-719 1651839 1652463 1652742 "MOEBIUS" 1653303 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-718 1651117 1651521 1651561 "MODULE" 1651566 NIL MODULE (NIL T) -9 NIL 1651605 NIL) (-717 1650685 1650781 1650971 "MODULE-" 1650976 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-716 1648365 1649049 1649376 "MODRING" 1650509 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-715 1645309 1646470 1646991 "MODOP" 1647894 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-714 1643897 1644376 1644653 "MODMONOM" 1645172 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-713 1633938 1642188 1642602 "MODMON" 1643534 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-712 1631094 1632782 1633058 "MODFIELD" 1633813 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-711 1630071 1630375 1630565 "MMLFORM" 1630924 T MMLFORM (NIL) -8 NIL NIL NIL) (-710 1629597 1629640 1629819 "MMAP" 1630022 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-709 1627676 1628443 1628484 "MLO" 1628907 NIL MLO (NIL T) -9 NIL 1629149 NIL) (-708 1625042 1625558 1626160 "MLIFT" 1627157 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-707 1624433 1624517 1624671 "MKUCFUNC" 1624953 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-706 1624032 1624102 1624225 "MKRECORD" 1624356 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-705 1623079 1623241 1623469 "MKFUNC" 1623843 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-704 1622467 1622571 1622727 "MKFLCFN" 1622962 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-703 1621744 1621846 1622031 "MKBCFUNC" 1622360 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-702 1618451 1621298 1621434 "MINT" 1621628 T MINT (NIL) -8 NIL NIL NIL) (-701 1617263 1617506 1617783 "MHROWRED" 1618206 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-700 1612642 1615798 1616203 "MFLOAT" 1616878 T MFLOAT (NIL) -8 NIL NIL NIL) (-699 1611999 1612075 1612246 "MFINFACT" 1612554 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-698 1608314 1609162 1610046 "MESH" 1611135 T MESH (NIL) -7 NIL NIL NIL) (-697 1606704 1607016 1607369 "MDDFACT" 1608001 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-696 1603499 1605863 1605904 "MDAGG" 1606159 NIL MDAGG (NIL T) -9 NIL 1606302 NIL) (-695 1593239 1602792 1602999 "MCMPLX" 1603312 T MCMPLX (NIL) -8 NIL NIL NIL) (-694 1592380 1592526 1592726 "MCDEN" 1593088 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-693 1590270 1590540 1590920 "MCALCFN" 1592110 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-692 1589195 1589435 1589668 "MAYBE" 1590076 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-691 1586807 1587330 1587892 "MATSTOR" 1588666 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-690 1582764 1586179 1586427 "MATRIX" 1586592 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-689 1578528 1579237 1579973 "MATLIN" 1582121 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-688 1568634 1571820 1571897 "MATCAT" 1576777 NIL MATCAT (NIL T T T) -9 NIL 1578194 NIL) (-687 1564990 1566011 1567367 "MATCAT-" 1567372 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-686 1563584 1563737 1564070 "MATCAT2" 1564825 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-685 1561696 1562020 1562404 "MAPPKG3" 1563259 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-684 1560677 1560850 1561072 "MAPPKG2" 1561520 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-683 1559176 1559460 1559787 "MAPPKG1" 1560383 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-682 1558255 1558582 1558759 "MAPPAST" 1559019 T MAPPAST (NIL) -8 NIL NIL NIL) (-681 1557866 1557924 1558047 "MAPHACK3" 1558191 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-680 1557458 1557519 1557633 "MAPHACK2" 1557798 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-679 1556895 1556999 1557141 "MAPHACK1" 1557349 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-678 1554974 1555595 1555899 "MAGMA" 1556623 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-677 1554453 1554698 1554789 "MACROAST" 1554903 T MACROAST (NIL) -8 NIL NIL NIL) (-676 1550871 1552692 1553153 "M3D" 1554025 NIL M3D (NIL T) -8 NIL NIL NIL) (-675 1544977 1549240 1549281 "LZSTAGG" 1550063 NIL LZSTAGG (NIL T) -9 NIL 1550358 NIL) (-674 1540934 1542108 1543565 "LZSTAGG-" 1543570 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-673 1538021 1538825 1539312 "LWORD" 1540479 NIL LWORD (NIL T) -8 NIL NIL NIL) (-672 1537597 1537825 1537900 "LSTAST" 1537966 T LSTAST (NIL) -8 NIL NIL NIL) (-671 1530763 1537368 1537502 "LSQM" 1537507 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-670 1529987 1530126 1530354 "LSPP" 1530618 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-669 1527799 1528100 1528556 "LSMP" 1529676 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-668 1524578 1525252 1525982 "LSMP1" 1527101 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-667 1518455 1523745 1523786 "LSAGG" 1523848 NIL LSAGG (NIL T) -9 NIL 1523926 NIL) (-666 1515150 1516074 1517287 "LSAGG-" 1517292 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-665 1512749 1514294 1514543 "LPOLY" 1514945 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-664 1512331 1512416 1512539 "LPEFRAC" 1512658 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-663 1510652 1511425 1511678 "LO" 1512163 NIL LO (NIL T T T) -8 NIL NIL NIL) (-662 1510304 1510416 1510444 "LOGIC" 1510555 T LOGIC (NIL) -9 NIL 1510636 NIL) (-661 1510166 1510189 1510260 "LOGIC-" 1510265 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-660 1509359 1509499 1509692 "LODOOPS" 1510022 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-659 1506782 1509275 1509341 "LODO" 1509346 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-658 1505320 1505555 1505908 "LODOF" 1506529 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-657 1501538 1503969 1504010 "LODOCAT" 1504448 NIL LODOCAT (NIL T) -9 NIL 1504659 NIL) (-656 1501271 1501329 1501456 "LODOCAT-" 1501461 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-655 1498591 1501112 1501230 "LODO2" 1501235 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-654 1496026 1498528 1498573 "LODO1" 1498578 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-653 1494907 1495072 1495377 "LODEEF" 1495849 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-652 1490146 1493037 1493078 "LNAGG" 1494025 NIL LNAGG (NIL T) -9 NIL 1494469 NIL) (-651 1489293 1489507 1489849 "LNAGG-" 1489854 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-650 1485429 1486218 1486857 "LMOPS" 1488708 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-649 1484832 1485220 1485261 "LMODULE" 1485266 NIL LMODULE (NIL T) -9 NIL 1485292 NIL) (-648 1482030 1484477 1484600 "LMDICT" 1484742 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-647 1481436 1481657 1481698 "LLINSET" 1481889 NIL LLINSET (NIL T) -9 NIL 1481980 NIL) (-646 1481135 1481344 1481404 "LITERAL" 1481409 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-645 1474298 1480069 1480373 "LIST" 1480864 NIL LIST (NIL T) -8 NIL NIL NIL) (-644 1473823 1473897 1474036 "LIST3" 1474218 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-643 1472830 1473008 1473236 "LIST2" 1473641 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-642 1470964 1471276 1471675 "LIST2MAP" 1472477 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-641 1470560 1470797 1470838 "LINSET" 1470843 NIL LINSET (NIL T) -9 NIL 1470877 NIL) (-640 1469221 1469891 1469932 "LINEXP" 1470187 NIL LINEXP (NIL T) -9 NIL 1470336 NIL) (-639 1467868 1468128 1468425 "LINDEP" 1468973 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-638 1464635 1465354 1466131 "LIMITRF" 1467123 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-637 1462938 1463234 1463643 "LIMITPS" 1464330 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-636 1457366 1462449 1462677 "LIE" 1462759 NIL LIE (NIL T T) -8 NIL NIL NIL) (-635 1456314 1456783 1456823 "LIECAT" 1456963 NIL LIECAT (NIL T) -9 NIL 1457114 NIL) (-634 1456155 1456182 1456270 "LIECAT-" 1456275 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-633 1448651 1455604 1455769 "LIB" 1456010 T LIB (NIL) -8 NIL NIL NIL) (-632 1444286 1445169 1446104 "LGROBP" 1447768 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-631 1442284 1442558 1442908 "LF" 1444007 NIL LF (NIL T T) -7 NIL NIL NIL) (-630 1441124 1441816 1441844 "LFCAT" 1442051 T LFCAT (NIL) -9 NIL 1442190 NIL) (-629 1438026 1438656 1439344 "LEXTRIPK" 1440488 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-628 1434770 1435596 1436099 "LEXP" 1437606 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-627 1434246 1434491 1434583 "LETAST" 1434698 T LETAST (NIL) -8 NIL NIL NIL) (-626 1432644 1432957 1433358 "LEADCDET" 1433928 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-625 1431834 1431908 1432137 "LAZM3PK" 1432565 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-624 1426751 1429911 1430449 "LAUPOL" 1431346 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-623 1426330 1426374 1426535 "LAPLACE" 1426701 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-622 1424269 1425431 1425682 "LA" 1426163 NIL LA (NIL T T T) -8 NIL NIL NIL) (-621 1423263 1423847 1423888 "LALG" 1423950 NIL LALG (NIL T) -9 NIL 1424009 NIL) (-620 1422977 1423036 1423172 "LALG-" 1423177 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-619 1422812 1422836 1422877 "KVTFROM" 1422939 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-618 1421735 1422179 1422364 "KTVLOGIC" 1422647 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-617 1421570 1421594 1421635 "KRCFROM" 1421697 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-616 1420474 1420661 1420960 "KOVACIC" 1421370 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-615 1420309 1420333 1420374 "KONVERT" 1420436 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-614 1420144 1420168 1420209 "KOERCE" 1420271 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-613 1417974 1418737 1419114 "KERNEL" 1419800 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-612 1417470 1417551 1417683 "KERNEL2" 1417888 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-611 1411240 1416009 1416063 "KDAGG" 1416440 NIL KDAGG (NIL T T) -9 NIL 1416646 NIL) (-610 1410769 1410893 1411098 "KDAGG-" 1411103 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-609 1403917 1410430 1410585 "KAFILE" 1410647 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-608 1398345 1403428 1403656 "JORDAN" 1403738 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-607 1397724 1397994 1398115 "JOINAST" 1398244 T JOINAST (NIL) -8 NIL NIL NIL) (-606 1397570 1397629 1397684 "JAVACODE" 1397689 T JAVACODE (NIL) -8 NIL NIL NIL) (-605 1393822 1395775 1395829 "IXAGG" 1396758 NIL IXAGG (NIL T T) -9 NIL 1397217 NIL) (-604 1392741 1393047 1393466 "IXAGG-" 1393471 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-603 1388271 1392663 1392722 "IVECTOR" 1392727 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-602 1387037 1387274 1387540 "ITUPLE" 1388038 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-601 1385539 1385716 1386011 "ITRIGMNP" 1386859 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-600 1384284 1384488 1384771 "ITFUN3" 1385315 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-599 1383916 1383973 1384082 "ITFUN2" 1384221 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-598 1381877 1382936 1383214 "ITAYLOR" 1383671 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-597 1370822 1376014 1377177 "ISUPS" 1380747 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-596 1369926 1370066 1370302 "ISUMP" 1370669 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-595 1365301 1369871 1369912 "ISTRING" 1369917 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-594 1364777 1365022 1365114 "ISAST" 1365229 T ISAST (NIL) -8 NIL NIL NIL) (-593 1363986 1364068 1364284 "IRURPK" 1364691 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-592 1362922 1363123 1363363 "IRSN" 1363766 T IRSN (NIL) -7 NIL NIL NIL) (-591 1360993 1361348 1361777 "IRRF2F" 1362560 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-590 1360740 1360778 1360854 "IRREDFFX" 1360949 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-589 1359355 1359614 1359913 "IROOT" 1360473 NIL IROOT (NIL T) -7 NIL NIL NIL) (-588 1355959 1357039 1357731 "IR" 1358695 NIL IR (NIL T) -8 NIL NIL NIL) (-587 1353572 1354067 1354633 "IR2" 1355437 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-586 1352672 1352785 1352999 "IR2F" 1353455 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-585 1352463 1352497 1352557 "IPRNTPK" 1352632 T IPRNTPK (NIL) -7 NIL NIL NIL) (-584 1349044 1352352 1352421 "IPF" 1352426 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-583 1347371 1348969 1349026 "IPADIC" 1349031 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-582 1346683 1346931 1347061 "IP4ADDR" 1347261 T IP4ADDR (NIL) -8 NIL NIL NIL) (-581 1346156 1346387 1346497 "IOMODE" 1346593 T IOMODE (NIL) -8 NIL NIL NIL) (-580 1345229 1345753 1345880 "IOBFILE" 1346049 T IOBFILE (NIL) -8 NIL NIL NIL) (-579 1344717 1345133 1345161 "IOBCON" 1345166 T IOBCON (NIL) -9 NIL 1345187 NIL) (-578 1344228 1344286 1344469 "INVLAPLA" 1344653 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-577 1333876 1336230 1338616 "INTTR" 1341892 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-576 1330211 1330953 1331818 "INTTOOLS" 1333061 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-575 1329797 1329888 1330005 "INTSLPE" 1330114 T INTSLPE (NIL) -7 NIL NIL NIL) (-574 1327750 1329720 1329779 "INTRVL" 1329784 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-573 1325352 1325864 1326439 "INTRF" 1327235 NIL INTRF (NIL T) -7 NIL NIL NIL) (-572 1324763 1324860 1325002 "INTRET" 1325250 NIL INTRET (NIL T) -7 NIL NIL NIL) (-571 1322760 1323149 1323619 "INTRAT" 1324371 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-570 1320023 1320606 1321225 "INTPM" 1322245 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-569 1316768 1317367 1318105 "INTPAF" 1319409 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-568 1311947 1312909 1313960 "INTPACK" 1315737 T INTPACK (NIL) -7 NIL NIL NIL) (-567 1308895 1311744 1311853 "INT" 1311858 T INT (NIL) -8 NIL NIL NIL) (-566 1308147 1308299 1308507 "INTHERTR" 1308737 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-565 1307586 1307666 1307854 "INTHERAL" 1308061 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-564 1305432 1305875 1306332 "INTHEORY" 1307149 T INTHEORY (NIL) -7 NIL NIL NIL) (-563 1296838 1298459 1300231 "INTG0" 1303784 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-562 1277411 1282201 1287011 "INTFTBL" 1292048 T INTFTBL (NIL) -8 NIL NIL NIL) (-561 1276660 1276798 1276971 "INTFACT" 1277270 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-560 1274087 1274533 1275090 "INTEF" 1276214 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-559 1272454 1273193 1273221 "INTDOM" 1273522 T INTDOM (NIL) -9 NIL 1273729 NIL) (-558 1271823 1271997 1272239 "INTDOM-" 1272244 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-557 1268211 1270139 1270193 "INTCAT" 1270992 NIL INTCAT (NIL T) -9 NIL 1271313 NIL) (-556 1267683 1267786 1267914 "INTBIT" 1268103 T INTBIT (NIL) -7 NIL NIL NIL) (-555 1266382 1266536 1266843 "INTALG" 1267528 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-554 1265865 1265955 1266112 "INTAF" 1266286 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-553 1259208 1265675 1265815 "INTABL" 1265820 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-552 1258549 1259015 1259080 "INT8" 1259114 T INT8 (NIL) -8 NIL NIL 1259159) (-551 1257889 1258355 1258420 "INT64" 1258454 T INT64 (NIL) -8 NIL NIL 1258499) (-550 1257229 1257695 1257760 "INT32" 1257794 T INT32 (NIL) -8 NIL NIL 1257839) (-549 1256569 1257035 1257100 "INT16" 1257134 T INT16 (NIL) -8 NIL NIL 1257179) (-548 1251479 1254192 1254220 "INS" 1255154 T INS (NIL) -9 NIL 1255819 NIL) (-547 1248719 1249490 1250464 "INS-" 1250537 NIL INS- (NIL T) -8 NIL NIL NIL) (-546 1247494 1247721 1248019 "INPSIGN" 1248472 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-545 1246612 1246729 1246926 "INPRODPF" 1247374 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-544 1245506 1245623 1245860 "INPRODFF" 1246492 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-543 1244506 1244658 1244918 "INNMFACT" 1245342 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-542 1243703 1243800 1243988 "INMODGCD" 1244405 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-541 1242211 1242456 1242780 "INFSP" 1243448 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-540 1241395 1241512 1241695 "INFPROD0" 1242091 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-539 1238250 1239460 1239975 "INFORM" 1240888 T INFORM (NIL) -8 NIL NIL NIL) (-538 1237860 1237920 1238018 "INFORM1" 1238185 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-537 1237383 1237472 1237586 "INFINITY" 1237766 T INFINITY (NIL) -7 NIL NIL NIL) (-536 1236559 1237103 1237204 "INETCLTS" 1237302 T INETCLTS (NIL) -8 NIL NIL NIL) (-535 1235175 1235425 1235746 "INEP" 1236307 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-534 1234424 1235072 1235137 "INDE" 1235142 NIL INDE (NIL T) -8 NIL NIL NIL) (-533 1233988 1234056 1234173 "INCRMAPS" 1234351 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-532 1232806 1233257 1233463 "INBFILE" 1233802 T INBFILE (NIL) -8 NIL NIL NIL) (-531 1228105 1229042 1229986 "INBFF" 1231894 NIL INBFF (NIL T) -7 NIL NIL NIL) (-530 1227013 1227282 1227310 "INBCON" 1227823 T INBCON (NIL) -9 NIL 1228089 NIL) (-529 1226265 1226488 1226764 "INBCON-" 1226769 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-528 1225744 1225989 1226080 "INAST" 1226194 T INAST (NIL) -8 NIL NIL NIL) (-527 1225171 1225423 1225529 "IMPTAST" 1225658 T IMPTAST (NIL) -8 NIL NIL NIL) (-526 1221617 1225015 1225119 "IMATRIX" 1225124 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-525 1220329 1220452 1220767 "IMATQF" 1221473 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-524 1218549 1218776 1219113 "IMATLIN" 1220085 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-523 1213127 1218473 1218531 "ILIST" 1218536 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-522 1211032 1212987 1213100 "IIARRAY2" 1213105 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-521 1206430 1210943 1211007 "IFF" 1211012 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-520 1205777 1206047 1206163 "IFAST" 1206334 T IFAST (NIL) -8 NIL NIL NIL) (-519 1200772 1205069 1205257 "IFARRAY" 1205634 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-518 1199952 1200676 1200749 "IFAMON" 1200754 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-517 1199536 1199601 1199655 "IEVALAB" 1199862 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-516 1199211 1199279 1199439 "IEVALAB-" 1199444 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-515 1198842 1199125 1199188 "IDPO" 1199193 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-514 1198092 1198731 1198806 "IDPOAMS" 1198811 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-513 1197399 1197981 1198056 "IDPOAM" 1198061 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-512 1196458 1196734 1196787 "IDPC" 1197200 NIL IDPC (NIL T T) -9 NIL 1197349 NIL) (-511 1195927 1196350 1196423 "IDPAM" 1196428 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-510 1195303 1195819 1195892 "IDPAG" 1195897 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-509 1194948 1195139 1195214 "IDENT" 1195248 T IDENT (NIL) -8 NIL NIL NIL) (-508 1191203 1192051 1192946 "IDECOMP" 1194105 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-507 1184041 1185126 1186173 "IDEAL" 1190239 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-506 1183205 1183317 1183516 "ICDEN" 1183925 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-505 1182276 1182685 1182832 "ICARD" 1183078 T ICARD (NIL) -8 NIL NIL NIL) (-504 1180336 1180649 1181054 "IBPTOOLS" 1181953 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-503 1175943 1179956 1180069 "IBITS" 1180255 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-502 1172666 1173242 1173937 "IBATOOL" 1175360 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-501 1170445 1170907 1171440 "IBACHIN" 1172201 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-500 1168274 1170291 1170394 "IARRAY2" 1170399 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-499 1164380 1168200 1168257 "IARRAY1" 1168262 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-498 1158489 1162792 1163273 "IAN" 1163919 T IAN (NIL) -8 NIL NIL NIL) (-497 1158000 1158057 1158230 "IALGFACT" 1158426 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-496 1157528 1157641 1157669 "HYPCAT" 1157876 T HYPCAT (NIL) -9 NIL NIL NIL) (-495 1157066 1157183 1157369 "HYPCAT-" 1157374 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-494 1156661 1156861 1156944 "HOSTNAME" 1157003 T HOSTNAME (NIL) -8 NIL NIL NIL) (-493 1156506 1156543 1156584 "HOMOTOP" 1156589 NIL HOMOTOP (NIL T) -9 NIL 1156622 NIL) (-492 1153138 1154516 1154557 "HOAGG" 1155538 NIL HOAGG (NIL T) -9 NIL 1156217 NIL) (-491 1151732 1152131 1152657 "HOAGG-" 1152662 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-490 1145736 1151327 1151476 "HEXADEC" 1151603 T HEXADEC (NIL) -8 NIL NIL NIL) (-489 1144483 1144706 1144969 "HEUGCD" 1145513 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-488 1143559 1144320 1144450 "HELLFDIV" 1144455 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-487 1141738 1143336 1143424 "HEAP" 1143503 NIL HEAP (NIL T) -8 NIL NIL NIL) (-486 1141001 1141290 1141424 "HEADAST" 1141624 T HEADAST (NIL) -8 NIL NIL NIL) (-485 1134867 1140916 1140978 "HDP" 1140983 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-484 1128855 1134502 1134654 "HDMP" 1134768 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-483 1128179 1128319 1128483 "HB" 1128711 T HB (NIL) -7 NIL NIL NIL) (-482 1121565 1128025 1128129 "HASHTBL" 1128134 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-481 1121041 1121286 1121378 "HASAST" 1121493 T HASAST (NIL) -8 NIL NIL NIL) (-480 1118819 1120663 1120845 "HACKPI" 1120879 T HACKPI (NIL) -8 NIL NIL NIL) (-479 1114487 1118672 1118785 "GTSET" 1118790 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-478 1107902 1114365 1114463 "GSTBL" 1114468 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-477 1100180 1106933 1107198 "GSERIES" 1107693 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-476 1099321 1099738 1099766 "GROUP" 1099969 T GROUP (NIL) -9 NIL 1100103 NIL) (-475 1098687 1098846 1099097 "GROUP-" 1099102 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-474 1097054 1097375 1097762 "GROEBSOL" 1098364 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-473 1095968 1096256 1096307 "GRMOD" 1096836 NIL GRMOD (NIL T T) -9 NIL 1097004 NIL) (-472 1095736 1095772 1095900 "GRMOD-" 1095905 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-471 1091026 1092090 1093090 "GRIMAGE" 1094756 T GRIMAGE (NIL) -8 NIL NIL NIL) (-470 1089492 1089753 1090077 "GRDEF" 1090722 T GRDEF (NIL) -7 NIL NIL NIL) (-469 1088936 1089052 1089193 "GRAY" 1089371 T GRAY (NIL) -7 NIL NIL NIL) (-468 1088123 1088529 1088580 "GRALG" 1088733 NIL GRALG (NIL T T) -9 NIL 1088826 NIL) (-467 1087784 1087857 1088020 "GRALG-" 1088025 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-466 1084561 1087369 1087547 "GPOLSET" 1087691 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-465 1083915 1083972 1084230 "GOSPER" 1084498 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-464 1079647 1080353 1080879 "GMODPOL" 1083614 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-463 1078652 1078836 1079074 "GHENSEL" 1079459 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-462 1072808 1073651 1074671 "GENUPS" 1077736 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-461 1072505 1072556 1072645 "GENUFACT" 1072751 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-460 1071917 1071994 1072159 "GENPGCD" 1072423 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-459 1071391 1071426 1071639 "GENMFACT" 1071876 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-458 1069957 1070214 1070521 "GENEEZ" 1071134 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-457 1064103 1069568 1069730 "GDMP" 1069880 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-456 1053445 1057874 1058980 "GCNAALG" 1063086 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-455 1051772 1052634 1052662 "GCDDOM" 1052917 T GCDDOM (NIL) -9 NIL 1053074 NIL) (-454 1051242 1051369 1051584 "GCDDOM-" 1051589 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-453 1049914 1050099 1050403 "GB" 1051021 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-452 1038530 1040860 1043252 "GBINTERN" 1047605 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-451 1036367 1036659 1037080 "GBF" 1038205 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-450 1035148 1035313 1035580 "GBEUCLID" 1036183 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-449 1034497 1034622 1034771 "GAUSSFAC" 1035019 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-448 1032864 1033166 1033480 "GALUTIL" 1034216 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-447 1031172 1031446 1031770 "GALPOLYU" 1032591 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-446 1028537 1028827 1029234 "GALFACTU" 1030869 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-445 1020342 1021842 1023450 "GALFACT" 1026969 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-444 1017730 1018388 1018416 "FVFUN" 1019572 T FVFUN (NIL) -9 NIL 1020292 NIL) (-443 1016996 1017178 1017206 "FVC" 1017497 T FVC (NIL) -9 NIL 1017680 NIL) (-442 1016639 1016821 1016889 "FUNDESC" 1016948 T FUNDESC (NIL) -8 NIL NIL NIL) (-441 1016254 1016436 1016517 "FUNCTION" 1016591 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-440 1013998 1014576 1015042 "FT" 1015808 T FT (NIL) -8 NIL NIL NIL) (-439 1012789 1013299 1013502 "FTEM" 1013815 T FTEM (NIL) -8 NIL NIL NIL) (-438 1011080 1011369 1011766 "FSUPFACT" 1012480 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-437 1009477 1009766 1010098 "FST" 1010768 T FST (NIL) -8 NIL NIL NIL) (-436 1008676 1008782 1008970 "FSRED" 1009359 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-435 1007375 1007631 1007978 "FSPRMELT" 1008391 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-434 1004681 1005119 1005605 "FSPECF" 1006938 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-433 986319 994650 994691 "FS" 998575 NIL FS (NIL T) -9 NIL 1000864 NIL) (-432 974962 977955 982012 "FS-" 982312 NIL FS- (NIL T T) -8 NIL NIL NIL) (-431 974490 974544 974714 "FSINT" 974903 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-430 972782 973483 973786 "FSERIES" 974269 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-429 971824 971940 972164 "FSCINT" 972662 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-428 968032 970768 970809 "FSAGG" 971179 NIL FSAGG (NIL T) -9 NIL 971438 NIL) (-427 965794 966395 967191 "FSAGG-" 967286 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-426 964836 964979 965206 "FSAGG2" 965647 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-425 962518 962798 963345 "FS2UPS" 964554 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-424 962152 962195 962324 "FS2" 962469 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-423 961030 961201 961503 "FS2EXPXP" 961977 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-422 960456 960571 960723 "FRUTIL" 960910 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-421 951869 955951 957309 "FR" 959130 NIL FR (NIL T) -8 NIL NIL NIL) (-420 946838 949512 949552 "FRNAALG" 950948 NIL FRNAALG (NIL T) -9 NIL 951555 NIL) (-419 942511 943587 944862 "FRNAALG-" 945612 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-418 942149 942192 942319 "FRNAAF2" 942462 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-417 940529 941003 941298 "FRMOD" 941961 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-416 938280 938912 939229 "FRIDEAL" 940320 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-415 937475 937562 937851 "FRIDEAL2" 938187 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-414 936608 937022 937063 "FRETRCT" 937068 NIL FRETRCT (NIL T) -9 NIL 937244 NIL) (-413 935720 935951 936302 "FRETRCT-" 936307 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-412 932808 934018 934077 "FRAMALG" 934959 NIL FRAMALG (NIL T T) -9 NIL 935251 NIL) (-411 930942 931397 932027 "FRAMALG-" 932250 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-410 924863 930417 930693 "FRAC" 930698 NIL FRAC (NIL T) -8 NIL NIL NIL) (-409 924499 924556 924663 "FRAC2" 924800 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-408 924135 924192 924299 "FR2" 924436 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-407 918648 921541 921569 "FPS" 922688 T FPS (NIL) -9 NIL 923245 NIL) (-406 918097 918206 918370 "FPS-" 918516 NIL FPS- (NIL T) -8 NIL NIL NIL) (-405 915399 917068 917096 "FPC" 917321 T FPC (NIL) -9 NIL 917463 NIL) (-404 915192 915232 915329 "FPC-" 915334 NIL FPC- (NIL T) -8 NIL NIL NIL) (-403 913982 914680 914721 "FPATMAB" 914726 NIL FPATMAB (NIL T) -9 NIL 914878 NIL) (-402 911655 912158 912584 "FPARFRAC" 913619 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-401 907048 907547 908229 "FORTRAN" 911087 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-400 904764 905264 905803 "FORT" 906529 T FORT (NIL) -7 NIL NIL NIL) (-399 902440 903002 903030 "FORTFN" 904090 T FORTFN (NIL) -9 NIL 904714 NIL) (-398 902204 902254 902282 "FORTCAT" 902341 T FORTCAT (NIL) -9 NIL 902403 NIL) (-397 900310 900820 901210 "FORMULA" 901834 T FORMULA (NIL) -8 NIL NIL NIL) (-396 900098 900128 900197 "FORMULA1" 900274 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-395 899621 899673 899846 "FORDER" 900040 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-394 898717 898881 899074 "FOP" 899448 T FOP (NIL) -7 NIL NIL NIL) (-393 897298 897997 898171 "FNLA" 898599 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-392 896027 896442 896470 "FNCAT" 896930 T FNCAT (NIL) -9 NIL 897190 NIL) (-391 895566 895986 896014 "FNAME" 896019 T FNAME (NIL) -8 NIL NIL NIL) (-390 894129 895092 895120 "FMTC" 895125 T FMTC (NIL) -9 NIL 895161 NIL) (-389 892875 894065 894111 "FMONOID" 894116 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-388 889703 890871 890912 "FMONCAT" 892129 NIL FMONCAT (NIL T) -9 NIL 892734 NIL) (-387 888895 889445 889594 "FM" 889599 NIL FM (NIL T T) -8 NIL NIL NIL) (-386 886319 886965 886993 "FMFUN" 888137 T FMFUN (NIL) -9 NIL 888845 NIL) (-385 885588 885769 885797 "FMC" 886087 T FMC (NIL) -9 NIL 886269 NIL) (-384 882667 883527 883581 "FMCAT" 884776 NIL FMCAT (NIL T T) -9 NIL 885271 NIL) (-383 881533 882433 882533 "FM1" 882612 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-382 879307 879723 880217 "FLOATRP" 881084 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-381 872882 877036 877657 "FLOAT" 878706 T FLOAT (NIL) -8 NIL NIL NIL) (-380 870320 870820 871398 "FLOATCP" 872349 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-379 869060 869898 869939 "FLINEXP" 869944 NIL FLINEXP (NIL T) -9 NIL 870037 NIL) (-378 868214 868449 868777 "FLINEXP-" 868782 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-377 867290 867434 867658 "FLASORT" 868066 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-376 864406 865274 865326 "FLALG" 866553 NIL FLALG (NIL T T) -9 NIL 867020 NIL) (-375 858142 861892 861933 "FLAGG" 863195 NIL FLAGG (NIL T) -9 NIL 863847 NIL) (-374 856868 857207 857697 "FLAGG-" 857702 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-373 855910 856053 856280 "FLAGG2" 856721 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-372 852761 853769 853828 "FINRALG" 854956 NIL FINRALG (NIL T T) -9 NIL 855464 NIL) (-371 851921 852150 852489 "FINRALG-" 852494 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-370 851301 851540 851568 "FINITE" 851764 T FINITE (NIL) -9 NIL 851871 NIL) (-369 843658 845845 845885 "FINAALG" 849552 NIL FINAALG (NIL T) -9 NIL 851005 NIL) (-368 838990 840040 841184 "FINAALG-" 842563 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-367 838358 838745 838848 "FILE" 838920 NIL FILE (NIL T) -8 NIL NIL NIL) (-366 837016 837354 837408 "FILECAT" 838092 NIL FILECAT (NIL T T) -9 NIL 838308 NIL) (-365 834732 836260 836288 "FIELD" 836328 T FIELD (NIL) -9 NIL 836408 NIL) (-364 833352 833737 834248 "FIELD-" 834253 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-363 831202 831987 832334 "FGROUP" 833038 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-362 830292 830456 830676 "FGLMICPK" 831034 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-361 826124 830217 830274 "FFX" 830279 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-360 825725 825786 825921 "FFSLPE" 826057 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-359 821714 822497 823293 "FFPOLY" 824961 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-358 821218 821254 821463 "FFPOLY2" 821672 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-357 817061 821137 821200 "FFP" 821205 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-356 812459 816972 817036 "FF" 817041 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-355 807585 811802 811992 "FFNBX" 812313 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-354 802514 806720 806978 "FFNBP" 807439 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-353 797147 801798 802009 "FFNB" 802347 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-352 795979 796177 796492 "FFINTBAS" 796944 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-351 792048 794268 794296 "FFIELDC" 794916 T FFIELDC (NIL) -9 NIL 795292 NIL) (-350 790710 791081 791578 "FFIELDC-" 791583 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-349 790279 790325 790449 "FFHOM" 790652 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-348 787974 788461 788978 "FFF" 789794 NIL FFF (NIL T) -7 NIL NIL NIL) (-347 783592 787716 787817 "FFCGX" 787917 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-346 779213 783324 783431 "FFCGP" 783535 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-345 774396 778940 779048 "FFCG" 779149 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-344 755792 764873 764959 "FFCAT" 770124 NIL FFCAT (NIL T T T) -9 NIL 771575 NIL) (-343 750990 752037 753351 "FFCAT-" 754581 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-342 750401 750444 750679 "FFCAT2" 750941 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 739722 743373 744593 "FEXPR" 749253 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-340 738722 739157 739198 "FEVALAB" 739282 NIL FEVALAB (NIL T) -9 NIL 739543 NIL) (-339 737881 738091 738429 "FEVALAB-" 738434 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-338 736447 737264 737467 "FDIV" 737780 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-337 733467 734208 734323 "FDIVCAT" 735891 NIL FDIVCAT (NIL T T T T) -9 NIL 736328 NIL) (-336 733229 733256 733426 "FDIVCAT-" 733431 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-335 732449 732536 732813 "FDIV2" 733136 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-334 731423 731744 731946 "FCTRDATA" 732267 T FCTRDATA (NIL) -8 NIL NIL NIL) (-333 730109 730368 730657 "FCPAK1" 731154 T FCPAK1 (NIL) -7 NIL NIL NIL) (-332 729208 729609 729750 "FCOMP" 730000 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-331 712910 716358 719896 "FC" 725690 T FC (NIL) -8 NIL NIL NIL) (-330 705273 709301 709341 "FAXF" 711143 NIL FAXF (NIL T) -9 NIL 711835 NIL) (-329 702549 703207 704032 "FAXF-" 704497 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-328 697601 701925 702101 "FARRAY" 702406 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-327 692495 694562 694615 "FAMR" 695638 NIL FAMR (NIL T T) -9 NIL 696098 NIL) (-326 691385 691687 692122 "FAMR-" 692127 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-325 690554 691307 691360 "FAMONOID" 691365 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-324 688340 689050 689103 "FAMONC" 690044 NIL FAMONC (NIL T T) -9 NIL 690430 NIL) (-323 687004 688094 688231 "FAGROUP" 688236 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-322 684799 685118 685521 "FACUTIL" 686685 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-321 683898 684083 684305 "FACTFUNC" 684609 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-320 676320 683201 683400 "EXPUPXS" 683754 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-319 673803 674343 674929 "EXPRTUBE" 675754 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-318 670074 670666 671396 "EXPRODE" 673142 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-317 655559 668723 669152 "EXPR" 669678 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 650113 650700 651506 "EXPR2UPS" 654857 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-315 649745 649802 649911 "EXPR2" 650050 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-314 641135 648898 649188 "EXPEXPAN" 649582 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-313 640935 641092 641121 "EXIT" 641126 T EXIT (NIL) -8 NIL NIL NIL) (-312 640415 640659 640750 "EXITAST" 640864 T EXITAST (NIL) -8 NIL NIL NIL) (-311 640042 640104 640217 "EVALCYC" 640347 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-310 639583 639701 639742 "EVALAB" 639912 NIL EVALAB (NIL T) -9 NIL 640016 NIL) (-309 639064 639186 639407 "EVALAB-" 639412 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-308 636432 637734 637762 "EUCDOM" 638317 T EUCDOM (NIL) -9 NIL 638667 NIL) (-307 634837 635279 635869 "EUCDOM-" 635874 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-306 622375 625135 627885 "ESTOOLS" 632107 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 622007 622064 622173 "ESTOOLS2" 622312 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-304 621758 621800 621880 "ESTOOLS1" 621959 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-303 615795 617403 617431 "ES" 620199 T ES (NIL) -9 NIL 621609 NIL) (-302 610742 612029 613846 "ES-" 614010 NIL ES- (NIL T) -8 NIL NIL NIL) (-301 607116 607877 608657 "ESCONT" 609982 T ESCONT (NIL) -7 NIL NIL NIL) (-300 606861 606893 606975 "ESCONT1" 607078 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-299 606536 606586 606686 "ES2" 606805 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-298 606166 606224 606333 "ES1" 606472 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-297 605382 605511 605687 "ERROR" 606010 T ERROR (NIL) -7 NIL NIL NIL) (-296 598774 605241 605332 "EQTBL" 605337 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-295 591277 594088 595537 "EQ" 597358 NIL -2147 (NIL T) -8 NIL NIL NIL) (-294 590909 590966 591075 "EQ2" 591214 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-293 586198 587247 588340 "EP" 589848 NIL EP (NIL T) -7 NIL NIL NIL) (-292 584798 585089 585395 "ENV" 585912 T ENV (NIL) -8 NIL NIL NIL) (-291 583892 584446 584474 "ENTIRER" 584479 T ENTIRER (NIL) -9 NIL 584525 NIL) (-290 580359 581847 582217 "EMR" 583691 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-289 579503 579688 579742 "ELTAGG" 580122 NIL ELTAGG (NIL T T) -9 NIL 580333 NIL) (-288 579222 579284 579425 "ELTAGG-" 579430 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-287 579011 579040 579094 "ELTAB" 579178 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-286 578137 578283 578482 "ELFUTS" 578862 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-285 577879 577935 577963 "ELEMFUN" 578068 T ELEMFUN (NIL) -9 NIL NIL NIL) (-284 577749 577770 577838 "ELEMFUN-" 577843 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-283 572593 575849 575890 "ELAGG" 576830 NIL ELAGG (NIL T) -9 NIL 577293 NIL) (-282 570878 571312 571975 "ELAGG-" 571980 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-281 569539 569818 570112 "ELABEXPR" 570604 T ELABEXPR (NIL) -8 NIL NIL NIL) (-280 562403 564206 565033 "EFUPXS" 568815 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-279 555853 557654 558464 "EFULS" 561679 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-278 553338 553696 554168 "EFSTRUC" 555485 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-277 543129 544695 546243 "EF" 551853 NIL EF (NIL T T) -7 NIL NIL NIL) (-276 542203 542614 542763 "EAB" 543000 T EAB (NIL) -8 NIL NIL NIL) (-275 541385 542162 542190 "E04UCFA" 542195 T E04UCFA (NIL) -8 NIL NIL NIL) (-274 540567 541344 541372 "E04NAFA" 541377 T E04NAFA (NIL) -8 NIL NIL NIL) (-273 539749 540526 540554 "E04MBFA" 540559 T E04MBFA (NIL) -8 NIL NIL NIL) (-272 538931 539708 539736 "E04JAFA" 539741 T E04JAFA (NIL) -8 NIL NIL NIL) (-271 538115 538890 538918 "E04GCFA" 538923 T E04GCFA (NIL) -8 NIL NIL NIL) (-270 537299 538074 538102 "E04FDFA" 538107 T E04FDFA (NIL) -8 NIL NIL NIL) (-269 536481 537258 537286 "E04DGFA" 537291 T E04DGFA (NIL) -8 NIL NIL NIL) (-268 530654 532006 533370 "E04AGNT" 535137 T E04AGNT (NIL) -7 NIL NIL NIL) (-267 529334 529840 529880 "DVARCAT" 530355 NIL DVARCAT (NIL T) -9 NIL 530554 NIL) (-266 528538 528750 529064 "DVARCAT-" 529069 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-265 521675 528337 528466 "DSMP" 528471 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-264 516456 517620 518688 "DROPT" 520627 T DROPT (NIL) -8 NIL NIL NIL) (-263 516121 516180 516278 "DROPT1" 516391 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-262 511236 512362 513499 "DROPT0" 515004 T DROPT0 (NIL) -7 NIL NIL NIL) (-261 509581 509906 510292 "DRAWPT" 510870 T DRAWPT (NIL) -7 NIL NIL NIL) (-260 504168 505091 506170 "DRAW" 508555 NIL DRAW (NIL T) -7 NIL NIL NIL) (-259 503801 503854 503972 "DRAWHACK" 504109 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-258 502532 502801 503092 "DRAWCX" 503530 T DRAWCX (NIL) -7 NIL NIL NIL) (-257 502047 502116 502267 "DRAWCURV" 502458 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-256 492515 494477 496592 "DRAWCFUN" 499952 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-255 489281 491210 491251 "DQAGG" 491880 NIL DQAGG (NIL T) -9 NIL 492153 NIL) (-254 477405 483874 483957 "DPOLCAT" 485809 NIL DPOLCAT (NIL T T T T) -9 NIL 486354 NIL) (-253 472241 473590 475548 "DPOLCAT-" 475553 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-252 465363 472102 472200 "DPMO" 472205 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-251 458388 465143 465310 "DPMM" 465315 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-250 457866 458080 458178 "DOMTMPLT" 458310 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-249 457299 457668 457748 "DOMCTOR" 457806 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456511 456779 456930 "DOMAIN" 457168 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450499 456146 456298 "DMP" 456412 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450099 450155 450299 "DLP" 450437 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 443921 449426 449616 "DLIST" 449941 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 440718 442774 442815 "DLAGG" 443365 NIL DLAGG (NIL T) -9 NIL 443595 NIL) (-243 439394 440058 440086 "DIVRING" 440178 T DIVRING (NIL) -9 NIL 440261 NIL) (-242 438631 438821 439121 "DIVRING-" 439126 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 436733 437090 437496 "DISPLAY" 438245 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430621 436647 436710 "DIRPROD" 436715 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429469 429672 429937 "DIRPROD2" 430414 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418244 424250 424303 "DIRPCAT" 424713 NIL DIRPCAT (NIL NIL T) -9 NIL 425553 NIL) (-237 415570 416212 417093 "DIRPCAT-" 417430 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 414857 415017 415203 "DIOSP" 415404 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411512 413769 413810 "DIOPS" 414244 NIL DIOPS (NIL T) -9 NIL 414473 NIL) (-234 411061 411175 411366 "DIOPS-" 411371 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 409884 410512 410540 "DIFRING" 410727 T DIFRING (NIL) -9 NIL 410837 NIL) (-232 409530 409607 409759 "DIFRING-" 409764 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407266 408538 408579 "DIFEXT" 408942 NIL DIFEXT (NIL T) -9 NIL 409236 NIL) (-230 405551 405979 406645 "DIFEXT-" 406650 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 402826 405083 405124 "DIAGG" 405129 NIL DIAGG (NIL T) -9 NIL 405149 NIL) (-228 402210 402367 402619 "DIAGG-" 402624 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397627 401169 401446 "DHMATRIX" 401979 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393239 394148 395158 "DFSFUN" 396637 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388317 392170 392482 "DFLOAT" 392947 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386580 386861 387250 "DFINTTLS" 388025 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383609 384601 385001 "DERHAM" 386246 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381410 383384 383473 "DEQUEUE" 383553 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 380664 380797 380980 "DEGRED" 381272 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 377094 377839 378685 "DEFINTRF" 379892 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 374649 375118 375710 "DEFINTEF" 376613 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373999 374269 374384 "DEFAST" 374554 T DEFAST (NIL) -8 NIL NIL NIL) (-217 368003 373594 373743 "DECIMAL" 373870 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365515 365973 366479 "DDFACT" 367547 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 365111 365154 365305 "DBLRESP" 365466 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362983 363344 363704 "DBASE" 364878 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362225 362463 362609 "DATAARY" 362882 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361331 362184 362212 "D03FAFA" 362217 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360438 361290 361318 "D03EEFA" 361323 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358388 358854 359343 "D03AGNT" 359969 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 357677 358347 358375 "D02EJFA" 358380 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356966 357636 357664 "D02CJFA" 357669 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356255 356925 356953 "D02BHFA" 356958 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355544 356214 356242 "D02BBFA" 356247 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 348741 350330 351936 "D02AGNT" 353958 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346509 347032 347578 "D01WGTS" 348215 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345576 346468 346496 "D01TRNS" 346501 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 344644 345535 345563 "D01GBFA" 345568 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 343712 344603 344631 "D01FCFA" 344636 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 342780 343671 343699 "D01ASFA" 343704 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 341848 342739 342767 "D01AQFA" 342772 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340916 341807 341835 "D01APFA" 341840 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339984 340875 340903 "D01ANFA" 340908 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 339052 339943 339971 "D01AMFA" 339976 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 338120 339011 339039 "D01ALFA" 339044 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337188 338079 338107 "D01AKFA" 338112 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336256 337147 337175 "D01AJFA" 337180 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329551 331104 332665 "D01AGNT" 334715 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 328888 329016 329168 "CYCLOTOM" 329419 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325622 326336 327063 "CYCLES" 328181 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324934 325068 325239 "CVMP" 325483 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 322775 323033 323402 "CTRIGMNP" 324662 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322211 322569 322642 "CTOR" 322722 T CTOR (NIL) -8 NIL NIL NIL) (-186 321720 321942 322043 "CTORKIND" 322130 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 321011 321327 321355 "CTORCAT" 321537 T CTORCAT (NIL) -9 NIL 321650 NIL) (-184 320609 320720 320879 "CTORCAT-" 320884 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 320071 320283 320391 "CTORCALL" 320533 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-182 319445 319544 319697 "CSTTOOLS" 319968 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315244 315901 316659 "CRFP" 318757 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 314719 314965 315057 "CRCEAST" 315172 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 313766 313951 314179 "CRAPACK" 314523 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313150 313251 313455 "CPMATCH" 313642 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312875 312903 313009 "CPIMA" 313116 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309223 309895 310614 "COORDSYS" 312210 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 308635 308756 308898 "CONTOUR" 309101 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304526 306638 307130 "CONTFRAC" 308175 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304406 304427 304455 "CONDUIT" 304492 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303494 304048 304076 "COMRING" 304081 T COMRING (NIL) -9 NIL 304133 NIL) (-171 302548 302852 303036 "COMPPROP" 303330 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302209 302244 302372 "COMPLPAT" 302507 NIL 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(-5 *2 (-645 (-645 (-295 (-954 *4))))) (-5 *1 (-382 *4)) @@ -11622,7 +10797,7 @@ (|partial| -12 (-5 *5 (-1179)) (-4 *6 (-13 (-308) (-1040 (-567)) (-640 (-567)) (-147))) (-4 *4 (-13 (-29 *6) (-1204) (-961))) - (-5 *2 (-2 (|:| |particular| *4) (|:| -2144 (-645 *4)))) + (-5 *2 (-2 (|:| |particular| *4) (|:| -4374 (-645 *4)))) (-5 *1 (-653 *6 *4 *3)) (-4 *3 (-657 *4)))) ((*1 *2 *3 *2 *4 *2 *5) (|partial| -12 (-5 *4 (-1179)) (-5 *5 (-645 *2)) @@ -11633,40 +10808,40 @@ (-12 (-5 *3 (-690 *5)) (-4 *5 (-365)) (-5 *2 (-2 (|:| |particular| (-3 (-1269 *5) "failed")) - (|:| -2144 (-645 (-1269 *5))))) + (|:| -4374 (-645 (-1269 *5))))) (-5 *1 (-668 *5)) (-5 *4 (-1269 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-645 (-645 *5))) (-4 *5 (-365)) (-5 *2 (-2 (|:| |particular| (-3 (-1269 *5) "failed")) - (|:| -2144 (-645 (-1269 *5))))) + (|:| -4374 (-645 (-1269 *5))))) (-5 *1 (-668 *5)) (-5 *4 (-1269 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-690 *5)) (-4 *5 (-365)) (-5 *2 (-645 (-2 (|:| |particular| (-3 (-1269 *5) 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(-688 *5 *6 *7)))) ((*1 *2 *3 *4) @@ -11684,7 +10859,7 @@ (-4 *7 (-13 (-29 *6) (-1204) (-961))) (-4 *6 (-13 (-308) (-1040 (-567)) (-640 (-567)) (-147))) (-5 *2 - (-2 (|:| |particular| (-1269 *7)) (|:| -2144 (-645 (-1269 *7))))) + (-2 (|:| |particular| (-1269 *7)) (|:| -4374 (-645 (-1269 *7))))) (-5 *1 (-803 *6 *7)) (-5 *4 (-1269 *7)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-690 *6)) (-5 *4 (-1179)) @@ -11696,27 +10871,27 @@ (-5 *5 (-1179)) (-4 *7 (-13 (-29 *6) (-1204) (-961))) (-4 *6 (-13 (-308) (-1040 (-567)) (-640 (-567)) (-147))) (-5 *2 - (-2 (|:| |particular| (-1269 *7)) (|:| -2144 (-645 (-1269 *7))))) + (-2 (|:| |particular| (-1269 *7)) (|:| -4374 (-645 (-1269 *7))))) (-5 *1 (-803 *6 *7)))) ((*1 *2 *3 *4 *5) (|partial| -12 (-5 *3 (-645 *7)) (-5 *4 (-645 (-114))) (-5 *5 (-1179)) (-4 *7 (-13 (-29 *6) (-1204) (-961))) (-4 *6 (-13 (-308) (-1040 (-567)) (-640 (-567)) (-147))) (-5 *2 - (-2 (|:| |particular| (-1269 *7)) (|:| -2144 (-645 (-1269 *7))))) + (-2 (|:| |particular| (-1269 *7)) (|:| -4374 (-645 (-1269 *7))))) (-5 *1 (-803 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-295 *7)) (-5 *4 (-114)) (-5 *5 (-1179)) (-4 *7 (-13 (-29 *6) (-1204) (-961))) (-4 *6 (-13 (-308) (-1040 (-567)) (-640 (-567)) (-147))) (-5 *2 - (-3 (-2 (|:| |particular| *7) (|:| -2144 (-645 *7))) *7 "failed")) + (-3 (-2 (|:| |particular| *7) (|:| -4374 (-645 *7))) *7 "failed")) (-5 *1 (-803 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *4 (-114)) (-5 *5 (-1179)) (-4 *6 (-13 (-308) (-1040 (-567)) (-640 (-567)) (-147))) (-5 *2 - (-3 (-2 (|:| |particular| *3) (|:| -2144 (-645 *3))) *3 "failed")) + (-3 (-2 (|:| |particular| *3) (|:| -4374 (-645 *3))) *3 "failed")) (-5 *1 (-803 *6 *3)) (-4 *3 (-13 (-29 *6) (-1204) (-961))))) ((*1 *2 *3 *4 *3 *5) (|partial| -12 (-5 *3 (-295 *2)) (-5 *4 (-114)) (-5 *5 (-645 *2)) @@ -11752,10 +10927,10 @@ (|partial| -12 (-5 *5 (-1 - (-3 (-2 (|:| |particular| *6) (|:| -2144 (-645 *6))) "failed") + (-3 (-2 (|:| |particular| *6) (|:| -4374 (-645 *6))) "failed") *7 *6)) (-4 *6 (-365)) 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\ No newline at end of file |